Journal articles: 'Viscoelastic plate with variable thickness'

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Khudayarov, Bakhtiyar, A. A. Tukhtaboev, O. R. Kucharov, Fozilzhon Turaev, and Nurilla Yuldashev. "Simulation of oscillation of a dam-plate of variable thickness." Bulletin of the National Technical University "KhPI" A series of "Information and Modeling" 1, no. 1-2 (9-10)) (2023): 27–39. http://dx.doi.org/10.20998/2411-0558.2023.01.02.

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The hereditary theory of viscoelasticity has provided ample opportunities for describing the dynamic processes of deformation of various materials. However, the implementation of these possibilities in many cases is difficult due to the lack of an adequate mathematical apparatus, especially in the study of dynamic processes in viscoelastic systems. There are fundamental reasons to believe that the apparatus of integral equations is very promising in this sense. The use of modern computer technology capabilities makes it possible to create effective mathematical modeling technologies for problems of great complexity, which include problems of dynamics and dynamic stability of viscoelastic elements of thin-walled structures with variable stiffness. Mathematical models of dynamic problems are constructed, efficient computational algorithms are developed, and forced vibrations of a dam-plate with variable stiffness are studied. The results of studies of problems on vibrations of a dam-plate of variable thickness are given, taking into account the viscoelastic properties of the material, the hydrodynamic pressure of water, soil and seismic load. Figs.:3, Refs.: 22 titles.

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Abdikarimov, Rustamkhan, Marco Amabili, Nikolai Ivanovich Vatin, and Dadakhan Khodzhaev. "Dynamic Stability of Orthotropic Viscoelastic Rectangular Plate of an Arbitrarily Varying Thickness." Applied Sciences 11, no. 13 (2021): 6029. http://dx.doi.org/10.3390/app11136029.

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The research object of this work is an orthotropic viscoelastic plate with an arbitrarily varying thickness. The plate was subjected to dynamic periodic load. Within the Kirchhoff–Love hypothesis framework, a mathematical model was built in a geometrically nonlinear formulation, taking into account the tangential forces of inertia. The Bubnov–Galerkin method, based on a polynomial approximation of the deflection and displacement, was used. The problem was reduced to solving systems of nonlinear integrodifferential equations. The solution of the system was obtained for an arbitrarily varying thickness of the plate. With a weakly singular Koltunov–Rzhanitsyn kernel with variable coefficients, the resulting system was solved by a numerical method based on quadrature formulas. The computational algorithm was developed and implemented in the Delphi algorithmic language. The plate’s dynamic stability was investigated depending on the plate’s geometric parameters and viscoelastic and inhomogeneous material properties. It was found that the results of the viscoelastic problem obtained using the exponential relaxation kernel almost coincide with the results of the elastic problem. Using the Koltunov–Rzhanitsyn kernel, the differences between elastic and viscoelastic problems are significant and amount to more than 40%. The proposed method can be used for various viscoelastic thin-walled structures such as plates, panels, and shells of variable thickness.

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Sun, Lin, Jingguo Qu, Gang Cheng, et al. "Numerical analysis for variable thickness plate with variable order fractional viscoelastic model." Communications in Nonlinear Science and Numerical Simulation 146 (July 2025): 108764. https://doi.org/10.1016/j.cnsns.2025.108764.

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Bock, Igor, and Mária Kečkemétyová. "An Optimal Control Problem for A Viscoelastic Plate in a Dynamic Contact with an Obstacle." Tatra Mountains Mathematical Publications 71, no. 1 (2018): 27–37. http://dx.doi.org/10.2478/tmmp-2018-0003.

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Abstract We deal with an optimal control problem governed by a nonlinear hyperbolic initial-boundary value problem describing the perpendicular vibrations of a simply supported anisotropic viscoelastic plate against a rigid obstacle. A variable thickness of a plate plays the role of a control variable. We verify the existence of an optimal thickness function.

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Abdikarimov, Rustamkhan, Dadakhan Khodzhaev, and Nikolay Vatin. "To Calculation of Rectangular Plates on Periodic Oscillations." MATEC Web of Conferences 245 (2018): 01003. http://dx.doi.org/10.1051/matecconf/201824501003.

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Geometrically nonlinear mathematical model of the problem of parametric oscillations of a viscoelastic orthotropic plate of variable thickness is developed using the classical Kirchhoff-Love hypothesis. The technique of the nonlinear problem solution by applying the Bubnov-Galerkin method at polynomial approximation of displacements (and deflection) and a numerical method that uses quadrature formula are proposed. The Koltunov-Rzhanitsyn kernel with three different rheological parameters is chosen as a weakly singular kernel. Parametric oscillations of viscoelastic orthotropic plates of variable thickness under the effect of an external load are investigated. The effect on the domain of dynamic instability of geometric nonlinearity, viscoelastic properties of material, as well as other physical-mechanical and geometric parameters and factors are taken into account. The results obtained are in good agreement with the results and data of other authors.

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I I, Safarov, Teshaev M Kh, Boltaev Z I, Ishmamatov M R, and Ruziyev T R. "Propagation of Proper Waves in a Viscoelastic Timoshenko Plate of Variable Thickness." International Journal of Engineering Trends and Technology 71, no. 1 (2023): 25–30. http://dx.doi.org/10.14445/22315381/ijett-v71i1p203.

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Normuminov, Bakhodir, Rustamkhan Abdikarimov, Dadakhan Khodzhaev, and Zulfiya Khafizova. "Parametric oscillations of viscoelastic orthotropic plates of variable thickness." IOP Conference Series: Materials Science and Engineering 896 (August 13, 2020): 012029. http://dx.doi.org/10.1088/1757-899x/896/1/012029.

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Mirsaidov, Mirziyod, Rustamkhan Abdikarimov, Bakhodir Normuminov, and Dadakhan Khodzhaev. "Dynamic analysis of an orthotropic viscoelastic cylindrical panel of variable thickness." E3S Web of Conferences 264 (2021): 02045. http://dx.doi.org/10.1051/e3sconf/202126402045.

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The intensive development of the modern industry is associated with the emergence of a variety of new composite materials. Plates, panels, and shells of variable thickness made of such materials are widely used in engineering and machine building. Modern technology for the manufacture of thin-walled structures of any configuration makes it possible to obtain structures with a given thickness variation law. Such thin-walled structures are subjected to various loads, including periodic ones. Nonlinear parametric vibrations of an orthotropic viscoelastic cylindrical panel of variable thickness are investigated without considering the elastic wave propagation. To derive a mathematical model of the problem, the Kirchhoff-Love theory is used in a geometrically nonlinear setting. The viscoelastic properties of a cylindrical panel are described by the hereditary Boltzmann-Volterra theory with a three-parameter Koltunov-Rzhanitsyn relaxation kernel. The problem is solved by the Bubnov-Galerkin method in combination with the numerical method. For the numerical implementation of the problem, an algorithm and a computer program were developed in the Delphi algorithmic language. Nonlinear parametric vibrations of orthotropic viscoelastic cylindrical panels under external periodic load were investigated. The influence of various physical, mechanical, and geometric parameters on the panel behavior, such as the thickness, viscoelastic and inhomogeneous properties of the material, external periodic load, were studied.

