Journal articles: 'Vibration of triangular Plate'

1

Xiang, Y., K. M. Liew, S. Kitipornchai, and C. M. Wang. "Vibration of Triangular Mindlin Plates Subject to Isotropic In-Plane Stresses." Journal of Vibration and Acoustics 116, no. 1 (1994): 61–66. http://dx.doi.org/10.1115/1.2930397.

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The influence of isotropic in-plane stresses on the fundamental vibration frequencies of thick triangular plates is investigated. Some critical buckling factors are also presented in the paper. Due to the lack of results and importance of this topic, the Rayleigh-Ritz method is applied to solve the governing eigenvalue function based on the Mindlin plate theory. The fundamental frequency parameters for triangular Mindlin plates subject to uniform tensile and compressive stresses with different combinations of free, simply supported, and clamped boundary conditions are determined. The solutions are presented in the form of design charts where the fundamental frequency parameters can easily be read for particular thickness to width ratios (t/b) and in-plane stresses. Since no other vibration solution for thick triangular plate is available, the thin triangular plate solutions obtained by setting the thickness to width ratio to be very small (say t/b = 0.001), where possible, are verified with known solutions from the open literature.

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Kemparaju, H.R, and Kumar Samal Prasanta. "Detailed Numerical Study of Free Vibration Analysis of Plates." Detailed Numerical Study of Free Vibration Analysis of Plates 2, no. 2 (2019): 1–11. https://doi.org/10.5281/zenodo.3375109.

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<em>Plates are widely used in aircraft, ship building, boiler and automobile applications. It is important to study the vibration characteristics of the plates in order to avoid the resonance in their working condition. Because catastrophic failure occurs in resonance condition due violent vibrations. So to avoid these resonance condition vibration analysis of plates are very important. In this article the modal frequencies and mode shapes of the plates were analysed numerically using ANSYS. Structural steel is considered as the plate material. All edges clamped (CCCC) and all edges free (FFFF) boundary conditions were considered for the study. The effect of parameters such as aspect ratio, thickness, area and shape of the plates on natural frequency was studied. The aspect ratios of 1, 1.5, 2 and 2.5 keeping the surface are same, is considered for the study. Plates of thickness 1 mm, 1.5 mm, 2 mm and 3 mm are analysed. The effect of shape of the plate is studied by considering various shapes like square, circular, equilateral triangle and right angular triangle with same area. It is observed that the natural frequency increases with increase of aspect ratio and thickness. As the surface area increases the natural frequency decreases. The values of natural frequencies of the plates descend in the order of circular, equilateral triangular, square and right angled triangular shapes for all edges free. Whereas the values of natural frequencies of the plates ascend in the order of circular, square, equilateral triangular and right angled triangular shapes for all edges fixed conditions.</em>

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Thinh, Tran Ich, and Ngo Nhu Khoa. "A new finite element for free vibration analysis of stiffened composite plates." Vietnam Journal of Mechanics 29, no. 4 (2007): 529–38. http://dx.doi.org/10.15625/0866-7136/29/4/5603.

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A new 6-noded stiffened triangular plate element for the analysis of stiffened composite plates based on Mindlins deformation plate theory has been developed. The stiffened plate element is a combination of basic triangular element and bar component. The element can accommodate any number of arbitrarily oriented stiffeners and obviates the use of mesh lines along the stiffeners. Free vibration analyses of stiffened laminated plates have been carried out with this element and the results are compared with those published. The finite element results show very good matching with the experimental ones.

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Shiau, Le-Chung, and Teng-Yuan Wu. "Free Vibration of Buckled Laminated Plates by Finite Element Method." Journal of Vibration and Acoustics 119, no. 4 (1997): 635–40. http://dx.doi.org/10.1115/1.2889774.

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Free vibration behavior of buckled composite plates are studied by using a high precision triangular plate element. This element is developed based on a simplified high order plate theory and von Ka´rma´n large deformation assumptions. The nonlinear governing equations of motion for the plates is linearized into two sets of equations by assuming small amplitude vibration of the laminates about its buckled static equilibrium profile. Results show that, in the postbuckling regime, the fundamental mode may be shifted from the first mode to the second due to squeezing effect of the in-plane force on the plate. For plate with certain boundary conditions, the natural frequency may have a sudden jump due to buckle pattern change of the plate in the postbuckling regime.

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Quintana, María Virginia, and Ricardo Oscar Grossi. "Free Vibrations of a Trapezoidal Plate with an Internal Line Hinge." Scientific World Journal 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/252084.

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This paper deals with a general variational formulation for the determination of natural frequencies and mode shapes of free vibrations of laminated thin plates of trapezoidal shape with an internal line hinge restrained against rotation. The analysis was carried out by using the kinematics corresponding to the classical laminated plate theory (CLPT). The eigenvalue problem is obtained by employing a combination of the Ritz method and the Lagrange multipliers method. The domain of the plate is transformed into a rectangular domain in the computational space by using nonorthogonal triangular coordinates and the transverse displacements are approximated with a set of simple polynomials automatically generated and expressed in the triangular coordinates. The developed algorithm allows obtaining approximate analytical solutions for mentioned plate with different geometries, aspect ratio, position of the line hinge, and boundary conditions including translational and rotational elastically restrained edges. It allows studying the influence of the mentioned line on the vibration frequencies and respective mode shapes. The algorithm can easily be programmed and it is numerically stable. Additionally, as a particular case, the results of triangular plates can be easily generated.

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Catania, Giuseppe, and Silvio Sorrentino. "Spectral modeling of vibrating plates with general shape and general boundary conditions." Journal of Vibration and Control 18, no. 11 (2011): 1607–23. http://dx.doi.org/10.1177/1077546311426593.

