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Journal articles on the topic 'Shells (Engineering) Vibration. Elastic plates and shells'

Author: Grafiati

Published: 4 June 2021

Last updated: 3 February 2022

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1

Ansari, R., J. Torabi, and M. Faghih Shojaei. "Free vibration analysis of embedded functionally graded carbon nanotube-reinforced composite conical/cylindrical shells and annular plates using a numerical approach." Journal of Vibration and Control 24, no. 6 (July 20, 2016): 1123–44. http://dx.doi.org/10.1177/1077546316659172.

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Free vibration analysis of embedded functionally graded carbon nanotube-reinforced composite (FG-CNTRC) conical, cylindrical shells and annular plates is carried out using the variational differential quadrature (VDQ) method. Pasternak-type elastic foundation is taken into consideration. It is assumed that the functionally graded nanocomposite materials have the continuous material properties defined according to extended rule of mixture. Based on the first-order shear deformation theory, the energy functional of the structure is calculated. Applying the generalized differential quadrature method and periodic differential operators in axial and circumferential directions, respectively, the discretized form of the energy functional is derived. Based on Hamilton’s principle and using the VDQ method, the reduced forms of mass and stiffness matrices are obtained. The comparison and convergence studies of the present numerical method are first performed and then various numerical results are presented. It is found that the volume fractions and functionally grading of carbon nanotubes play important roles in the vibrational characteristics of FG-CNTRC cylindrical, conical shells and annular plates.

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2

Yang, Chuanmeng, Guoyong Jin, Weijian Xu, and Zhigang Liu. "A Modified Fourier Solution for Free Damped Vibration Analysis of Sandwich Viscoelastic-Core Conical Shells and Annular Plates with Arbitrary Restraints." International Journal of Applied Mechanics 08, no. 08 (December 2016): 1650094. http://dx.doi.org/10.1142/s1758825116500940.

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In this paper, arbitrary boundary conditions including classical and elastic ones are considered in analyzing the vibration and damping characteristics of the sandwich conical shells and annular plates using a simple and efficient modified Fourier solution. The displacement field is expressed as the linear combination of a standard Fourier series and several supplementary terms. The addition of these terms make the Fourier series expansion applicable to any boundary conditions, and the Fourier series expansions improved drastically regarding its accuracy and convergence. Instead of adopting conventional differentiation procedure, a Rayleigh–Ritz technique based on the energy function is conducted which leads to a set of algebraic equations. Then natural frequencies and loss factors can be obtained by solving the algebraic equations. Accuracy and reliability of the current method are checked by comparing the present results with the existing solutions. Influences of some vital parameters on the free vibration and damping performance of sandwich shells and plates are discussed. The detailed effect of restraints from different directions on the frequencies and loss factors is investigated. So, the method can provide a guide to design sandwich structures with desired vibration characteristic and well damping performance by reasonably adjusting the boundary condition. Some new numerical results are presented for future validation of various approximate/numerical methods.

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3

Zhao, De-Min, Shan-Peng Li, Yun Zhang, and Jian-Lin Liu. "Nonlinear Vibration of an Elastic Soft String: Large Amplitude and Large Curvature." Mathematical Problems in Engineering 2018 (July 22, 2018): 1–11. http://dx.doi.org/10.1155/2018/7909876.

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Mechanical nonlinear vibration of slender structures, such as beams, strings, rods, plates, and even shells occurs extensively in a variety of areas, spanning from aerospace, automobile, cranes, ships, offshore platforms, and bridges to MEMS/NEMS. In the present study, the nonlinear vibration of an elastic string with large amplitude and large curvature has been systematically investigated. Firstly, the mechanics model of the string undergoing strong geometric deformation is built based on the Hamilton principle. The nonlinear mode shape function was used to discretize the partial differential equation into ordinary differential equation. The modified complex normal form method (CNFM) and the finite difference scheme are used to calculate the critical parameters of the string vibration, including the time history diagram, configuration, total length, and fundamental frequency. It is shown that the calculation results from these two methods are close, which are different with those from the linear equation model. The numerical results are also validated by our experiment, and they take excellent agreement. These analyses may be helpful to engineer some soft materials and can also provide insight into the design of elementary structures in sensors, actuators and resonators, etc.

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4

Babenkova, E., and J. Kaplunov. "Radiation conditions for a semi-infinite elastic strip." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2056 (April 8, 2005): 1163–79. http://dx.doi.org/10.1098/rspa2004.1402.

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High-frequency vibrations of a semi-infinite elastic strip with traction-free faces are considered. The conditions on end data that are derived do not allow non-radiating in Sommerfeld's sense of polynomial modes at thickness resonance frequencies. These represent a high-frequency analogue of the well-known decay conditions in statics that agree with the classical Saint-Venant principle. The proposed radiation conditions are applied to the construction of boundary conditions in the theories of high-frequency long-wave vibrations describing slow-varying motions in the vicinity of thickness resonance frequencies. The derivation is based on the Laplace transform technique along with the asymptotic methodology that is typical for thin plates and shells.