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Voropay, Alexey, and Pavel Yegorov. "THE INFLUENCE OF MASS AND INERTIAL CHARACTERISTICS OF AN ADDITIONAL VISCOELASTIC SUPPORT IN THE NONSTATIONARY DEFORMING OF A RECTANGULAR PLATE." Bulletin of the National Technical University "KhPI". Series: Mathematical modeling in engineering and technologies, no. 1 (March 5, 2021): 15–23. http://dx.doi.org/10.20998/2222-0631.2020.01.02.

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The nonstationary loading of a mechanical system consisting of a rectangular elastic isotropic plate and an additional viscoelastic support is investigated. The main attention is devoted to taking into account the mass and inertial characteristics of the additional viscoelastic support during modeling. As the main object, to which an additional support is attached, a plate of medium thickness within the framework of Timoshenko's hypotheses is considered. Since the focus of the paper is on the influence of the additional support, the plate itself is assumed to be hinged for simplicity of its model. We point out that the results presented are applicable to other objects that have additional supports (beams, plates and shells, which can have different supports along the contour and different shapes in plan). Nonstationary deformation is caused by the application of an external transverse disturbing load to the plate. The influence of the additional support on the deformation of the plate is replaced by the application of an unknown additional variable concentrated force, which, in fact, is the reaction of interaction between the plate and the additional support. The determination of this unknown reaction is reduced to solving the first kind Volterra integral equation. In this work, the main analytical relations for obtaining integral equations or their systems are derived, and an algorithm for their solving is presented. The results of calculations for specific numerical values are described. Moreover, the effect of an additional viscoelastic support on the plate is considered, both with and without taking into account the mass and inertial characteristics of the support. It is shown that for small masses the effect is practically absent, which can serve as an indirect proof of the correctness of the model obtained. As the main conclusion, it can be pointed out that the mass and inertial characteristics of the additional viscoelastic support have a noticeable effect on the vibration process, on both the amplitude and phase characteristics.

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Jafari, Nasrin, Mojtaba Azhari, and Amin Heidarpour. "Local buckling of thin and moderately thick variable thickness viscoelastic composite plates." Structural Engineering and Mechanics 40, no. 6 (2011): 783–800. http://dx.doi.org/10.12989/sem.2011.40.6.783.

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Alipour, M. M., and M. Shariyat. "Semi-analytical buckling analysis of heterogeneous variable thickness viscoelastic circular plates on elastic foundations." Mechanics Research Communications 38, no. 8 (2011): 594–601. http://dx.doi.org/10.1016/j.mechrescom.2011.09.001.

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Voropay, Alexey. "USING OPERATOR METHOD AND EFROS TRANSFORM FOR TAKING INTO ACCOUNT DISSIPATIVE PROPERTIES OF DEFORMABLE STRUCTURAL ELEMENTS." Vibrations in engineering and technology, no. 3(94) (November 26, 2019): 83–90. http://dx.doi.org/10.37128/2306-8744-2019-3-11.

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An approach for taking into account the dissipative properties of deformable structural elements (and in particular internal friction in the material) is proposed. This approach, based on the operator method and Efros transformation, is applied to analytical solutions obtained in the framework of elasticity theory, which can be represented as integrals of convolution type. The direct Laplace transform is applied to the operator equation. It is shown in the paper that changing to the Laplace variable enables one to pass from the relations taking into account dissipation energy to those for an elastic plate in the image space. The Efros theorem is used to perform the inverse Laplace transform of the complex function obtained. The posed problem is reduced to finding an unknown transforming function. Numerical calculations showed that in the problem considered (for small values of the time variable) the law of this function variation is very close to the law of normal distribution (Gaussian) with variable dispersion. Since the integral equations are discretized the kernel numerical modification is proposed by the Efros theorem. This modification is carried out by multiplying the discrete analogs of the original kernels by the special matrix obtained on the basis of the Gauss integral. The example of computing elastic and viscoelastic plate deflection is given, kernels of convolution integrals are presented for the "elastic" solution taking into account dissipation energy (internal friction in the material of the plate). Transversal impulse action on rectangular isotropic plates of medium thickness is considered. The plates are assumed to be hinged along the whole boundary. The plate deforming is simulated by the Timoshenko’s refined theory. It is possible to relatively quickly recalculate the deflections and deformations of the plate, taking into account internal friction for different values of the dissipation coefficients.

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Khudayarov, B. A. "Computational Experiments to Evaluate the Approaches to the Modeling of Viscoelastic Plates Motion Based on Various Theories." Mechanical Engineering and Computer Science, no. 9 (December 2, 2018): 15–33. http://dx.doi.org/10.24108/0918.0001412.

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Mathematical and computer modeling of the flutter of elements and units of the aircraft design is an actual scientific problem; its study is stimulated by the failure of aircraft elements, parts of space and jet engines. In view of the complexity of the flutter phenomenon of aircraft elements, simplifying assumptions are used in many studies. However, these assumptions, as a rule, turn out to be so restrictive that the mathematical model ceases to reflect the real conditions with sufficient accuracy. Therefore, results of theoretical and experimental studies are in bad agreement.At present, the problem of panel flutter is very relevant. Improvement of characteristics of military and civil aircraft inevitably requires reducing their weight, and consequently, the rigidity of paneling, which increases the possibility of a panel flutter. The concept of creating the aircraft with a variable shape, which would inevitably lead to a reduction in paneling thickness are actively discussed. Finally, the use of new materials and, in particular, composites, changes physical properties of the panels and can also lead to a flutter.The above-mentioned scientific problem gives grounds to assert that the development of adequate mathematical models, numerical methods and algorithms for solving nonlinear integral-differential equations of dynamic problems of the hereditary theory of viscoelasticity is actual.In connection with this, the development of mathematical models of individual elements of aircraft made of composite material is becoming very important.Generalized mathematical models of non-linear problems of the flutter of viscoelastic isotropic plates, streamlined by a supersonic gas flow, are constructed in the paper on the basis of integral models. To study oscillation processes in plates, a numerical algorithm is proposed for solving nonlinear integro-differential equations with singular kernels. Based on the developed computational algorithm, a package of applied programs is created. The effect of the singularity parameter in heredity kernels on the vibrations of structures with viscoelastic properties is numerically investigated. In a wide range of changes in plate parameters, critical flutter velocities are determined. Numerical solutions of the problem of viscoelastic plate flutter are compared for different models. It is shown that the most adequate theory for investigating a wide class of problems of the hereditary theory of viscoelasticity is the geometric nonlinear Kirchhoff-Love theory with consideration of elastic waves propagation. It is established that an account of viscoelastic properties of plate material leads to 40-60% decrease in the critical flutter velocity.

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Hwu, Chyanbin, and Wilfried Becker. "Stroh formalism for various types of materials and deformations." Journal of Mechanics 38 (2022): 433–44. http://dx.doi.org/10.1093/jom/ufac031.