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The analysis and design of lightweight plate structures require efficient computational tools, because exact analytical solutions for vibrating plates are currently known only for some standard shapes in conjunction with a few basic boundary conditions. This paper deals with vibration analysis of Kirchhoff plates of general shape with non-standard boundary conditions, adopting a Rayleigh-Ritz approach. Three different coordinate mappings are considered, using different kinds of functions: 1) trigonometric and polynomial interpolation functions for mapping the shape of the plate, 2) trigonometric and polynomial interpolation functions for mapping a constraint domain of general shape, 3) products of linearly independent eigenfunctions evaluated from a standard beam in flexural vibration for describing the transverse displacement field of the plate. Flexural free vibration analysis of different shaped plates is then performed using the same approach: skew, trapezoid and triangular plates, plates with parabolic curved edges, sectors of circular plates, circular and elliptic annular plates. Purely elastic plates are considered, but the method may also be applied to the analysis of viscoelastic plates. The results are compared with those available in the literature and using standard finite element analysis.

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Lather, Neeraj, Ankit Kumar, Parvesh Yadav, Reeta Bhardwaj, and Amit Sharma. "Vibrational frequency of triangular plate having circular thickness." Vibroengineering Procedia 52 (November 25, 2023): 67–73. http://dx.doi.org/10.21595/vp.2023.23370.

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In the current research, modes of frequency of isotropic tapered triangular plate having 1-D (one dimensional) circular thickness and 1-D (one dimensional) linear temperature profile for clamped boundary conditions are discussed. Authors implemented Rayleigh Ritz technique to solve the frequency equation of isotropic triangular plate and computed the first four modes with a distinct combination of plate parameters. Authors have performed the convergence study of modes of frequency of the isotropic triangular plate. Also, conducted comparative analysis of modes of frequency of the current study with available published papers and the results presented in tabular form. The aim of the present study is to show the impact of a one dimensional circular thickness and one dimensional linear temperature on modes of frequency of vibration of an isotropic tapered triangular plate.

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Shiau, Le-Chung, and Shih-Yao Kuo. "Free Vibration of Thermally Buckled Composite Sandwich Plates." Journal of Vibration and Acoustics 128, no. 1 (2005): 1–7. http://dx.doi.org/10.1115/1.2149388.

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A high precision triangular plate element is developed for the free vibration analysis of thermally buckled composite sandwich plates. Due to an uneven thermal expansion in the two principal material directions, the buckling mode of the plate may change from one pattern to another in the postbuckling region for certain fiber orientation and aspect ratio of the plate. Because of this buckle pattern change, the sequence of natural frequencies of the plate is also suddenly altered. By examining the buckling and free vibration modes of the plate, a clear picture of buckle pattern change and vibration mode shifting is presented. Numerical results show that if the shape of a free vibration mode is similar to the plate buckling mode then the natural frequency of that mode will drop to zero when the temperature reaches the buckling temperature.

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9

Crandall, Stephen H., and Wei-Qiu Zhu. "Wide band random vibration of an equilateral triangular plate." Probabilistic Engineering Mechanics 1, no. 1 (1986): 5–12. http://dx.doi.org/10.1016/0266-8920(86)90004-4.

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Papkov, Stanislav, and Jnan Ranjan Banerjee. "A New Method for Free Vibration Analysis of Triangular Isotropic and Orthotropic Plates of Isosceles Type Using an Accurate Series Solution." Mathematics 11, no. 3 (2023): 649. http://dx.doi.org/10.3390/math11030649.

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In this paper, a new method based on an accurate analytical series solution for free vibration of triangular isotropic and orthotropic plates is presented. The proposed solution is expressed in terms of undetermined arbitrary coefficients, which are exactly satisfied by the governing differential equation in free vibration. The approach used is based on an innovative extension of the superposition method through the application of a modified system of trigonometric functions. The boundary conditions for bending displacements and bending rotations on the sides of the triangular plate led to an infinite system of linear algebraic equations in terms of the undetermined coefficients. Following this development, the paper then presents an algorithm to solve the boundary value problem for isotropic and orthotropic triangular plates for any kinematic boundary conditions. Of course, the boundary conditions with zero displacements and zero rotations on all sides correspond to the case when the plate is fully clamped all around. The convergence of the proposed method is examined by numerical simulation applying stringent accuracy requirements to fulfill the prescribed boundary conditions. Some of the computed numerical results are compared with published results and finally, the paper draws significant conclusions.

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11

Li, Fei-Hao, Bin Han, Ai-Hua Zhang, Kai Liu, Ying Wang, and Tian-Jian Lu. "A Three-Dimensional Vibration Theory for Ultralight Cellular Sandwich Plates Subjected to Linearly Varying In-Plane Distributed Loads." Materials 16, no. 11 (2023): 4086. http://dx.doi.org/10.3390/ma16114086.

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Thin structural elements such as large-scale covering plates of aerospace protection structures and vertical stabilizers of aircraft are strongly influenced by gravity (and/or acceleration); thus, exploring how the mechanical behaviors of such structures are affected by gravitational field is necessary. Built upon a zigzag displacement model, this study establishes a three-dimensional vibration theory for ultralight cellular-cored sandwich plates subjected to linearly varying in-plane distributed loads (due to, e.g., hyper gravity or acceleration), with the cross-section rotation angle induced by face sheet shearing accounted for. For selected boundary conditions, the theory enables quantifying the influence of core type (e.g., close-celled metal foams, triangular corrugated metal plates, and metal hexagonal honeycombs) on fundamental frequencies of the sandwich plates. For validation, three-dimensional finite element simulations are carried out, with good agreement achieved between theoretical predictions and simulation results. The validated theory is subsequently employed to evaluate how the geometric parameters of metal sandwich core and the mixture of metal cores and composite face sheets influence the fundamental frequencies. Triangular corrugated sandwich plate possesses the highest fundamental frequency, irrespective of boundary conditions. For each type of sandwich plate considered, the presence of in-plane distributed loads significantly affects its fundamental frequencies and modal shapes.