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5

Ling, Zheng, Xie Ronglu, Wang Yi, and Adel El-Sabbagh. "Topology Optimization of Constrained Layer Damping on Plates Using Method of Moving Asymptote (MMA) Approach." Shock and Vibration 18, no. 1-2 (2011): 221–44. http://dx.doi.org/10.1155/2011/830793.

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Damping treatments have been extensively used as a powerful means to damp out structural resonant vibrations. Usually, damping materials are fully covered on the surface of plates. The drawbacks of this conventional treatment are also obvious due to an added mass and excess material consumption. Therefore, it is not always economical and effective from an optimization design view. In this paper, a topology optimization approach is presented to maximize the modal damping ratio of the plate with constrained layer damping treatment. The governing equation of motion of the plate is derived on the basis of energy approach. A finite element model to describe dynamic performances of the plate is developed and used along with an optimization algorithm in order to determine the optimal topologies of constrained layer damping layout on the plate. The damping of visco-elastic layer is modeled by the complex modulus formula. Considering the vibration and energy dissipation mode of the plate with constrained layer damping treatment, damping material density and volume factor are considered as design variable and constraint respectively. Meantime, the modal damping ratio of the plate is assigned as the objective function in the topology optimization approach. The sensitivity of modal damping ratio to design variable is further derived and Method of Moving Asymptote (MMA) is adopted to search the optimized topologies of constrained layer damping layout on the plate. Numerical examples are used to demonstrate the effectiveness of the proposed topology optimization approach. The results show that vibration energy dissipation of the plates can be enhanced by the optimal constrained layer damping layout. This optimal technology can be further extended to vibration attenuation of sandwich cylindrical shells which constitute the major building block of many critical structures such as cabins of aircrafts, hulls of submarines and bodies of rockets and missiles as an invaluable design tool.

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6

Muhammad, Adnan. "Technical Review: Indirect Tire Pressure Monitoring Systems and Tire Vibrations." Tire Science and Technology 47, no. 2 (April 1, 2019): 102–17. http://dx.doi.org/10.2346/tire.18.460403.

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ABSTRACT Indirect tire pressure monitoring systems (ITPMSs) have been an active area of research for the past 2 decades. Researchers worldwide have strived to develop estimation techniques for the detection of the change in tire pressure by using the vibration information present in the speed signal. Different groups have used a torsional vibration model for the tire, owing to its torsional stiffness and rotational moment of inertia. The standard antilock braking system (ABS) speed sensor signal is analyzed for these vibrations. Different estimation algorithms try to detect the change in this vibration frequency, which indicates the change in the torsional stiffness of the tire as a result of variation in the pressure. Tire vibrations have been studied in great detail for the past 5 decades, and there are various models of tire vibrations available in the literature. These models range from physics-based analytical models to finite element models (FEMs). Analytical models take benefit from the mathematics developed for rotating elastic thin shells and plates, whereas FEMs use simulation tools to develop vibration models of the tire. A detailed literature survey of ITPMSs and tire vibration models reveals that there is no correlation between the vibrations detected in the speed signal and the vibrations predicted in the tire vibration models. Researchers have developed tire vibration models that do not take into consideration the effects of vibrations on the speed signal; although, to the best of our knowledge, signal processing and estimation experts who have developed methods for ITPMSs have not validated the true source of observed vibrations in the speed signal and could not present a viable theoretical explanation. In this review, a comprehensive study of the ITPMS techniques and tire vibration models is presented, with an aim to find a correlation between them. The review begins with a brief introduction to the topic followed by state of the art, then a detailed review of ITPMSs and the methods for their realizations in the automotive industry. Finally, tire vibration models are presented in detail, and possible links between vibration models and ITPMS vibrations are sorted.

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7

Brasil, Reyolando M. L. R. F., and Carlos E. N. Mazzilli. "A General FEM Formulation of Nonlinear Dynamics Applied to Accessing the Statical Loading Effect Upon the Dynamic Response of Planar Frames." Applied Mechanics Reviews 46, no. 11S (November 1, 1993): S110—S117. http://dx.doi.org/10.1115/1.3122625.

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This paper initially discusses the dynamics of discrete structural systems of geometricaly nonlinear behaviour costituted by linear elastic materials. Two formulations are derived, namely global and incremental. They are both suitable to general FE modelling, as the matrix equations of motion are written in explicit form. Matrices and vectors involved are characterized in terms of constraint equations defined within the continuum discretization. In principle, such formulations are applicable to any structural theory, as the theories of beams, plates and shells. As an example, the Bernoulli-Euler beam element is studied herewith. Both global and incremental formulations capture the effect geometrical nonlinearities have upon inertial and elastic forces alike. The ANDROS FEM program, developed by the authors, which is based upon the global formulation, has been successfully used in several nonlinear analyses. From this general background, the paper proceeds to consider the effect statical loading may have upon the free undamped vibration frequencies of a structure. It is shown that the tangent stiffness matrix of the incremental formulation should be used in the resultant eingenvalue problem. In some cases, axial forces are seen to have a strong influence on the internal resonance tuning. It is shown, in a sample structure thus tuned and subjected to dynamical loading, that a nonlinear regime may appear in the response.