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Abstract The Stroh formalism is a complex variable formulation developed originally for solving the problems of two-dimensional linear anisotropic elasticity. By separation of the third variable for the linear variation of displacements along the thickness direction, it was proved to be applicable for the problems with coupled stretching-bending deformation. By the Radon transform which maps a three-dimensional solid to a two-dimensional plane, it can be applied to the three-dimensional deformation. By the elastic-viscoelastic correspondence principle, it is also valid for the viscoelastic materials in the Laplace domain. By expansion of the matrix dimension, it can be generalized to the coupled-field materials such as piezoelectric, piezomagnetic and magneto-electro-elastic materials. By introducing a small perturbation on the material constants, it can also be applied to the degenerate materials such as isotropic materials. Thus, in this paper, the Stroh formalism for several different types of materials (anisotropic elastic, piezoelectric, piezomagnetic, magneto-electro-elastic, viscoelastic) and deformations (two-dimensional, coupled stretching-bending, three-dimensional) are organized together and presented in the same mathematical form.

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Tichy, J. A., and C. P. Ku. "A Thin Film Flow Rupture Model for Newtonian and Viscoelastic Fluids." Journal of Tribology 110, no. 4 (1988): 712–17. http://dx.doi.org/10.1115/1.3261718.

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The problem of specifying adequate boundary conditions in two-dimensional steady incompressible flow between a cylinder and a plane for Newtonian fluids has been studied for many years. Unfortunately, Newtonian boundary conditions cannot be readily transposed to the case of viscoelastic fluids. In the present paper we consider the case of the second-order Rivlin-Ericksen fluid in prescribing suitable boundary conditions. The crux of the issue is that there are at least three possible stresses to be considered: (1) the transverse normal stress σy, (2) the longitudinal normal stress σx, and (3) the mechanical pressure p. The former, σy, is constant across the film and this variable is the one which carries load and measured by an experimental “pressure” tap. In the process of developing the viscoelastic model, a Newtonian model is developed which uses the Birkhoff-Hays separation conditions, considers surface tension as the Coyne-Elrod model but invokes the thin film assumption. The equations of motion are satisfied along and across the separated interface. Variation of the transverse normal stress profile with a minimum film thickness ratio, a surface tension parameter and Deborah number is shown. An earlier paper [6] shows that inconsistencies arise in applying simple rupture models (Gumbel or Swift-Stieber) to viscoelastic fluids. A relatively complicated model of this type is necessary to portray the basic behavior of film rupture in viscoelastic fluids.

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Grigoryeva, Ludmila. "Transient responses in Piezoceramic Multilayer Actuators Taking into Account External Viscoelastic Layer." Strength of Materials and Theory of Structures, no. 105 (November 30, 2020): 255–66. http://dx.doi.org/10.32347/2410-2547.2020.105.255-266.

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The work develops a generalized approach to the study of thickness (radial) vibrations arising in the piezoceramic plates, cylinders, spheres under electrical loads. The state of the problem and the main approaches, used in the problems of studying the oscillations of electroelastic bodies, are described. The use of multilayer elements with electroded interface surfaces and variable direction of polarization of the layers increases the conversion efficiency of electrical energy into mechanical energy, so multilayer piezoceramic plates, cylinders, spheres with changing polarization directions with electroded interfaces are considered. Because of piezoelectric elements are often embedded in the housing and supplemented with matching layers to protect against mechanical damage, it is necessary to study their effect on the oscillations of the element. The proposed approach makes it possible to study the vibrations of plane, cylindrical and spherical bodies with layers made of various electroelastic and elastic materials. Numerical implementation is carried out using finite differences. Nonstationary oscillations of PZT-4 ceramic elements at zero initial conditions are investigated. Oscillations of multilayer plates, cylinders and spheres with and without an external elastic or viscoelastic reinforcing layer under impulse and harmonic unsteady loads are investigated and compared. There are found own frequencies for 5-layer bodies of different geometry with and without an external layer. The first natural frequency for cylinder and sphere corresponds to the radial mode of oscillations, while the second natural frequency for cylinders and spheres and the first for flat bodies are almost equal and correspond to thickness mode. The transient processes in the elements under impulse loads and the influence of the outer elastic layer (housing or matching layer) are studied, taking into account the Rayleigh attenuation. It is established that for a flat layer the outer layer increases the amplitude and the period of free vibrations after removing the load, and for cylinders and spheres it decreases. The presence of an elastic layer enhances the third and dampens the fourth natural frequency of the transducer, thereby expanding the frequency range of its operation.

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Бегун, Александра Сергеевна, and Лариса Валентиновна Ковтанюк. "Deformating of a viscoelastic disk rotating with acceleration." Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния, no. 3(45) (December 29, 2020): 143–51. http://dx.doi.org/10.37972/chgpu.2020.66.88.014.

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Рассматривается деформирование вязкоупругого диска, вращающегося с изменяющейся скоростью (разгон, торможение и вращение с постоянной скоростью). Для математического моделирования процесса деформирования используется теория течения. При предположении плоского напряженного состояния получена система дифференциальных уравнений для определения полей напряжений, обратимых и необратимых деформаций и перемещений. Численное решение этой системы уравнений найдено с помощью конечно-разностного метода. В случае решения осесимметричной задачи используется метод конечных элементов, реализованный в пакете Freefem++. Рассмотрено деформирование полого диска и диска с жестким включением, как постоянной толщины, так и переменной. The deformation of a viscoelastic disk rotating with a changing speed is considered. Within the framework of the theory of flow, relations are obtained that allow one to calculate the fields of stresses, strains, displacements, and velocities. To solve these equations in the case of a plane stress state, the finite-difference method is used, in the case of an axisymmetric problem, the finite element method implemented in the Freefem ++ package is used. Acceleration, braking and rotation at a constant speed are considered. The deformation of a hollow disk and a disk with a hard inclusion of both a constant thickness and a variable is considered.

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Бегун, Александра Сергеевна, and Лариса Валентиновна Ковтанюк. "Deformating of a viscoelastic disk rotating with acceleration." Вестник Чувашского государственного педагогического университета им. И.Я. Яковлева. Серия: Механика предельного состояния, no. 3(45) (December 29, 2020): 143–51. http://dx.doi.org/10.37972/chgpu.2020.66.88.014.

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Рассматривается деформирование вязкоупругого диска, вращающегося с изменяющейся скоростью (разгон, торможение и вращение с постоянной скоростью). Для математического моделирования процесса деформирования используется теория течения. При предположении плоского напряженного состояния получена система дифференциальных уравнений для определения полей напряжений, обратимых и необратимых деформаций и перемещений. Численное решение этой системы уравнений найдено с помощью конечно-разностного метода. В случае решения осесимметричной задачи используется метод конечных элементов, реализованный в пакете Freefem++. Рассмотрено деформирование полого диска и диска с жестким включением, как постоянной толщины, так и переменной. The deformation of a viscoelastic disk rotating with a changing speed is considered. Within the framework of the theory of flow, relations are obtained that allow one to calculate the fields of stresses, strains, displacements, and velocities. To solve these equations in the case of a plane stress state, the finite-difference method is used, in the case of an axisymmetric problem, the finite element method implemented in the Freefem ++ package is used. Acceleration, braking and rotation at a constant speed are considered. The deformation of a hollow disk and a disk with a hard inclusion of both a constant thickness and a variable is considered.