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12

Ioannides, E., and P. Grootenhuis. "A Finite Element Analysis of the Harmonic Response of Damped Five-Layer Plates." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 199, no. 4 (1985): 311–17. http://dx.doi.org/10.1243/pime_proc_1985_199_128_02.

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Solutions have been obtained for the harmonic vibrations of five-layer plates by means of a finite element method. This method is an extension of a previously developed analysis for three-layer plates. The five-layer plates contain two constrained viscoelastic layers which provide the damping. The degenerate case when the thickness of the middle elastic layer becomes zero and the plate is reduced to a four-layer one has also been included in the solution procedure. Moreover, the method allows for the study of both torsional and transverse vibrations of five (or four)-layer beams treated as vibrating plates with a large aspect ratio. As in the case of three-layer plates, triangular finite elements are used to allow for a greater variety of shapes. In the analysis damping is introduced by replacing the real moduli of the viscoelastic material by complex equivalent moduli which account for the phase difference between strain and stress. The present method allows for the non-linear stress-strain behaviour of the viscoelastic layers, the effects of the rotatory inertia and the extension within the viscoelastic layers. The finite element computations have been verified by comparison with experimental results for four-layer and five-layer beams in transverse and torsional vibrations and a five-layer square plate in transverse vibration.

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13

Tsushima, Natsuki, Yuta Hayashi, and Tomohiro Yokozeki. "Dispersion Analysis of Plane Wave Propagation in Lattice-Based Mechanical Metamaterial for Vibration Suppression." Aerospace 11, no. 8 (2024): 637. http://dx.doi.org/10.3390/aerospace11080637.

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Phononic crystals based on lattice structures provide important wave dispersion characteristics as band structures, showing excellent compatibility with additive manufacturing. Although the lattice structures have shown the potential for vibration suppression, a design guideline to control the frequency range of the bandgap has not been well established. This paper studies the dispersion characteristics of plane wave propagation in lattice-based mechanical metamaterials to realize effective vibration suppression for potential aerospace applications. Triangular and hexagonal periodic lattice structures are mainly studied in this paper. The influence of different geometric parameters on the bandgap characteristics is investigated. A finite element approach with Floquet–Bloch’s principles is implemented to effectively evaluate the dispersion characteristics of waves in lattice structures, which is validated numerically and experimentally with a 3D-printed lattice plate. Based on numerical studies with the developed analysis framework, the influences of the geometric parameters of lattice plate structures on dispersion characteristics can mainly be categorized into three patterns: change in specific branches related to in-plane or out-of-plane vibrations, upward/downward shift in frequency range, and drastic change in dispersion characteristics. The results obtained from the study provide insight into the design of band structures to realize vibration suppression at specific frequencies for engineering applications.

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CHAKRABARTI, A., and A. H. SHEIKH. "A NEW TRIANGULAR ELEMENT BASED ON HIGHER ORDER SHEAR DEFORMATION THEORY FOR FLEXURAL VIBRATION OF COMPOSITE PLATES." International Journal of Structural Stability and Dynamics 02, no. 02 (2002): 163–84. http://dx.doi.org/10.1142/s0219455402000506.

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A triangular element based on Reddy's higher order shear deformation theory is developed for free vibration analysis of composite plates. In the Reddy's plate theory, the transverse shear stress varies in a parabolic manner across the plate thickness and vanishes at the top and bottom surfaces of the plate. Moreover, it does not involve any additional unknowns. Thus the plate theory is quite simple and elegant. Unfortunately, such an attractive plate theory cannot be exploited as expected in finite element analysis, primarily due to the difficulties in satisfying the inter-element continuity requirement. This has inspired us to develop the present element, which has three corner nodes and three mid-side nodes with the same number of degrees of freedom. To demonstrate the performance of the element, numerical examples of isotropic and composite plates under different situations are solved. The results are compared with the analytical solutions and other published results, which show the accuracy and range of applicability of the proposed element in the problem of vibration analysis.

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Tai, Huynh Huu, Nguyen Van Hieu, and Vu Duy Thang. "Bending and free vibration behaviors of composite plates using the C0-HSDT based four-node element with in-plane rotations." Journal of Science and Technology in Civil Engineering (STCE) - NUCE 14, no. 1 (2020): 42–53. http://dx.doi.org/10.31814/stce.nuce2020-14(1)-04.

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In this paper the smoothed four-node element with in-plane rotations MISQ24 is combined with a C0-type higher-order shear deformation theory (C0-HSDT) to propose an improved linear quadrilateral plate element for static and free vibration analyses of laminated composite plates. This improvement results in two additional degrees of freedom at each node and require no shear correction factors while ensuring the high precision of numerical solutions. Composite plates with different lay-ups, boundary conditions and various geometries such as rectangular, skew and triangular plates are analyzed using the proposed element. The obtained numerical results are compared with those from previous studies in the literature to demonstrate the effectiveness, the reliability and the accuracy of the present element. Keywords: composite laminated plates; bending problems; free vibration; C0-HSDT; MISQ24.

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Ponnusamy, P. "Wave propagation in electro‐magneto‐elastic solid plate of polygonal cross‐sections." Multidiscipline Modeling in Materials and Structures 9, no. 1 (2013): 23–48. http://dx.doi.org/10.1108/15736101311329142.