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8

Rossikhin, Yury A., and Marina V. Shitikova. "Analysis of damped vibrations of thin bodies embedded into a fractional derivative viscoelastic medium." Journal of the Mechanical Behaviour of Materials 21, no. 5-6 (April 1, 2013): 155–59. http://dx.doi.org/10.1515/jmbm-2013-0002.

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AbstractDamped vibrations of elastic thin bodies, such as plates and circular cylindrical shells, embedded into a viscoelastic medium, the rheological features of which are described by fractional derivatives, are considered in the present article. Besides the forces of viscous friction, a thin body is subjected to the action of external forces dependent on the coordinates of the middle surface and time. The boundary conditions are proposed in such a way that the governing equations allow the Navier-type solution. The Laplace integral transform method and the method of expansion of all functions entering into the set of governing equations in terms of the eigenfunctions of the given problem are used as the methods of solution. It is shown that as a result of such a procedure, the systems of equations in the generalized coordinates could be reduced to infinite sets of uncoupled equations, each of which describes damped vibrations of a mechanical oscillator based on the fractional derivative Kelvin-Voigt model.

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9

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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10

Olaosebikan, Lekan. "Vibration analysis of elastic spherical shells." International Journal of Engineering Science 24, no. 10 (January 1986): 1637–54. http://dx.doi.org/10.1016/0020-7225(86)90138-2.

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11

Hu, X. X., C. W. Lim, T. Sakiyama, Z. R. Li, and W. K. Wang. "Free vibration of elastic helicoidal shells." International Journal of Mechanical Sciences 47, no. 6 (June 2005): 941–60. http://dx.doi.org/10.1016/j.ijmecsci.2005.01.001.

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12

Kapania, Rakesh K. "Review of Vibration of Laminated Shells and Plates." AIAA Journal 42, no. 9 (September 2004): 1946–47. http://dx.doi.org/10.2514/1.14207.

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13

Ribeiro, Pedro. "Linear modes of vibration of cylindrical shells in composite laminates reinforced by curvilinear fibres." Journal of Vibration and Control 22, no. 20 (August 9, 2016): 4141–58. http://dx.doi.org/10.1177/1077546315571661.

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Modes of vibration of thin cylindrical shells made up of layers with curvilinear fibres (variable stiffness composite laminates (VSCL) shells) are investigated in the linear regime. A p-version finite element type formulation is developed for that purpose; in the absence of data on vibrations of cylindrical VSCL shells, the formulation is verified by comparisons with published data on laminated shells reinforced by straight fibres and on VSCL plates. Parametric studies are performed, in order to investigate how curvilinear fibre paths can influence the modes of vibration. It is found that curvilinear fibre paths can have a very large effect, larger than on plates, on the natural frequencies and natural mode shapes of vibration of cylindrical shells. Factors that strongly influence the modes of vibration of VSCL shells are found; these include the fibre orientation at boundaries and in relation to principal normal sections.

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14

Kuznetsov, E. N., and W. B. Hall. "Bending instability and vibration of plates and shallow shells." Dynamics and Stability of Systems 1, no. 3 (January 1986): 236–48. http://dx.doi.org/10.1080/02681118608806016.

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15

Hong, T., J. G. Teng, and Y. F. Luo. "Axisymmetric shells and plates on tensionless elastic foundations." International Journal of Solids and Structures 36, no. 34 (December 1999): 5277–300. http://dx.doi.org/10.1016/s0020-7683(98)00228-5.

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16

Hornung, Peter, Martin Rumpf, and Stefan Simon. "On material optimisation for nonlinearly elastic plates and shells." ESAIM: Control, Optimisation and Calculus of Variations 26 (2020): 82. http://dx.doi.org/10.1051/cocv/2020053.

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This paper investigates the optimal distribution of hard and soft material on elastic plates. In the class of isometric deformations stationary points of a Kirchhoff plate functional with incorporated material hardness function are investigated and a compliance cost functional is taken into account. Under symmetry assumptions on the material distribution and the load it is shown that cylindrical solutions are stationary points. Furthermore, it is demonstrated that the optimal design of cylindrically deforming, clamped rectangular plates is non trivial, i.e. with a material distribution which is not just depending on one axial direction on the plate. Analytical results are complemented with numerical optimization results using a suitable finite element discretization and a phase field description of the material phases. Finally, using numerical methods an outlook on the optimal design of non isometrically deforming plates and shells is given.