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Shariyat, M., and M. M. Alipour. "A power series solution for vibration and complex modal stress analyses of variable thickness viscoelastic two-directional FGM circular plates on elastic foundations." Applied Mathematical Modelling 37, no. 5 (2013): 3063–76. http://dx.doi.org/10.1016/j.apm.2012.07.037.

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Wan, Hao Chuan, Ling Zheng, and Yi Nong Li. "Thickness Optimization Study of Constrained Damping Plate." Applied Mechanics and Materials 226-228 (November 2012): 436–39. http://dx.doi.org/10.4028/www.scientific.net/amm.226-228.436.

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Based on Kirchhoff hypothesis, the vibration equations of constrained damping plate are established and the equations are solved. Influence of the thicknesses of constrained layer and viscoelastic layer on structural vibration character are analyzed, the curves of natural frequency and loss factor with different thicknesses of viscoelastic layer and constrained layer are obtained. The figures indicated that it is not the more thickness of the viscoelastic layer and constrained layer the higher of the loss factor. Both of the thicknesses have optimum values, which are interact. The relationship between of loss factor and added mass is investigated. The results show that various thickness plans can obtain the same loss factor but very different added mass. So it is very necessary to optimize the thickness of viscoelastic layer and constrained layer to obtain the best damping effect.

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Wang, Yan, and Zhong Min Wang. "Stability of a Cracked Viscoelastic Plate of Varying Thickness Subjected to Follower Force." Advanced Materials Research 243-249 (May 2011): 298–303. http://dx.doi.org/10.4028/www.scientific.net/amr.243-249.298.

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The stability of the cracked visoelastic rectangular plate of varying thickness subjected to uniformly distributed tangential follower force is investigated. Two models describing thickness variation are parabolic and linear variations along one edge of the plate. This is done in order to show how critical loads for cracked visoelastic thin plate subjected to follower force can be obtained using the two-dimensional viscoelastic differential constitutive relation and the thin-plate theory. The differential equations in the Laplace domain are established. The complex eigen-value equations are derived by the differential quadrature method. The generalized eigen-value under different boundary conditions is calculated. The effects of the plate parameters, the crack parameters and the dimensionless delay time on the stability of the viscoelastic plates are analyzed. The crack is found to change the type of instability and reduce the stability of varying thickness viscoelastic plate.

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Zenkour, Ashraf M., and Hela D. El-Shahrany. "Active control of a sandwich plate with reinforced magnetostrictive faces and viscoelastic core, resting on elastic foundation." Journal of Intelligent Material Systems and Structures 33, no. 10 (2021): 1321–37. http://dx.doi.org/10.1177/1045389x211053047.

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The current study presents a vibration investigation of a laminated plate considering a viscoelastic core with embedded magnetostrictive layers. The simply-supported plate is supported via Pasternak’s substrate medium. Based on different plate theories and employing Hamilton’s principle, the system of governing differential equations is derived. The mechanical properties of the viscoelastic core are described depend on the time varies based on Kelvin–Voigt model. Actuating magnetostrictive layers are utilized to control the vibration damping process of the system with the assistance of feedback and constant gain distributed control. The analytical solution is obtained to investigate the influence of half wave numbers, thickness ratios, core thickness, aspect ratios, lamination schemes, elastic foundation parameters, damping coefficient, feedback coefficient magnitude, magnetostrictive layers location, on the vibrational behavior of laminated plate. Some observations about the vibration damping process of the present plate are displayed. The results refer to that the vibration suppression rate depends on the thickness of the plate, the feedback control value, the foundation constants, and the viscoelastic structural damping significantly. Moreover, the study can be providing benchmark tests to validate future contributions on the viscoelastic smart structural issues and developing the design of smart viscoelastic structures and control of their vibrations.

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Cui, Yuhuan, Zhang Qi, Jingguo Qu, Aimin Yang, Qunwei Zhang, and Yunchen Liu. "Numerical solutions of the viscoelastic plate of fractional variable order." Thermal Science 27, no. 5 Part A (2023): 3869–75. http://dx.doi.org/10.2298/tsci2305869c.

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The fractional variable-order constitutive model for the viscoelastic plate is analyzed. The fractional variable-order constitutive equations for the plates are solved numerically using the shifted Bernstein polynomials directly in time domain. Numerical displacement of Polyurea and HDPE viscoelastic plates at a variety of loads was investigated. The results show that Polyurea has better bending resistance than HDPE viscoelastic plates, which verifies the practicability of the algorithm.

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Mongkolwongrojn, M., J. Panichakorn, S. Supawanich, and S. Chutima. "Analysis of Two Surfaces under Viscoelastic Contact." Advanced Materials Research 818 (September 2013): 77–82. http://dx.doi.org/10.4028/www.scientific.net/amr.818.77.

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This paper presents the analysis of the contact surfaces between a rigid cylinder and a soft plate for viscoelastic material. The contact pressure and deformation of the plate in contact region were determined using finite element technique. Moreover, the characteristics of two surfaces of cylindrical roller and plate under elastohydrodynamic lubrication with nonNewtonian fluid were examined using finite difference technique with full adaptive multigrid method . In this study the simulation of viscoelastic material in contact was under taken to determine the effects of material behaviors on the deformation of plate compared to the elastic materials. The results indicated that the deformation shapes were nonlinearly dependent with the applied loads. Furthermore, the deformation of elastic material would reach a certain value in a period of time whereas the deformation of viscoelastic material was increased inconsistently with time. The film pressure and film thickness profiles in the contact regime were investigated at various loads. The minimum film thickness occurs near the trailing edge of contact region and becomes very small under heavy loads.

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de Lima, A. M. G., M. H. Stoppa, D. A. Rade, and V. Steffen Jr. "Sensitivity Analysis of Viscoelastic Structures." Shock and Vibration 13, no. 4-5 (2006): 545–58. http://dx.doi.org/10.1155/2006/917967.

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In the context of control of sound and vibration of mechanical systems, the use of viscoelastic materials has been regarded as a convenient strategy in many types of industrial applications. Numerical models based on finite element discretization have been frequently used in the analysis and design of complex structural systems incorporating viscoelastic materials. Such models must account for the typical dependence of the viscoelastic characteristics on operational and environmental parameters, such as frequency and temperature. In many applications, including optimal design and model updating, sensitivity analysis based on numerical models is a very usefull tool. In this paper, the formulation of first-order sensitivity analysis of complex frequency response functions is developed for plates treated with passive constraining damping layers, considering geometrical characteristics, such as the thicknesses of the multi-layer components, as design variables. Also, the sensitivity of the frequency response functions with respect to temperature is introduced. As an example, response derivatives are calculated for a three-layer sandwich plate and the results obtained are compared with first-order finite-difference approximations.