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PurposeThis paper aims to describe the method for solving vibration problem of electro‐magneto‐elastic plate of polygonal (triangle, square, pentagon and hexagon) cross‐sections using Fourier expansion collocation method (FECM).Design/methodology/approachA mathematical model is developed to study the wave propagation in an electro‐magneto‐elastic plate of polygonal cross‐sections using the theory of elasticity. The frequency equations are obtained from the arbitrary cross‐sectional boundary conditions, since the boundary is irregular in shape; it is difficult to satisfy the boundary conditions along the surface of the plate directly. Hence, the FECM is applied along the boundary to satisfy the boundary conditions. The roots of the frequency equations are obtained by using the secant method, applicable for complex roots.FindingsFrom the literature survey, it is clear that the free vibration of electro‐magneto‐elastic plate of polygonal cross‐sections have not been analyzed by any of the researchers, also the previous investigations in the vibration problems of electro‐magneto‐elastic plates are based on the traditional circular cross‐sections only. So, in this paper, the wave propagation in electro‐magneto‐elastic plate of polygonal cross‐sections is studied using the FECM. The computed non‐dimensional frequencies are plotted in the form of dispersion curves and their characteristics are discussed.Originality/valueThe researchers have discussed the circular, rectangular, triangular and square cross‐sectional plates by the boundary conditions. In this problem, the author studied the vibrations of polygonal (triangle, square, pentagon and hexagon) cross‐sectional plates using the geometrical relation which is applicable to all the cross‐sections. The problem may be extended to any kinds of cross‐sections by using the proper geometrical relations.

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Wanji, Chen, and Y. K. Cheung. "Refined triangular discrete Kirchhoff plate element for thin plate bending, vibration and buckling analysis." International Journal for Numerical Methods in Engineering 41, no. 8 (1998): 1507–25. http://dx.doi.org/10.1002/(sici)1097-0207(19980430)41:8<1507::aid-nme351>3.0.co;2-t.

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Hota, Sasank Sekhar, Payodhar Padhi, and Mrutyunjay Rout. "Free Vibration of Perforated Plates." Noise & Vibration Worldwide 40, no. 5 (2009): 35–40. http://dx.doi.org/10.1260/095745609788549239.

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A subparametric triangular plate bending element of first order shear deformation has been combined for the first time with the approach of constraints that helps maintain uniform mesh size and shape even while dealing with cutouts of arbitrary shapes. This is a distinct improvement over the existing practices of cutout modeling. Further the formulation being based on the subparametric element offers the scope of achieving matching modes, which enables the model to remain free from problems of locking and spurious zero energy modes while solving problems of very thin plates. Benchmark examples on free vibration of rectangular plates with cutouts have been solved to test the accuracy of the model. The author's own problems are also presented on mode shapes.

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Nguyen-Thoi, T., M. H. Nguyen-Thoi, T. Vo-Duy, and N. Nguyen-Minh. "Development of the Cell-based Smoothed Discrete Shear Gap Plate Element (CS-FEM-DSG3) using Three-Node Triangles." International Journal of Computational Methods 12, no. 04 (2015): 1540015. http://dx.doi.org/10.1142/s0219876215400150.

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The paper presents the formulation and recent development of the cell-based smoothed discrete shear gap plate element (CS-FEM-DSG3) using three-node triangles. In the CS-FEM-DSG3, each triangular element will be divided into three sub-triangles, and in each sub-triangle, the original plate element DSG3 is used to compute the strains and to avoid the transverse shear locking. Then the cell-based strain smoothing technique (CS-FEM) is used to smooth the strains on these three sub-triangles. The numerical examples illustrate four superior properties of the CS-FEM-DSG3 including: (1) being a strong competitor to many existing three-node triangular plate elements in the static analysis; (2) giving high accurate solutions for problems with skew geometries in the static analysis; (3) giving high accurate solutions in free vibration analysis; (4) providing accurate values of high frequencies of plates by using only coarse meshes. Due to its superior and simple properties, the CS-FEM-DSG3 has been now developed for various analyses such as: flat shells, stiffened plates, functionally graded plates, composite plates, piezoelectricity composite plates, cracked plate and plates resting on the viscoelastic foundation subjected to moving loads, etc.

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Subramanian, G., and T. S. Balasubramanian. "Adaptation of a high precision triangular element for stepped plate vibration." Journal of Sound and Vibration 108, no. 1 (1986): 172–75. http://dx.doi.org/10.1016/s0022-460x(86)80325-x.

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21

Abrate, S. "Vibration of point supported triangular plates." Computers & Structures 58, no. 2 (1996): 327–36. http://dx.doi.org/10.1016/0045-7949(95)99820-n.

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An, Gaocheng, Wenkang Wang, Hongquan Dong, Baoyu Liu, Wei Song, and Zhenhua Hu. "Parameter Optimization of Vibration Reduction Structure for Low-Speed, Multi-Acting Cam Ring Motor." Actuators 12, no. 10 (2023): 388. http://dx.doi.org/10.3390/act12100388.

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To address the issue of serious torque pulsation and optimize the output characteristics of multi-acting cam ring motors at low speed, a sensitivity analysis was conducted on the parameters of the triangular groove at the valve plate. Firstly, a mathematical model of the flow area between the rotor hole and the valve plate hole was established. Then, a numerical simulation model was built to study the motor output characteristics. Finally, the coupling effect of the triangular groove parameters on the motor torque pulsation rate was analyzed based on the response surface methodology. The results show that the motor torque pulsation rate can be reduced by 55% when adjusting depth angle θ1, width angle θ2, and length l. The influence order of design parameters on the pulsation rate is θ1>l>θ2; among all parameter combinations, the coupling of the triangular groove between the depth angle and the length has the most significant effect on the pulsation rate.

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Nguyen-Thoi, T., T. Rabczuk, V. Ho-Huu, L. Le-Anh, H. Dang-Trung, and T. Vo-Duy. "An Extended Cell-Based Smoothed Three-Node Mindlin Plate Element (XCS-MIN3) for Free Vibration Analysis of Cracked FGM Plates." International Journal of Computational Methods 14, no. 02 (2017): 1750011. http://dx.doi.org/10.1142/s0219876217500116.