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17

Zhang, Shun-Qi, Guo-Zhong Zhao, Mekala Narasimha Rao, Rüdiger Schmidt, and Ying-Jie Yu. "A review on modeling techniques of piezoelectric integrated plates and shells." Journal of Intelligent Material Systems and Structures 30, no. 8 (March 15, 2019): 1133–47. http://dx.doi.org/10.1177/1045389x19836169.

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Piezoelectric materials embedded into plates and shells make the structures being capable of sensing and actuation, usually called smart structures, which are frequently used for shape and vibration control, noise control, health monitoring, and energy harvesting. To give a precise prediction of static and dynamic behavior of smart structures, the linear/nonlinear multi-physics coupled modeling technique is of great importance. The article attempts to present the available research on modeling of piezoelectric integrated plates and shells, including (1) through thickness hypotheses for beams, plates, and shells; (2) geometrically nonlinear theories for plates and shells; (3) electroelastic material linear/nonlinear modeling; (4) multi-physics coupled modeling; and (5) modeling of advanced piezo-fiber composite bonded structures.

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18

Urrutia-Galicia, J. L., and L. J. Arango. "ON THE FUNDAMENTAL FREQUENCIES AND MODES OF FREE VIBRATION OF CYLINDRICAL SHELLS." Transactions of the Canadian Society for Mechanical Engineering 15, no. 2 (June 1991): 147–59. http://dx.doi.org/10.1139/tcsme-1991-0009.

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The fundamental frequencies and modes of free vibration of simply supported circular cylindrical shells are explored. The results include the fundamental frequencies ωmn and the modes (m,n) of steel cylindrical shells which are presented in the form of a nomogram, see Figure 6. Besides, single more general formulas are given for cylindrical shells made out of any elastic material which turn out to be very suitable for design and analysis purposes.

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19

Lewicka, Marta, L. Mahadevan, and Mohammad Reza Pakzad. "Models for elastic shells with incompatible strains." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2165 (May 8, 2014): 20130604. http://dx.doi.org/10.1098/rspa.2013.0604.

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The three-dimensional shapes of thin lamina, such as leaves, flowers, feathers, wings, etc., are driven by the differential strain induced by the relative growth. The growth takes place through variations in the Riemannian metric given on the thin sheet as a function of location in the central plane and also across its thickness. The shape is then a consequence of elastic energy minimization on the frustrated geometrical object. Here, we provide a rigorous derivation of the asymptotic theories for shapes of residually strained thin lamina with non-trivial curvatures, i.e. growing elastic shells in both the weakly and strongly curved regimes, generalizing earlier results for the growth of nominally flat plates. The different theories are distinguished by the scaling of the mid-surface curvature relative to the inverse thickness and growth strain, and also allow us to generalize the classical Föppl–von Kármán energy to theories of prestrained shallow shells.

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20

Jain, R. K., and Y. Nath. "Nonlinear Axisymmetric Static Analysis of Shallow Spherical Shells on Winkler-Pasternak Foundation." Journal of Offshore Mechanics and Arctic Engineering 109, no. 1 (February 1, 1987): 28–34. http://dx.doi.org/10.1115/1.3256986.

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In the present investigation nonlinear static analysis of thin axisymmetric circular plates, annular plates and shallow spherical shells resting on linear elastic Winkler-Pasternak foundation under uniformly distributed normal loads, has been carried out. Donnell-type governing differential equations expressed in terms of normal displacement and stress function have been employed and solved using Chebyshev series. A convergence study for Chebyshev series has been conducted. The influence of foundation stiffness parameters (K and G) on the response of circular plates, annulus and spherical shells has been studied for both the clamped and simply supported immovable edge conditions. A few typical snap-through results for shells are also included.

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21

Qatu, Mohamad S. "Vibration of Homogeneous and Composite Thick Barrel Shells." Journal of Vibration and Control 10, no. 3 (March 2004): 319–41. http://dx.doi.org/10.1177/1077546304031845.

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This paper presents a vibration analysis for homogeneous and laminated composite deep, thick barrel shells using recently derived equations of elastic deformation. Assuming a first-order linear displacement field, the equations include accurate force and moment resultants, in which the stresses over the thickness of the shell are integrated exactly on a trapezoidal-like cross-section of a shell element. Exact solutions were obtained for thick barrel, open and closed, shells having shear diaphragm boundary conditions and cross-ply lamination sequence. The results were compared with previously obtained results where various other thick shell theories were used. The effects of various parameters including radii of curvature on shell frequencies are studied.

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22

Stepanov, Alexey B., and Stuart S. Antman. "Radially Symmetric Steady States of Nonlinearly Elastic Plates and Shells." Journal of Elasticity 124, no. 2 (January 19, 2016): 243–78. http://dx.doi.org/10.1007/s10659-015-9567-9.

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23

Khatri, K. N. "Vibration Control of Conical Shells Using Viscoelastic Materials." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 206, no. 3 (May 1992): 167–78. http://dx.doi.org/10.1243/pime_proc_1992_206_113_02.