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Zenkour, A. M., and M. Sobhy. "Elastic Foundation Analysis of Uniformly Loaded Functionally Graded Viscoelastic Sandwich Plates." Journal of Mechanics 28, no. 3 (2012): 439–52. http://dx.doi.org/10.1017/jmech.2012.53.

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AbstractThis paper deals with the static response of simply supported functionally graded material (FGM) viscoelastic sandwich plates subjected to transverse uniform loads. The FG sandwich plates are considered to be resting on Pasternak's elastic foundations. The sandwich plate is assumed to consist of a fully elastic core sandwiched by elastic-viscoelastic FGM layers. Material properties are graded according to a power-law variation from the interfaces to the faces of the plate. The equilibrium equations of the FG sandwich plate are given based on a trigonometric shear deformation plate theory. Using Illyushin's method, the governing equations of the viscoelastic sandwich plate can be solved. Parametric study on the bending analysis of FG sandwich plates is being investigated. These parameters include (i) power-law index, (ii) plate aspect ratio, (iii) side-to-thickness ratio, (iv) loading type, (v) foundation stiffnesses, and (vi) time parameter.

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Feri, Maziyar, Michael Krommer, and Akbar Alibeigloo. "Three-Dimensional Thermoelasticity Analysis of Viscoelastic FGM Plate Embedded in Piezoelectric Layers under Thermal Load." Applied Sciences 13, no. 1 (2022): 353. http://dx.doi.org/10.3390/app13010353.

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Due to the high importance of viscoelastic materials in modern industrial applications, besides the intensive popularity of piezoelectric smart structures, analyzing their thermoelastic response in extreme temperature conditions inevitably becomes very important. Accordingly, this research explores the thermoviscoelastic response of sandwich plates made of a functionally-graded Boltzmann viscoelastic core and two surrounding piezoelectric face-layers subjected to electrothermal load in the platform of three-dimensional elasticity theory. The relaxation modulus of the FG viscoelastic layer across the thickness follows the power law model. the plate’s governing equations are expressed in the Laplace domain to handle mathematical complications corresponding to the sandwich plate with a viscoelastic core. Then, the state-space method, combined with Fourier expansion, is utilized to extract the plate response precisely. Finally, the obtained solution is converted to the time domain using the inverse Laplace technique. Verification of the present formulation is compared with those reported in the published papers. Finally, the influences of plate dimension, temperature gradient, and relaxation time constant on the bending response of the above-mentioned sandwich plate are examined. As an interesting finding, it is revealed that increasing the length-to-thickness ratio leads to a decrease in deflections and an increase in stresses.

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Xie, Quanmin, Fengxiang Xu, Zhen Zou, Xiaoqiang Niu, and Zhuang Dong. "Natural Frequency Analysis and Optimization Design of Rectangular Thin Plates With Nonlinear Variable-Thickness." International Journal of Acoustics and Vibration 27, no. 4 (2022): 367–81. http://dx.doi.org/10.20855/ijav.2022.27.41894.

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Variable-thickness thin plate structures have been widely employed in many engineering applications, such as the automotive industry, aviation industry and civil structures. In this paper, natural frequency and optimization design of nonlinear variable-thickness rectangular thin plates are performed. For this purpose, theoretical solutions of dimensionless natural frequency of the bidirectional linear variable-thickness thin plates are conducted on the three classical boundaries to verify the correctness of a conducted numerical model. Then the natural frequencies of variable thickness plates with different forms including bidirectional and unidirectional nonlinear were compared. Additionally, the difference in vibration characteristics between the thin plate of variable thickness and the corresponding thin plate of equal mass are compared and analyzed, and the results show that when the middle part of the thin plate is thick, the natural frequency increases by a greater percentage. Finally, a new bidirectional stepped variable-thickness plate is proposed to improve the natural frequency of variable-thickness thin plates. Inspired by the stepped idea, the square and circle division methods are employed to improve the natural frequency of variable thickness thin plates, as the optimal design is carried out. The results show that the nonlinear variable thickness after performing an optimal design could significantly improve the natural frequency of thin plates. The finding provides useful insight into the structural design of variable thickness plates for free vibration.

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Ghorbanpour Arani, Ali, and Elham Haghparast. "Size-Dependent Vibration of Axially Moving Viscoelastic Micro-Plates Based on Sinusoidal Shear Deformation Theory." International Journal of Applied Mechanics 09, no. 02 (2017): 1750026. http://dx.doi.org/10.1142/s1758825117500260.

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In the present research, vibration and instability of axially moving viscoelastic micro-plate is investigated. Sinusoidal shear deformation theory (SSDT) is utilized due to its accuracy of polynomial functions than other plate theories. Based on Kelvin’s model, the viscoelastic structural properties of micro-plate are taken into consideration. The modified couple stress theory (MCST) is employed because of its capability to interpret the size effect. Using Hamilton’s principle, equations of motion are obtained and solved by hybrid analytical–numerical solution at different boundary conditions. Influences of various parameters such as size effect, axially moving speed, viscoelastic structural damping coefficient, thickness and aspect ratio on the vibration characteristics of moving viscoelastic micro-plate are discussed in detail. The results indicated that the critical speed of moving micro-plate is strongly dependent on the aspect ratio, therefore, the low aspect ratio should be considered for optimum design of this kind of moving micro-devices. The results of this investigation can be used in design and manufacturing of axially moving systems at the micro-scale such as micro-magnetic tapes.

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ZHOU, Yinfeng. "Dynamic Behaviors of Axially Moving Viscoelastic Plate with Varying Thickness." Chinese Journal of Mechanical Engineering 22, no. 02 (2009): 276. http://dx.doi.org/10.3901/cjme.2009.02.276.

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Yin-feng, Zhou, and Wang Zhong-min. "Vibrations of axially moving viscoelastic plate with parabolically varying thickness." Journal of Sound and Vibration 316, no. 1-5 (2008): 198–210. http://dx.doi.org/10.1016/j.jsv.2008.02.040.

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Djalilov, M. L., and T. M. Sаbirjаnov. "ANALYSIS OF THE GENERAL EQUATIONS OF THE TRANSVERSE VIBRATION OF A PIECEWISE HOMOGENEOUS VISCOELASTIC PLATE." American Journal Of Applied Science And Technology 02, no. 04 (2022): 18–28. http://dx.doi.org/10.37547/ajast/volume02issue04-03.

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This article discusses the analysis of the general equations of the transverse vibration of a piecewise homogeneous viscoelastic plate obtained in the “Oscillation of bilayer plates of constant thickness”.

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Abd El-Aziz, Mohamed. "The effects of variable fluid properties and viscous dissipation on forced convection of viscoelastic liquids in a thin film over an unsteady stretching sheet." Canadian Journal of Physics 88, no. 8 (2010): 607–16. http://dx.doi.org/10.1139/p10-043.