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A cell-based smoothed three-node Mindlin plate element (CS-MIN3) was recently proposed and proven to be robust for static and free vibration analyses of Mindlin plates. The method improves significantly the accuracy of the solution due to softening effect of the cell-based strain smoothing technique. In addition, it is very flexible to apply for arbitrary complicated geometric domains due to using only three-node triangular elements which can be easily generated automatically. However so far, the CS-MIN3 has been only developed for isotropic material and for analyzing intact structures without possessing internal cracks. The paper hence tries to extend the CS-MIN3 by integrating itself with functionally graded material (FGM) and enriched functions of the extended finite element method (XFEM) to give a so-called extended cell-based smoothed three-node Mindlin plate (XCS-MIN3) for free vibration analysis of cracked FGM plates. Three numerical examples with different conditions are solved and compared with previous published results to illustrate the accuracy and reliability of the XCS-MIN3 for free vibration analysis of cracked FGM plates.

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Abrate, S. "Maximizing the Fundamental Natural Frequency of Triangular Composite Plates." Journal of Vibration and Acoustics 118, no. 2 (1996): 141–46. http://dx.doi.org/10.1115/1.2889641.

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While many advances were made in the analysis of composite structures, it is generally recognized that the design of composite structures must be studied further in order to take full advantage of the mechanical properties of these materials. This study is concerned with maximizing the fundamental natural frequency of triangular, symmetrically laminated composite plates. The natural frequencies and mode shapes of composite plates of general triangular planform are determined using the Rayleigh-Ritz method. The plate constitutive equations are written in terms of stiffness invariants and nondimensional lamination parameters. Point supports are introduced in the formulation using the method of Lagrange multipliers. This formulation allows studying the free vibration of a wide range of triangular composite plates with any support condition along the edges and point supports. The boundary conditions are enforced at a number of points along the boundary. The effects of geometry, material properties and lamination on the natural frequencies of the plate are investigated. With this stiffness invariant formulation, the effects of lamination are described by a finite number of parameters regardless of the number of plies in the laminate. We then determine the lay-up that will maximize the fundamental natural frequency of the plate. It is shown that the optimum design is relatively insensitive to the material properties for the commonly used material systems. Results are presented for several cases.

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Yanyutin, Yevgeniy Grigor'yevich, and Andrey Sergeevich Sharapata. "Impulse deformation of triangular plates based on the classical theory." Bulletin of Kharkov National Automobile and Highway University, no. 95 (December 16, 2021): 165. http://dx.doi.org/10.30977/bul.2219-5548.2021.95.0.165.

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This article discusses the impulse effects of various loads on triangular, isosceles, elastic, isotropic plates. Analytical solutions of the direct problem of determining the internal moments and deflections of the plate, as well as the numerical results of calculations of specific loading case are presented. Goal. The goal is to develop a method for solving direct problems of determining internal moments and deflections in rectangular triangular, isosceles, elastic, thin, isotropic plates. Methodology. To solve the direct problem, the Navier method, the classical theory of modeling vibrations of thin plates and the Laplace transform are used. Results. A technique has been obtained that allows one to obtain numerical and analytical dependences for calculating the internal moments and deflections in a triangular plate. Originality. For the first time, a technique was developed for solving direct non-stationary problems to determine the internal moments and deflections in rectangular triangular, isosceles, elastic, thin, isotropic plates based on the classical theory. Practical value. The obtained analytical dependences can be used to simulate impulse vibrations of square and isosceles rectangular triangular thin isotropic elastic plates, which can be critical structural elements.

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Wang, Changsheng, Xiaoxiao Sun, Xiangkui Zhang, and Ping Hu. "High-order quasi-conforming triangular Reissner-Mindlin plate element." Engineering Computations 35, no. 8 (2018): 2722–52. http://dx.doi.org/10.1108/ec-11-2017-0446.

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PurposeA higher-order Reissner-Mindlin plate element method is presented based on the framework of assumed stress quasi-conforming method and Hellinger-Reissner variational principle. A novel six-node triangular plate element is proposed by utilizing this method for the static and free vibration analysis of Reissner-Mindlin plates.Design/methodology/approachFirst, the initial assumed stress field is derived by using the fundamental analytical solutions which satisfy all governing equations. Then the stress matrix is treated as the weighted function to weaken the strain-displacement equations after the strains are derived by using the constitutive equations. Finally, the arbitrary order Timoshenko beam function is adopted as the string-net functions along each side of the element for strain integration.FindingsThe proposed element can pass patch test and is free from shear locking and spurious zero energy modes. Numerical tests show that the element can give high-accurate solutions, good convergence and is a good competitor to other models.Originality/valueThis work gives new formulations to develop high-order Reissner-Mindlin plate element, and the new strategy exhibits advantages of both analytical and discrete methods.

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Inoue, K., D. P. Townsend, and J. J. Coy. "Optimum Design of a Gearbox for Low Vibration." Journal of Mechanical Design 115, no. 4 (1993): 1002–7. http://dx.doi.org/10.1115/1.2919247.

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A computer program was developed for designing a low vibration gearbox. The code is based on a finite element shell analysis, a modal analysis, and a structural optimization method. In the finite element analysis, a triangular shell element with 18 degrees-of-freedom is used. In the optimization method, the overall vibration energy of the gearbox is used as the objective function and is minimized at the exciting frequency by varying the finite element thickness. Modal analysis is used to derive the sensitivity of the vibration energy with respect to the design variable. The sensitivity is representative of both eigenvalues and eigenvectors. The optimum value is computed by the gradient projection method and a unidimensional search procedure under the constraint condition of constant weight. The computer code is applied to a design problem derived from an experimental gearbox in use at the NASA Lewis Research Center. The top plate and two side plates of the gearbox are redesigned and the contribution of each surface to the total vibration is determined. Results show that even the optimization of the top plate alone is effective in reducing total gearbox vibration.

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German, Daniel J. "Accurate analytical solution for free vibration of the simply supported triangular plate." AIAA Journal 27, no. 5 (1989): 647–51. http://dx.doi.org/10.2514/3.10156.

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Nallim, L. G., B. M. Luccioni, and R. O. Grossi. "A Rayleigh-Ritz approach to transverse vibration of isotropic polygonal plates with variable thickness." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 216, no. 3 (2002): 213–22. http://dx.doi.org/10.1177/146441930221600302.