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The vibration and damping analysis of multi-layered conical shells incorporating layers of viscoelastic materials in addition to elastic ones, the former causing dissipation of vibratory energy, is the subject matter of this paper. The analysis given herein uses Hamilton's variational principle for deriving equations of motion of a general multi-layered conical shell. In view of the correspondence principle of linear viscoelasticity which is valid for harmonic vibrations, the solution is obtained by replacing the moduli of viscoelastic layers by complex moduli. An approximate solution for axisymmetric vibrations of multi-layered conical shells with two end conditions—simply supported edges and clamped edges—is obtained by utilizing the Galerkin procedure. The damping effectiveness in terms of the system loss factor for all families of modes of vibrations for three-, five- and seven-layered shells is evaluated and its variation with geometrical parameters is investigated.

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24

Nguyen, Pham Dinh, Vu Dinh Quang, Vu Thi Thuy Anh, and Nguyen Dinh Duc. "Nonlinear Vibration of Carbon Nanotube Reinforced Composite Truncated Conical Shells in Thermal Environment." International Journal of Structural Stability and Dynamics 19, no. 12 (December 2019): 1950158. http://dx.doi.org/10.1142/s021945541950158x.

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This paper is concerned with the nonlinear vibration and dynamic response of carbon nanotube (CNT) reinforced composite truncated conical shells resting on elastic foundations in a thermal environment. The material properties of shells are assumed to be temperature-dependent and graded in the thickness direction according to various linear functions. The nonlinear equations of motion are expressed in the form of two-component deflection function and solved by the analytical method. Detailed studies for the influences of various types of distribution and volume fractions of CNTs, geometrical parameters, Winkler and Pasternak elastic foundations on the dynamic response and nonlinear vibration of CNT polymer composite truncated conical shells are examined and the comparison study is carried out to verify the accuracy and efficiency of the proposed method.

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25

Sun, C. T., and G. Chen. "Elastic-plastic finite element analysis of thermoplastic composite plates and shells." AIAA Journal 30, no. 2 (February 1992): 513–18. http://dx.doi.org/10.2514/3.10946.

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26

BRISCHETTO, SALVATORE. "AN EXACT 3D SOLUTION FOR FREE VIBRATIONS OF MULTILAYERED CROSS-PLY COMPOSITE AND SANDWICH PLATES AND SHELLS." International Journal of Applied Mechanics 06, no. 06 (December 2014): 1450076. http://dx.doi.org/10.1142/s1758825114500768.

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A 3D free vibration analysis of multilayered structures is proposed. An exact solution is developed for the differential equations of equilibrium written in general orthogonal curvilinear coordinates. The equations consider a geometry for shells without simplifications and allow the analysis of spherical shell panels, cylindrical shell panels, cylindrical closed shells and plates. The method is based on a layer-wise approach, the continuity of displacements and transverse shear/normal stresses is imposed at the interfaces between the layers of the structures. Results are given for multilayered composite and sandwich plates and shells. A free vibration analysis is proposed for a number of vibration modes, thickness ratios, imposed wave numbers, geometries and multilayer configurations embedding isotropic and orthotropic composite materials. These results can also be used as reference solutions for plate and shell 2D models developed for the analysis of multilayered structures.

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27

Wang, C. M., K. Y. Lam, and X. Q. He. "Green Functions for Axisymmetric Bending and Vibration of Thick Cylindrical Shells." Advances in Structural Engineering 1, no. 2 (April 1997): 143–57. http://dx.doi.org/10.1177/136943329700100206.

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It is shown herein that the axisymmetric bending and vibration problems of thick (Mindlin) cylindrical shells are analogous to the corresponding bending and vibration problems of Timoshenko beams resting on Winkler foundation. The Green functions for solving these two analogous problems are derived. Based on these Green functions, exact bending and vibration results may be obtained. The validity of the solutions has been verified via comparison studies with previous researchers' numerical results. Sample exact bending and vibration results are also presented for cylindrical shells in view to provide useful benchmark checks for researchers and engineers working on cylindrical shells and Timoshenko beams on elastic foundation.

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Sandeep, S. H., and C. V. Srinivasa. "Hybrid Sandwich Panels: A Review." International Journal of Applied Mechanics and Engineering 25, no. 3 (September 1, 2020): 64–85. http://dx.doi.org/10.2478/ijame-2020-0035.

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AbstractA high specific stiffness, high specific strength, and tailoring the properties for specific application have attracted the attention of the researchers to work in the field of laminated composites and Sandwich structures. Rapid use of these laminated composites and Sandwich structures necessitated the development of new theories that suitable for the bending, buckling and vibration analysis. Many articles were published on free vibration of beams, plates, shells laminated composites and sandwich structures. In this article, a review on free vibration analysis of shear deformable isotropic beams, plates, shells, laminated composites and sandwich structures based on various theories and the exact solution is presented. In addition to this, the literature on finite element modeling of beams, plates, shells laminated composites and sandwich structures based on classical and refined theories is also reviewed. The present article is an attempt to review the available literature, made in the past few decades on free flexural vibration response of Fiber Metal laminated Composites and Sandwich panels using different analytical models, numerical techniques, and experimental methods.