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An analysis is performed to study the effect of variable viscosity and variable thermal conductivity on the flow and heat transfer of a thin viscoelastic liquid (obeying Walters' liquid B model) film on a horizontal unsteady stretching sheet taking into account the effect of viscous dissipation. The fluid viscosity is assumed to decrease exponentially with temperature but the thermal conductivity is assumed to vary as a linear function of temperature. Numerical solutions are obtained for some representative values of the viscosity and thermal conductivity variation parameters, unsteadiness parameter, and Eckert number. Typical temperature and velocity profiles, dimensionless film thickness, free-surface velocity and temperature, local skin-friction coefficient, and the local surface heat flux are obtained for a wide range of governing parameters. In general, it is found that a viscoelastic fluid is more sensitive to the variable fluid properties effect than a Newtonian fluid. Also, for constant and (or) variable fluid properties, the film thickness and the local surface heat flux of a viscoelastic fluid is small compared to that of a Newtonian fluid. For all values of the variable viscosity parameter and for both viscoelastic and Newtonian fluid films, the viscous dissipation effect increases the free-surface temperature significantly whereas it reduces the heat transfer rate markedly. However, viscous dissipation does not influence the velocity profiles of both Newtonian and viscoelastic liquid films impressively although the film thickness changes noticeably.

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Ryabov, Victor M., Boris A. Yartsev, and Ludmila V. Parshina. "Coupled vibrations of viscoelastic three-layer composite plates. 2. Numerical experiments." Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 8, no. 1 (2021): 88–100. http://dx.doi.org/10.21638/spbu01.2021.108.

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Results of numerical studies of the influence of reinforcement orientation of hard layers and the relative thickness of the soft layer of an isotropic viscoelastic polymer on the values of natural frequencies and coefficients of mechanical losses are discussed. In a symmetrical three-layer plate, a bending-torsion interaction arises, generating mutual transformations of the eigenmodes of the coupled vibration modes, if at least one of its own forms in plate directions is characterized by an even number quarters of a wave, and another proper form - an odd number of quarters the waves. In an unsymmetrical asymmetric three-layer plate, bending-bending interaction arises, generating mutual transformations eigenmodes of coupled vibration modes in two mutually orthogonal planes if in the main directions of the plate both of their own forms characterized by either an even or an odd number of quarters of a wave. It was found that each mode of natural vibrations of three-layer plates corresponds to the effective relative thickness of the soft isotropic layer viscoelastic polymer.

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Normuminov, B., R. Abdikarimov, B. Eshmatov, and D. Yulchiyev. "Dynamics of viscoelastic orthotropic shallow shells of variable thickness." IOP Conference Series: Materials Science and Engineering 883 (July 21, 2020): 012214. http://dx.doi.org/10.1088/1757-899x/883/1/012214.

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Amanieh, Hamid Reza Talebi, Seyed Alireza Seyed Roknizadeh, and Arash Reza. "Nonlinear Vibration Analysis of Viscoelastic Smart Sandwich Plates Through the use of Fractional Derivative Zener Model." International Journal of Structural Stability and Dynamics 21, no. 05 (2021): 2150061. http://dx.doi.org/10.1142/s0219455421500619.

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In this paper, the nonlinear vibrational behavior of a sandwich plate with embedded viscoelastic material is studied through the use of constitutive equations with fractional derivatives. The studied sandwich structure is consisted of a viscoelastic core that is located between the faces of functionally graded magneto-electro-elastic (FG-MEE). In order to determine the frequency-dependent feature of the viscoelastic layer, four-parameter fractional derivative model is utilized. The material properties of FG-MEE face sheets have been distributed considering the power law scheme along the thickness. In addition, for derivation of the governing equations on the sandwich plate, first-order shear deformation plate theory along with von Karman-type of kinematic nonlinearity are implemented. The derived partial differential equations (PDEs) have been transformed to the ordinary differential equations (ODEs) through the Galerkin method. After that, the nonlinear vibration equations for the sandwich plate have been solved by multiple time scale perturbation technique. Moreover, for evaluating the effect of different parameters such as electric and magnetic fields, fractional order, the ratio of the core-to-face thickness and the power low index on the nonlinear vibration characteristics of sandwich plates with FG-MEE face sheets, the parametric analysis has been performed. The obtained results revealed the enhanced nonlinear natural frequency through an increment in the fractional order. Furthermore, the prominent influence of fractional order on the nonlinear frequency of sandwich plate was declared at the negative electric potential and positive magnetic potential.

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37

Strathdee, J., W. H. Robinson, and E. M. Haines. "Moving loads on ice plates of finite thickness." Journal of Fluid Mechanics 226 (May 1991): 37–61. http://dx.doi.org/10.1017/s0022112091002288.

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The response of a floating ice plate to a moving load is given in terms of a pair of Green's functions. General expressions for these Green's functions are derived for the case of an infinite isotropic plate of uniform thickness supported on a fluid base of uniform depth. The distributions of stress and strain in the vicinity of a concentrated load receive significant contributions from waves of length comparable with the plate thickness and their description necessitates an exact description of thickness effects. Circumstances in which the classical thin-plate theory can be recovered are discussed. The steady-state response to a uniformly moving load displays a so-called ‘critical’ behaviour for load velocities in the neighbourhood of a threshold value at which radiation commences. At the critical speed the amplitude is limited by dissipative forces in the ice plate. To describe this a simple viscoelastic term is included in our model. Calculations indicate that thin-plate theory is accurate to within 5% for distances greater than twenty times the ice thickness.

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38

Jin, Suhua, Jiaquan Xie, Jingguo Qu, and Yiming Chen. "A Numerical Method for Simulating Viscoelastic Plates Based on Fractional Order Model." Fractal and Fractional 6, no. 3 (2022): 150. http://dx.doi.org/10.3390/fractalfract6030150.

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In this study, an efficacious method for solving viscoelastic dynamic plates in the time domain is proposed for the first time. The differential operator matrices of different orders of Bernstein polynomials algorithm are adopted to approximate the ternary displacement function. The approximate results are simulated by code. In addition, it is proved that the proposed method is feasible and effective through error analysis and mathematical examples. Finally, the effects of external load, side length of plate, thickness of plate and boundary condition on the dynamic response of square plate are studied. The numerical results illustrate that displacement and stress of the plate change with the change of various parameters. It is further verified that the Bernstein polynomials algorithm can be used as a powerful tool for numerical solution and dynamic analysis of viscoelastic plates.

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Despres, Clément, Patrice Masson, Eric Ducasse, Michel Castaings, and Nicolas Quaegebeur. "Characterization of complex stiffness and thickness of isotropic, viscoelastic plates using multi-modal Lamb waves." Journal of the Acoustical Society of America 155, no. 3_Supplement (2024): A291. http://dx.doi.org/10.1121/10.0027542.