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This paper presents a simple, computationally efficient and highly accurate numerical model for the study of free vibration behaviour of polygonal plates with variable thickness. The approach developed is based on the Rayleigh-Ritz method and the use of non-orthogonal right triangular coordinates. The deflection of the plate is approximated by a set of beam characteristic orthogonal polynomials generated using the Gram-Schmidt procedure. The algorithm is quite general and can be used to study plates with any combinations of clamped, simply supported and free edge support conditions and also different taper and geometric parameters. Several examples are solved and some results are compared with existing values in the literature. New results are also presented for tapered polygonal plates with different geometrical shapes and combinations of boundary conditions. For some polygonal plates, their mode shapes of free vibration are shown. The study of this problem is of practical importance for a better understanding of the vibration of polygonal plates which are commonly encountered in modern technology.

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30

Truong-Thi, T., T. Vo-Duy, V. Ho-Huu, and T. Nguyen-Thoi. "Static and Free Vibration Analyses of Functionally Graded Carbon Nanotube Reinforced Composite Plates using CS-DSG3." International Journal of Computational Methods 17, no. 03 (2019): 1850133. http://dx.doi.org/10.1142/s0219876218501335.

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This study presents an extension of the cell-based smoothed discrete shear gap method (CS-DSG3) using three-node triangular elements for the static and free vibration analyses of carbon nanotube reinforced composite (CNTRC) plates. The single-walled carbon nanotubes (SWCNTs) are assumed to be uniformly distributed (UD) and functionally graded (FG) distributed along the thickness direction. The material properties of carbon nanotube-reinforced composite plates are estimated according to the rule of mixture. The governing equations are developed based on the first-order shear deformation plate theory (FSDT). In the CS-DSG3, each triangular element will be divided into three sub-triangles, and in each sub-triangle, the stabilized discrete shear gap method is used to compute the strains and to avoid the transverse shear locking. Then the strain smoothing technique on the whole triangular element is used to smooth the strains on these three sub-triangles. Effects of several parameters, such as the different distribution of carbon nanotubes (CNTs), nanotube volume fraction, boundary condition and width-to-thickness ratio of plates are investigated. In addition, the effect of various orientation angles of CNTs is also examined in detail. The accuracy and reliability of the proposed method are verified by comparing its numerical solutions with those of other available results in the literature.

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31

Nguyen-Thoi, T., T. Bui-Xuan, G. R. Liu, and T. Vo-Duy. "Static and Free Vibration Analysis of Stiffened Flat Shells by a Cell-Based Smoothed Discrete Shear Gap Method (CS-FEM-DSG3) Using Three-Node Triangular Elements." International Journal of Computational Methods 15, no. 06 (2018): 1850056. http://dx.doi.org/10.1142/s0219876218500561.

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A cell-based smoothed discrete shear gap method (CS-FEM-DSG3) using three-node triangular element was recently proposed for static, free vibration and buckling analyses of stiffened Mindlin plates. The CS-FEM-DSG3 element is a significant improvement of the original DSG3 element by using smoothing technique to soften the stiffness of the DSG3 element while it has still inherited the locking-free feature of the former. In this paper, the CS-FEM-DSG3 is further extended for the static and free vibration analyses of stiffened flat shells by combining the original plate element CS-FEM-DSG3 with Allman’s plane stress element and a linearly isotropic two-node stiffened beam element. The compatibility of displacement field of stiffeners and shell is applied at the contact positions. Numerical results of the proposed element are compared with those of some existing methods to demonstrate the accuracy and reliability of the proposed method.

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32

Mirza, S., and Y. Alizadeh. "Free vibration of partially supported triangular plates." Computers & Structures 51, no. 2 (1994): 143–50. http://dx.doi.org/10.1016/0045-7949(94)90045-0.

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33

Kitipornchai, S., K. M. Liew, Y. Xiang, and C. M. Wang. "Free vibration of isosceles triangular mindlin plates." International Journal of Mechanical Sciences 35, no. 2 (1993): 89–102. http://dx.doi.org/10.1016/0020-7403(93)90068-6.

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34

Mirza, Shaukat, and Mohan Bijlani. "Vibration of triangular plates of variable thickness." Computers & Structures 21, no. 6 (1985): 1129–35. http://dx.doi.org/10.1016/0045-7949(85)90167-1.

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35

Inoue, Katsumi, Masashi Yamanaka, and Masahiko Kihara. "Optimum Stiffener Layout for the Reduction of Vibration and Noise of Gearbox Housing." Journal of Mechanical Design 124, no. 3 (2002): 518–23. http://dx.doi.org/10.1115/1.1480817.

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Dynamic excitation from the gears generates vibration modes in the gearbox which causes radiation of unwanted structure-borne noise. To reduce the noise as well as the vibration, the stiffened plate construction is frequently used for the housing, where the rib stiffener layout is the key to this design. In this paper, the most effective position of stiffeners in order to reduce the vibration and noise radiation is searched and discussed. The analysis considers first a plate fixed at edges and excited at its center, and then a simplified rectangular gearbox excited at the shaft bearing locations. The housing of a simplified single-stage gearbox is modeled by triangular finite shell elements. It is excited by a set of harmonic forces which are applied at the bearing positions. The rib stiffener is modeled by beam elements, and its optimum layout is searched by a genetic algorithm. The vibration energy is adopted as the objective function to be minimized for the design for low vibration. On the other hand, the radiated sound power is the objective function for low noise. Although the noise is caused by the vibration, the optimum stiffener layout to realize low noise is not always identical to the layout that yields low vibration because of the difference in radiation efficiency. This is numerically clarified first from the viewpoint of the vibration mode of a plate. In the case of the design for the gearbox housing concerned, the vibration mode which causes the difference in radiation efficiency is not presented. Consequently, the optimum stiffener is placed along the line from the point of excitation to a fixed point, which reduces the vibration deflection of the faces with bearings as well as the in-plane displacement of the bearings.