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Narita, Y., and A. Leissa. "Vibrations of Completely Free Shallow Shells of Curvilinear Planform." Journal of Applied Mechanics 53, no. 3 (September 1, 1986): 647–51. http://dx.doi.org/10.1115/1.3171825.

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A method is presented for the free vibration analysis of shallow shells having free edges of arbitrary curvilinear shape. The method of Ritz which was developed for free rectangular plates is extended to the present problem. Components of displacement are expressed as algebraic polynomials. Shells of arbitrary curvature may be treated. Results are obtained for the previously unsolved vibration problems of cylindrical, spherical and hyperbolic paraboloidal shells having free edges of circular and elliptical planform. Convergence of the method is demonstrated. Comparisons with previous solutions are made in the case of zero curvature (i.e., a flat plate). Effects of increasing curvature and ellipticity upon vibration frequencies are examined.

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30

Shah, Abdul Ghafar, Tahir Mahmood, Muhammad N. Naeem, and Shahid H. Arshad. "Vibration characteristics of fluid-filled cylindrical shells based on elastic foundations." Acta Mechanica 216, no. 1-4 (June 20, 2010): 17–28. http://dx.doi.org/10.1007/s00707-010-0346-1.

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31

Yu, Y. Y. "On equations for large deflections of elastic plates and shallow shells." Mechanics Research Communications 18, no. 6 (November 1991): 373–84. http://dx.doi.org/10.1016/0093-6413(91)90050-7.

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32

Qatu, Mohamad S. "Recent research advances in the dynamic behavior of shells: 1989-2000, Part 1: Laminated composite shells." Applied Mechanics Reviews 55, no. 4 (July 1, 2002): 325–50. http://dx.doi.org/10.1115/1.1483079.

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Laminated composite shells are increasingly being used in various engineering applications including aerospace, mechanical, marine, and automotive engineering. With the increasing awareness of and sensitivity to structural noise and vibration, research covering the dynamic behavior of composite shells has received considerable attention. The purpose of this article is to review most of the recent research done in this field. Review of the literature on the dynamic behavior of homogeneous shells is covered in Part 2 of this article to be published in the September 2002 issue of AMR. Research on shell dynamics is found to be mainly free vibration analyses. The review is conducted with emphasis given to the theory being applied (thin, thick, 3D, nonlinear, …), the analysis method (exact, Ritz, finite elements, …), complicating effects (initial stress, imperfection, added masses and springs, elastic supports, rotating shells, and others), and the various shell geometries that were subject to vibration research (cylindrical, conical, spherical, and others). There are 374 references cited in this review article.

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33

Zhu, Yunpeng, You Wang, Zhong Luo, Qingkai Han, and Deyou Wang. "Similitude design for the vibration problems of plates and shells: A review." Frontiers of Mechanical Engineering 12, no. 2 (January 23, 2017): 253–64. http://dx.doi.org/10.1007/s11465-017-0418-1.

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34

Tu, Jian Xin, Zhi Ren Wang, Han Zhu, and Ping Wang. "The Nonlinear Random Vibration of a Clamped Rectangular Thin Plate in Magnetic Field." Applied Mechanics and Materials 628 (September 2014): 127–32. http://dx.doi.org/10.4028/www.scientific.net/amm.628.127.

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In this paper, the magneto-elastic nonlinear random vibration of a clamped rectangular thin plate in magnetic field is studied. According to the magneto-elastic theory of plates and shells and the theory of structural random vibration, the magneto-elastic nonlinear random vibration equation of a clamped rectangular thin plate in a magnetic field is derived. Then the nonlinear random vibration equation is transferred into the Ito differential equation, and the Ito differential equation is solved using FPK equation method. Thus the numerical characteristics of displacement response and velocity response of the rectangular thin plate are obtained. Finally, through a numerical example, the influences of magnetic field parameters on the numerical characteristics are discussed, and some methods which can be used to effectively control the random vibration responses of the plate are given.

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35

Bicos, Andrew S., and George S. Springer. "Analysis of free damped vibration of laminated composite plates and shells." International Journal of Solids and Structures 25, no. 2 (1989): 129–49. http://dx.doi.org/10.1016/0020-7683(89)90003-6.

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36

Tj, Haryadi Gunawan, Takashi Mikami, Shunji Kanie, and Motohiro Sato. "Free vibration characteristics of cylindrical shells partially buried in elastic foundations." Journal of Sound and Vibration 290, no. 3-5 (March 2006): 785–93. http://dx.doi.org/10.1016/j.jsv.2005.04.014.

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37

Hussain, Muzamal, Muhammad Nawaz Naeem, and Mohammad Reza Isvandzibaei. "Effect of Winkler and Pasternak elastic foundation on the vibration of rotating functionally graded material cylindrical shell." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232, no. 24 (January 22, 2018): 4564–77. http://dx.doi.org/10.1177/0954406217753459.