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This paper presents an approach exploiting the sensitivity of Lamb waves for characterizing the mechanical and geometrical properties of plates. The analytical sensitivity functions are first derived in the case of an isotropic plate and are integrated into an iterative inverse problem to optimize its mechanical and geometrical properties based on a zero-finding approach (Gauss-Newton algorithm for a multivariable problem). This method is validated numerically for a viscoelastic plate and shows high accuracy and low computational cost when compared to existing methods. The design af an experimental setup based on dedicated air-coupled transducers is proposed by optimizing the shape and size of the transducers in order to increase sensitivity of the measred signals with respect to the mechanical parameters of the structure of insterest. Experimental validation demonstrates the ability of the methodto assess simultaneously the viscoelastic properties and the thickness of isotropic plate-like structures.

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40

Kostopoulos, V., and D. Th Korontzis. "Damping Characteristics of Vibrated Composite Plates." Advanced Composites Letters 9, no. 6 (2000): 096369350000900. http://dx.doi.org/10.1177/096369350000900604.

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The free vibration response of [±Θ] ns orthogonal, simply supported (all around) composite laminated plates was studied, assuming linear viscoelastic behaviour of the constitutive lamina material. The problem was solved numerically and the results were verified in the special case of [0]2 n laminate against the analytical solution, which is also provided. Stability and convergence problems were discussed analytically. Eigenfrequency values and modal damping characteristics were calculated for the first nine mode shapes. Furthermore, keeping constant the plate thickness, the effect of the lamina thickness on the vibration characteristics of the plate was examined.

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41

Huang, Zhicheng, Huanyou Peng, Xingguo Wang, and Fulei Chu. "Modeling and Vibration Control of Sandwich Composite Plates." Materials 16, no. 3 (2023): 896. http://dx.doi.org/10.3390/ma16030896.

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A finite element dynamic model of the sandwich composite plate was developed based on classical laminate theory and Hamilton’s principle. A 4-node, 7-degree-of-freedom three-layer plate cell is constructed to simulate the interaction between the substrate, the viscoelastic damping layer, and the piezoelectric material layer. Among them, the viscoelastic layer is referred to as the complex constant shear modulus model, and the equivalent Rayleigh damping is introduced to represent the damping of the substrate. The established dynamics model has too many degrees of freedom, and the obtained dynamics model has good controllability and observability after adopting the joint reduced-order method of dynamic condensation in physical space and equilibrium in state space. The optimal quadratic (LQR) controller is designed for the active control of the sandwich panel, and the parameters of the controller parameters, the thickness of the viscoelastic layer, and the optimal covering position of the sandwich panel are optimized through simulation analysis. The results show that the finite element model established in this paper is still valid under different boundary conditions and different covering methods, and the model can still accurately and reliably represent the dynamic characteristics of the original system after using the joint step-down method. Under different excitation signals and different boundary conditions, the LQR control can effectively suppress the vibration of the sandwich plate. The optimal cover position of the sandwich plate is near the solid support end and far from the free-degree end. The parameters of controller parameters and viscoelastic layer thickness are optimized from several angles, respectively, and a reasonable optimization scheme can be selected according to the actual requirements.

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42

Lv, Yunlei, Yaqiu Liu, Xiang Li, Lina Lu, and Adil Malik. "Automated Shape Correction for Wood Composites in Continuous Pressing." Forests 15, no. 7 (2024): 1118. http://dx.doi.org/10.3390/f15071118.

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Abstract: The effective and comprehensive utilization of forest resources has become the theme of the global “dual-carbon strategy”. Forestry restructured wood is a kind of wood-based panel made of wood-based fiber composite material by high-temperature and high-pressure restructuring–molding, and has become an important material in the field of construction, furniture manufacturing, as well as derivative processing for its excellent physical and mechanical properties, decorative properties, and processing performance. Taking Medium Density Fiberboard (MDF) as the recombinant material as the research object, an event-triggered synergetic control mechanism based on interventional three-way decision making is proposed for the viscoelastic multi-field coupling-distributed agile control of the “fixed thickness section” in the MDF continuous flat-pressing process, where some typical quality control problems of complex plate shape deviations including thickness, slope, depression, and bump tend to occur. Firstly, the idea of constructing the industrial event information of continuous hot pressing based on information granulation is proposed, and the information granulation model of the viscoelastic plate shape process mechanism is established by combining the multi-field coupling effect. Secondly, an FMEA-based cyber granular method for diagnosing and controlling the plate thickness diagnosis and control failure information expression of continuous flat pressing is proposed for the problems of plate thickness control failure and plate thickness deviation defect elimination that are prone to occur in the continuous flat-pressing process. The precise control of the plate thickness in the production process is realized based on event-triggered control to achieve the intelligent identification and processing of the various types of faults. The application test is conducted in the international mainstream production line of a certain type of continuous hot-pressing equipment for the production of 18 mm plate thickness; the synergistic effect is basically synchronized after 3 s, the control accuracy reaches 30%, and the average value of the internal bond strength is 1.40, which ensures the integrity of the slab. Practical tests show that the method in the actual production is feasible and effective, with detection and control accuracy of up to ± 0.05 mm, indicating that in the production of E0- and E1-level products, the rate of superior products can reach more than 95%.

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Kudryavtsev, B. Y. "THE FLUTTER OF A PLATE OF VARIABLE THICKNESS." Izvestiya MGTU MAMI 6, no. 1 (2012): 249–55. http://dx.doi.org/10.17816/2074-0530-70024.

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The stability of a rectangular plate of variable thickness, being in a supersonic flow of gas, was investigated by application of the linear piston theory. The critical velocity of the gas flow was calculated. The problem of thickness distribution optimization was solved.

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Yartsev, B. A., V. M. Ryabov, and L. V. Parshina. "Dissipative properties of three-layered composite structures. 4. Numerical experiment." Transactions of the Krylov State Research Centre 3, no. 401 (2022): 58–70. http://dx.doi.org/10.24937/2542-2324-2022-3-401-58-70.

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Object and purpose of research. The study is concerned with a three-layer plate formed by two rigid anisotropic layers and a soft medium isotropic layer of viscoelastic polymer. Each rigid layer presents anisotropic structure formed by a finite number of randomly oriented orthotropic viscoelastic layers of composites. The paper is intended to study the influence of reinforcement orientation of rigid layers, relative thickness of the soft layer of an isotropic viscoelastic polymer and the ambient temperature on values values of natural frequencies and mechanical loss factors of the coupled damped oscillations in symmetric and assymetric plates. Materials and methods. Numerical experiment using a computer program implementing the previously proposed method for solving coupled differential equations of damped oscillations in anisotropic three-layer plates [2]. Main results. It was shown that in unsupported globally monoclinic symmetrical three-layer rectangular plate a bendingtorsional interaction occurs, generating mutual transformations of the eigenforms of the coupled oscillation modes if at least in one of the directions of the plate one of the eigenforms is characterized by an even number of quarters of the wave, and the other eigenform is characterized by an odd number of quarters of the wave. In unsupported globally orthotropic asymmetric three-layer rectangular plate interaction of bending modes of oscillations occurs in two mutually orthogonal planes, if both eigenforms are characterized by either an even or an odd number of wave quarters in main directions of the plate. It was found that each mode of natural oscillations of both symmetric and asymmetric three-layer plates has its own effective relative thickness of the soft layer of an isotropic viscoelastic polymer corresponding to the maximum level of dissipative properties. A further increase in the relative thickness is often accompanied by a decrease in values of the mechanical loss factors. The significant influence of ambient temperature on natural frequencies values and mechanical loss factors of all considered oscillation modes of symmetric and asymmetric unsupported rectangular three-layer composite plates is demonstrated. Conclusion. It was found that coupled damped oscillations of a symmetric three-layer plate are described by two systems of differential equations, with structures close to that of the systems of corresponding differential equations describing the damped oscillations of a quasi-homogeneous monoclinic plate. At the same time, the coupled damped oscillations of an asymmetric three-layer plate are described by two systems of differential equations that coincide with the systems of corresponding differrential equations describing the damped oscillations of a globally orthotropic three-layer plate.