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36

Singh, B., and S. M. Hassan. "TRANSVERSE VIBRATION OF TRIANGULAR PLATE WITH ARBITRARY THICKNESS VARIATION AND VARIOUS BOUNDARY CONDITIONS." Journal of Sound and Vibration 214, no. 1 (1998): 29–55. http://dx.doi.org/10.1006/jsvi.1998.1554.

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37

Natarajan, S., A. J. M. Ferreira, S. Bordas, E. Carrera, M. Cinefra, and A. M. Zenkour. "Analysis of Functionally Graded Material Plates Using Triangular Elements with Cell-Based Smoothed Discrete Shear Gap Method." Mathematical Problems in Engineering 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/247932.

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A cell-based smoothed finite element method with discrete shear gap technique is employed to study the static bending, free vibration, and mechanical and thermal buckling behaviour of functionally graded material (FGM) plates. The plate kinematics is based on the first-order shear deformation theory and the shear locking is suppressed by the discrete shear gap method. The shear correction factors are evaluated by employing the energy equivalence principle. The material property is assumed to be temperature dependent and graded only in the thickness direction. The effective properties are computed by using the Mori-Tanaka homogenization method. The accuracy of the present formulation is validated against available solutions. A systematic parametric study is carried out to examine the influence of the gradient index, the plate aspect ratio, skewness of the plate, and the boundary conditions on the global response of the FGM plates. The effect of a centrally located circular cutout on the global response is also studied.

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38

Muc, Aleksander. "Triangular Functionally Graded Porous Moderately Thick Plates—Deformations and Free Vibrations." Journal of Composites Science 5, no. 10 (2021): 276. http://dx.doi.org/10.3390/jcs5100276.

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Since the finite element analysis of deformations for plates made of functionally graded materials cannot be carried out with the use of commercial FE packages, aconsistent method of analytical analysis is proposed in the paper. The method of the analysis is based on the application of the weighted residuals and the Bubnov–Galerkin method. The 2D formulation of moderately thick plates is adopted herein for classical and transverse shear deformation plate models (first and third order). Plate deformations subjected to uniform normalpressure and free vibrations are considered. The validity of the analytical model was verified by the comparison of results with FE analysis for isotropic plates. Two correction multipliers were proposed in order to take into account the unsymmetric composition of functionally graded porous plate walls.

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39

Xu, Gang-Gang, Ren-Sheng Li, Xing-Lin Gao, Xiao-Dong Wen, Zi-Jiang Liu, and Xiao-Wei Sun. "A local-resonance elastic metamaterial for the transport of wheel-rail vertical vibrations." Journal of Physics: Conference Series 2390, no. 1 (2022): 012021. http://dx.doi.org/10.1088/1742-6596/2390/1/012021.

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Abstract The subwavelength artificial elastic metamaterials can be used for efficient transmission of vibration energies in a tunable frequency range. A local-resonance equal-thickness elastic metamaterial plate is designed in this work. The triangular resonators in the rhombic unit cell are used to exploit the valley degeneracy of the out-of-plane locally resonant modes under hexagonal symmetry conditions. The resonators consist of high-density cores wrapped by soft elastic material, and the differences in the intrinsic frequencies produce a topological band gap caused by the double resonant effect. The reversal of the energy bands proves that the band gap has a non-trivial topology effect, i.e., there exists edge states with robustness and high transmission efficiency. This structure can be utilized in railway transportation as an advanced elastic wave medium material to improve the efficiency of sensing and harvesting the energy of vertical vibrations between vehicles and rails.

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40

Zegang, Sun, Li Yundong, Liang Ning, and Zhong Hongmin. "Study on Restraining Cavitation of Axial Piston Pump Based on Structure of Cylinder Block and Valve Plate Triangular Throttling Groove." Shock and Vibration 2022 (January 25, 2022): 1–10. http://dx.doi.org/10.1155/2022/6918936.

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Raising the rotational speed is an effective way to improve the power density of axial piston pump, but high rotational speed tends to cause plunger cavity and valve plate throttling groove cavitation. The cavitation of axial piston pump must reduce its volumetric efficiency and cause vibration and noise. In order to reduce the cavitation of axial piston pump and improve the performance of axial piston pump, the optimization of anticavitation structure parameters of cylinder block and valve plate throttling groove is studied in this paper. Firstly, according to the condition of no cavitation in the piston cavity fluid, the mathematical model of the ratio of plunger cavity diameter to axial piston pump cylinder block kidney hole hydraulic diameter is established. It is found that when the ratio is small, the cavitation degree of the piston cavity is weakened. Secondly, this paper analyzes and studies the influence of the valve plate triangular throttling groove structure parameters on the cavitation flow of the triangular throttling groove. It is found that reducing the structural parameters γ or θ can reduce the cavitation intensity of the triangular throttling groove fluid. Finally, combined with the analysis result of the ratio of piston cavity between the piston cavity diameter and the cylinder block kidney hole hydraulic diameter and the research results of the anticavitation of the valve plate triangular throttling groove, the optimized structure of anticavitation of the axial piston pump is proposed, and the simulation results show that the improved axial piston pump has better anticavitation performance.

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41

Wang, D. W., H. S. Tzou, and H. J. Lee. "Control of Nonlinear Electro/Elastic Beam and Plate Systems (Finite Element Formulation and Analysis)." Journal of Vibration and Acoustics 126, no. 1 (2004): 63–70. http://dx.doi.org/10.1115/1.1640357.