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In this paper, vibration characteristics of rotating functionally graded cylindrical shell resting on Winkler and Pasternak elastic foundations have been investigated. These shells are fabricated from functionally graded materials. Shell dynamical equations are derived by using the Hamilton variational principle and the Langrangian functional framed from the shell strain and kinetic energy expressions. Elastic foundations, namely Winkler and Pasternak moduli are inducted in the tangential direction of the shell. The rotational motions of the shells are due to the Coriolis and centrifugal acceleration as well as the hoop tension produced in the rotating case. The wave propagation approach in standard eigenvalue form has been employed in order to derive the characteristic frequency equation describing the natural frequencies of vibration in rotating functionally graded cylindrical shell. The complex exponential functions, with the axial modal numbers that depend on the boundary conditions stated at edges of a cylindrical shell, have been used to compute the axial modal dependence. In our new investigation, frequency spectra are obtained for circumferential wave number, length-to-radius ratio, height-to-radius ratio with simply supported–simply supported and clamped–clamped boundary conditions without elastic foundation. Also, the effect of elastic foundation on the rotating cylindrical shells is examined with the simply supported–simply supported edge. To check the validity of the present method, the fundamental natural frequencies of non-rotating isotropic and functionally graded cylindrical shells are compared with the open literature. Also, a comparison is made for infinitely long rotating with the earlier published paper.

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38

Zimny, Pawel§. "Magneto-thermo-elastic vibration of thin shells under a surge current." COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering 17, no. 3 (1998): 407–11. http://dx.doi.org/10.1108/03321649810369500.

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39

Ma, Xiangtao, Kuo Tian, Hongqing Li, Yan Zhou, Peng Hao, and Bo Wang. "Concurrent multi-scale optimization of hybrid composite plates and shells for vibration." Composite Structures 233 (February 2020): 111635. http://dx.doi.org/10.1016/j.compstruct.2019.111635.

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40

Van Phu, Khuc, Dao Huy Bich, and Le Xuan Doan. "Nonlinear thermal vibration and dynamic buckling of eccentrically stiffened sandwich-FGM cylindrical shells containing fluid." Journal of Reinforced Plastics and Composites 38, no. 6 (December 1, 2018): 253–66. http://dx.doi.org/10.1177/0731684418814636.

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The governing equations for analysing thermal vibration and dynamic buckling of eccentrically stiffened sandwich functionally graded cylindrical shells full filled with fluid and surrounded by elastic foundations in thermal environment are derived by using the classical shell theory, the geometrical nonlinearity in von Karman-Donnell sense, the smeared stiffener technique and Pasternak’s foundation model. Solutions of the problem are established according to the Galerkin’s method and Runge–Kutta method. The effects of fluid pressure, stiffeners, geometrical ratios, temperature and elastic foundation on the dynamic responses of shells are investigated.

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41

Ye, Tiangui, Guoyong Jin, Yuehua Chen, Xianglong Ma, and Zhu Su. "Free vibration analysis of laminated composite shallow shells with general elastic boundaries." Composite Structures 106 (December 2013): 470–90. http://dx.doi.org/10.1016/j.compstruct.2013.07.005.

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42

Brischetto, Salvatore. "Three-Dimensional Exact Free Vibration Analysis of Spherical, Cylindrical, and Flat One-Layered Panels." Shock and Vibration 2014 (2014): 1–29. http://dx.doi.org/10.1155/2014/479738.

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The paper proposes a three-dimensional elastic analysis of the free vibration problem of one-layered spherical, cylindrical, and flat panels. The exact solution is developed for the differential equations of equilibrium written in orthogonal curvilinear coordinates for the free vibrations of simply supported structures. These equations consider an exact geometry for shells without simplifications. The main novelty is the possibility of a general formulation for different geometries. The equations written in general orthogonal curvilinear coordinates allow the analysis of spherical shell panels and they automatically degenerate into cylindrical shell panel, cylindrical closed shell, and plate cases. Results are proposed for isotropic and orthotropic structures. An exhaustive overview is given of the vibration modes for a number of thickness ratios, imposed wave numbers, geometries, embedded materials, and angles of orthotropy. These results can also be used as reference solutions to validate two-dimensional models for plates and shells in both analytical and numerical form (e.g., closed solutions, finite element method, differential quadrature method, and global collocation method).

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43

Ebrahimi, Farzad, Ali Dabbagh, and Abbas Rastgoo. "Vibration analysis of porous metal foam shells rested on an elastic substrate." Journal of Strain Analysis for Engineering Design 54, no. 3 (April 2019): 199–208. http://dx.doi.org/10.1177/0309324719852555.