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Sobhy, Mohammed, and Ashraf M. Zenkour. "Nonlocal Thermal and Mechanical Buckling of Nonlinear Orthotropic Viscoelastic Nanoplates Embedded in a Visco-Pasternak Medium." International Journal of Applied Mechanics 10, no. 08 (2018): 1850086. http://dx.doi.org/10.1142/s1758825118500862.

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This paper discusses the thermal and mechanical buckling of simply supported and clamped orthotropic viscoelastic graphene sheets (nanoplates) embedded in a visco-Pasternak elastic medium. For this purpose, the nonlocal continuum mechanical model is employed with two-variable plate theory. The material of the present nanoplate is assumed to be orthotropic and viscoelastic. The modified nonlinear Kelvin–Voigt viscoelastic model is utilized to formulate the constitutive relations depending on the viscoelastic structural damping coefficient. Moreover, the visco-Pasternak elastic medium is composed of both viscoelastic and shear layers. The viscoelastic layer includes a set of dashpots and elastic springs connected in parallel. In accordance with the two-variable theory, two governing equations are derived via Hamilton’s principle. These equations are analytically solved for various boundary conditions to obtain the explicit solution for critical buckling temperature and buckling load. The present buckling load and buckling temperature both are compared well with the published ones in the literature. In addition, various numerical studies are thoroughly carried out, concentrating on the influences of the plate geometric, nonlocal parameter, structural damping coefficient, elastic foundation parameters, foundation damping parameter and boundary conditions on the critical buckling load and temperature of the nanoplates. The results show that the involvement of the viscidity of the nanoplate and viscoelastic foundation enhances the strength of the nanoplates and therefore increases the resistance of them to external loads.

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46

Tang, Liling, and Feng Jin. "Influence of viscoelastic interfaces on power transmission through an elastic plate by finite piezoelectric transducers." Journal of Vibration and Control 23, no. 7 (2016): 1193–205. http://dx.doi.org/10.1177/1077546315591335.

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A finite elastic plate, partially covered by piezoelectric patches on two sides to periodically charge or recharge electronic devices operating in a sealed armor, is considered to study the effects of a viscoelastic interface on the resonant frequency, transformation ratio, efficiency, displacement and stress distributions of the structure. Based on the shear-slip model, we apply the Fourier series method to analyze the symmetric thickness-twist modes of the system containing an imperfect viscoelastic interface. An examination of the numerical results confirms the good convergence and high precision of the Fourier series method. If an appropriate thickness ratio is chosen, the energy-trapping phenomenon is well presented. The numerical results also reveal that the transformation ratio, efficiency and displacement of the system decrease for weaker interfaces, whereas the resonant frequency is not sensitive to interface damping parameters. This result could provide a theoretical guide to design high-performance piezoelectric plate transformers.

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Joseph, Shince V., and SC Mohanty. "Buckling and free vibration analysis of skew sandwich plates with viscoelastic core and functionally graded material constraining layer." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 233, no. 1 (2017): 369–81. http://dx.doi.org/10.1177/0954410017727024.

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The present study is concerned with the free vibration and buckling analysis of a skew sandwich plate with a viscoelastic material core fixed between a functionally graded material constraining layer and a base layer of elastic material. The sandwich plate theory is followed to obtain the governing equations of motion in which the displacement fields of the viscoelastic core are assumed to have a linear variation between those of the two face layers. Finite element method based on first-order shear deformation theory is used to develop the governing equations of motion of the plate. The effects of different parameters such as skew angle, aspect ratio, thickness ratio, and volume fraction index on static and dynamic characteristics of the plate are examined. The increase in the skew angle has increasing effect on both natural the frequencies and critical buckling loads, whereas the fundamental loss factor decreases. The volume fraction index and various boundary conditions also have significant effects on the static and dynamic behavior of the plate.

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48

Reddy, G. S., and Md Hafeez. "Simulation of variable thickness aluminum alloy plate casting." Journal of Physics: Conference Series 2837, no. 1 (2024): 012092. http://dx.doi.org/10.1088/1742-6596/2837/1/012092.

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Abstract The simulation of variable thickness aluminum alloy plate casting is investigated to understand the solidification process and mitigate macro shrinkage in castings. Aluminium alloys offer versatile properties suitable for diverse applications, gaining prominence, especially in electric vehicle manufacturing. Incorporating rare earth elements like Nd into aluminum alloys enhances corrosion resistance, while grain refinement treatments further augment this attribute. This study utilizes sand molds with varying thicknesses to cast Al-13%Si alloy into variable-thickness plate casting. Simulation outcomes reveal the absence of shrinkage porosity, with the last solidification events occurring in risers and sprue. Silicon’s role in reducing shrinkage porosity is highlighted, alongside advancements in grain refinement techniques for enhanced mechanical properties. The temperature distribution and cooling curves affirm directional solidification, aligning with desired temperature gradients. The manuscript underscores the dependence of simulation results on quality input data, emphasizing the critical role of temperature-dependent properties and initial boundary conditions. The continuous audit of simulation process data, focusing on fundamentals such as turbulence, modulus ratios, and directional solidification, is identified as essential for refining predictive models. This study contributes to the continuous improvement philosophy in manufacturing by providing insights into optimizing casting processes through simulations. By bridging the gap between simulation and real-world outcomes, this research enhances the reliability and applicability of solidification models, paving the way for advancements in aluminum alloy casting simulations. Notably, the automotive industry’s shift towards aluminum components underscores the importance of these findings in manufacturing practices.

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Ye, Zhiming. "Nonlinear vibration of circular plate with variable thickness." Journal of Shanghai University (English Edition) 2, no. 1 (1998): 27–34. http://dx.doi.org/10.1007/s11741-998-0023-y.

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Chaves, E. W. V., G. R. Fernandes, and W. S. Venturini. "Plate bending boundary element formulation considering variable thickness." Engineering Analysis with Boundary Elements 23, no. 5-6 (1999): 405–18. http://dx.doi.org/10.1016/s0955-7997(98)00097-6.

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Journal articles on the topic 'Viscoelastic plate with variable thickness'

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