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Adaptive structures involving large imposed deformation often go beyond the boundary of linear theory and they should be treated as “nonlinear” structures. A generic nonlinear finite element formulation for vibration sensing and control analysis of laminated electro/elastic nonlinear shell structures is derived based on the virtual work principle. A generic curved triangular piezoelectric shell element is proposed based on the layerwise constant shear angle theory. The dynamic system equations, equations of electric potential output and feedback control force defined in a matrix form are derived. The modified Newton-Raphson method is adopted for nonlinear dynamic analysis of large and complex piezoelectric/elastic/control structures. A finite element code for vibration sensing and control analysis of nonlinear active piezoelectric structronic systems is developed. The developed piezoelectric shell element and finite element code are validated and then applied to control analysis of flexible electro-elastic (piezoelectric/elastic) structural systems. Vibration control of constant-curvature electro/elastic beam and plate systems are studied. Time-history responses of free and controlled nonlinear electro/elastic beam and plate systems are presented and nonlinear effects discussed.

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42

Quoc, Tran Huu, Tran Minh Tu, and Vu Van Tham. "Free vibration and dynamic response of sandwich composite plates with auxetic honeycomb core." Journal of Science and Technology in Civil Engineering (STCE) - HUCE 15, no. 4 (2021): 1–14. http://dx.doi.org/10.31814/stce.huce(nuce)2021-15(4)-01.

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This paper deals with the free vibration and dynamic responses of composite sandwich plates. The sandwich plate has three layers in which two face sheets are made of isotropic material, and the core layer is made of auxetic honeycomb structures with a negative Poisson's ratio. A smoothed finite element model based on the first-order shear deformation theory is established for the analysis purpose. In the model, only the linear approximation is necessary, and the discrete shear gap method for triangular plate elements is used to avoid the shear locking. The Newmark direct integration technique is used to capture the dynamic responses of the sandwich plates. The convergence study is made, and the accuracy of present results is validated by comparison with available data in the literature. The influence of geometrical parameters, material properties, and boundary conditions are explored and discussed. Numerical results show that auxetic materials have several different responses compared to conventional materials, and these behaviors are strongly influenced by the internal structure of the auxetic material.

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43

Sakiyama, Takeshi, Hiroshi Matsuda, and Chihiro Morita. "Free Vibration Analysis of Anisotropic Right Triangular Plates." Journal of applied mechanics 4 (2001): 171–81. http://dx.doi.org/10.2208/journalam.4.171.

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44

Karunasena, W., S. Kitipornchai, and F. G. A. Al-Bermani. "Free vibration of cantilevered arbitrary triangular Mindlin plates." International Journal of Mechanical Sciences 38, no. 4 (1996): 431–42. http://dx.doi.org/10.1016/0020-7403(95)00060-7.

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Malhotra, S. K., N. Ganesan, and M. A. Veluswami. "Vibration and damping analysis of orthotropic triangular plates." Journal of Sound and Vibration 130, no. 3 (1989): 379–86. http://dx.doi.org/10.1016/0022-460x(89)90064-3.

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46

Singh, B., and V. Saxena. "TRANSVERSE VIBRATION OF TRIANGULAR PLATES WITH VARIABLE THICKNESS." Journal of Sound and Vibration 194, no. 4 (1996): 471–96. http://dx.doi.org/10.1006/jsvi.1996.0373.

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Karunasena, W., and S. Kitipornchai. "FREE VIBRATION OF SHEAR-DEFORMABLE GENERAL TRIANGULAR PLATES." Journal of Sound and Vibration 199, no. 4 (1997): 595–613. http://dx.doi.org/10.1006/jsvi.1996.0613.

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48

Ge, Chang. "Numerical Simulation of Vibration Deflection Effects on the Energy Efficiency of Ultrasonic Transducer for Sonochemistry." Mathematical Problems in Engineering 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/591352.

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The energy efficiency of ultrasound transducers for sonochemistry applications was studied from the point of view of vibration deflection effects of different transducer structures, including the configurations of rectangular plate, cylindrical shell, triangular strip array, rectangular strip array, and pentagonal strip array. It was found that the deflections are not uniform over the transducer surface with the maximum deflection locating at the geometry center of transducers. The simulated maximum deflection of rectangular plate results in the value of2.5×10-16, which is larger than the maximum deflection of cylindrical shell with the value of2×10-16. This finding suggests that the envelope deflection volume of two transducers has significant difference, which has been neglected in the design and selection of ultrasound transducer. For this reason, a quantitative index involving the envelope deflection volume was proposed to compare the efficiency of ultrasound transducers. Based on the simulation results, the triangular strip array transducer structure with higher ultrasound generation efficiency was proposed, which was also theoretically validated by the MATLAB simulation.

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49

Zhang, Bo, Cheng Li, Limin Zhang, and Feng Xie. "Size-Dependent Free Vibration of Non-Rectangular Gradient Elastic Thick Microplates." Symmetry 14, no. 12 (2022): 2592. http://dx.doi.org/10.3390/sym14122592.

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The free vibration of isotropic gradient elastic thick non-rectangular microplates is analyzed in this paper. To capture the microstructure-dependent effects of microplates, a negative second-order gradient elastic theory with symmetry is utilized. The related equations of motion and boundary conditions are obtained using the energy variational principle. A closed-form solution is presented for simply supported free-vibrational rectangular microplates with four edges. A C1-type differential quadrature finite element (DQFE) is applied to solve the free vibration of thick microplates. The DQ rule is extended to the straight-sided quadrilateral domain through a coordinate transformation between the natural and Cartesian coordinate systems. The Gauss–Lobato quadrature rule and DQ rule are jointly used to discretize the strain and kinetic energies of a generic straight-sided quadrilateral plate element. Selective numerical examples are validated against those available in the literature. Finally, the impact of various parameters on the free vibration characteristics of annular sectorial and triangular microplates is shown. It indicates that the strain gradient and inertia gradient effects can result in distinct changes in both vibration frequencies and mode shapes.

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Kobayashi, Tsutomu, Hidekazu Tai, and Sadayuki Ueha. "Vibrating-plate viscometer using a triangular bimorph transducer." Journal of the Acoustical Society of Japan (E) 18, no. 5 (1997): 223–30. http://dx.doi.org/10.1250/ast.18.223.

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Journal articles on the topic 'Vibration of triangular Plate'

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