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In this article, the vibration problem of an embedded cylindrical shell consisted of porous metal foam is solved via an analytical method with respect to the influences of various porosity distributions. Three types of porosity distribution across the thickness are covered, namely, uniform, symmetric, and asymmetric. The strain–displacement relations of the shell are assumed to be derived on the basis of the first-order shear deformation shell theory. Then, the achieved relations will be incorporated with the Hamilton’s principle in order to reach the Navier equations of the cylindrical shell. Next, the well-known Galerkin’s method is utilized to calculate the natural frequencies of the system. The influences of both simply supported and clamped boundary conditions are included. In order to show the accuracy of the presented method, the results of the present research are compared with those reported by former published papers. The reported results show that an increase in the porosity coefficient can decrease the frequency of the shell. Also, the stiffness of the system can be lesser decreased while symmetric porosity distribution is chosen.

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44

Sabik, A., and I. Kreja. "Large thermo-elastic displacement and stability FEM analysis of multilayered plates and shells." Thin-Walled Structures 71 (October 2013): 119–33. http://dx.doi.org/10.1016/j.tws.2013.05.002.

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45

Sato, M., S. Harasawa, Y. Konishi, T. Maruyama, and S. J. Park. "Power Law of Critical Buckling in Structural Members Supported by a Winkler Foundation." Journal of Mechanics 33, no. 3 (December 12, 2016): 369–74. http://dx.doi.org/10.1017/jmech.2016.112.

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AbstractIn the fields of engineering, nanoscience, and biomechanics, thin structural members, such as beams, plates, and shells, that are supported by an elastic medium are used in several applications. There is a possibility that these thin structures might buckle under severe loading conditions; higher-order, complicated elastic buckling modes can be found owing to the balance of rigidities between the thin members and elastic supports. In this study, we have shown a new and simple ‘power law’ relation between the critical buckling strain (or loads) and rigidity parameters in structural members supported by an elastic medium, which can be modelled as a Winkler foundation. The following structural members have been considered in this paper: i) a slender beam held by an outer elastic support under axial loading, ii) cylindrical shells supported by an inner elastic core under hydrostatic pressure (plane strain condition), and iii) complete spherical shells that are filled with an inner elastic medium.

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46

Qin, Zhaoye, Zhengbao Yang, Jean Zu, and Fulei Chu. "Free vibration analysis of rotating cylindrical shells coupled with moderately thick annular plates." International Journal of Mechanical Sciences 142-143 (July 2018): 127–39. http://dx.doi.org/10.1016/j.ijmecsci.2018.04.044.

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47

Wang, Yan Qing, Yun Fei Liu, and Jean W. Zu. "Nonlinear vibration of magnetoelectroelastic nanoscale shells embedded in elastic media in thermoelectromagnetic fields." Journal of Intelligent Material Systems and Structures 30, no. 15 (July 18, 2019): 2331–47. http://dx.doi.org/10.1177/1045389x19862382.

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This study investigates the nonlinear vibration of magnetoelectroelastic composite cylindrical nanoshells embedded in elastic media for the first time. The small-size effect and thermoelectromagnetic loadings are considered. Based on the nonlocal elasticity theory and Donnell’s nonlinear shell theory, the nonlinear governing equations and the corresponding boundary conditions are derived using Hamilton’s principle. Then, the Galerkin method is utilized to transform the governing equations into a nonlinear ordinary differential equation and subsequently the method of multiple scales is employed to obtain an approximate analytical solution to nonlinear frequency response. The present results are verified by the comparison with the published ones in the literature. Finally, an extensive parametric study is conducted to examine the effects of the nonlocal parameter, the external magnetic potential, the external electric potential, the temperature change, and the elastic media on the nonlinear vibration characteristics of magnetoelectroelastic composite nanoshells.

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48

Tokuda, N., and Y. Sakata. "Application of Static Condensation Method to Vibration Analysis of Thin Cylindrical Shells." Journal of Pressure Vessel Technology 111, no. 3 (August 1, 1989): 275–84. http://dx.doi.org/10.1115/1.3265675.

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A simple formula is proposed, by which the error in the natural frequencies introduced by using the static condensation method can be evaluated prior to the numerical computation, though its effective applicability is found in simple structures such as plates and shells. The effectiveness of the proposed formula is examined in the vibration analysis of thin cylindrical shells having freely supported ends by using various reduction patterns. Not only the accuracy of natural frequencies, but also that of modal displacements and the corresponding modal stresses are investigated by comparing with the results obtained without reduction and with the exact analytical solutions given by Arnold and Warburton.

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49

Song, Zhiyong, Qingjie Cao, and Qiyi Dai. "Free vibration of truncated conical shells with elastic boundary constraints and added mass." International Journal of Mechanical Sciences 155 (May 2019): 286–94. http://dx.doi.org/10.1016/j.ijmecsci.2019.02.039.

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50

Hinton, E., M. Özakça, and N. V. R. Rao. "Free vibration analysis and shape optimization of variable thickness plates, prismatic folded plates and curved shells." Journal of Sound and Vibration 181, no. 4 (April 1995): 553–66. http://dx.doi.org/10.1006/jsvi.1995.0157.

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