scholarly journals A dynamic coefficient matrix method for the free vibration of thin rectangular isotropic plates

2021 ◽  
Author(s):  
Supun Jayasinghe ◽  
Seyed M. Hashemi
Keyword(s):  
Exact Solution ◽  
Free Vibration ◽  
Free Vibration Analysis ◽  
Flexural Vibration ◽  
Coefficient Matrix ◽  
Dynamic Coefficient ◽  
Rectangular Plates ◽  
Various Boundary Conditions ◽  
Unique Method ◽  
Benchmark Solutions

The free flexural vibration of thin rectangular plates is revisited. A new, quasi-exact solution to the governing differential equation is formed by following a unique method of decomposing the governing equation into two beam-like expressions. Using the proposed quasi-exact solution, a Dynamic Coefficient Matrix (DCM) method is formed and used to investigate the free lateral vibration of a rectangular thin plate, subjected to various boundary conditions. Exploiting a special code written on MATLAB, the flexural natural frequencies of the plate are found by sweeping the frequency domain in search of specific frequencies that yield a zero determinant. Results are validated extensively both by the limited exact results available in the open literature and by numerical studies using ANSYS and in-house conventional FEM programs using both 12- and 16-DOF plate elements. The accuracy of all methods for lateral free vibration analysis is assessed and critically examined through benchmark solutions. It is envisioned that the proposed quasi-exact solution and the DCM method will allow engineers to more conveniently investigate the vibration behaviour of two-dimensional structural components during the preliminary design stages, before a detailed design begins.

scholarly journals A Dynamic Coefficient Matrix Method for the Free Vibration of Thin Rectangular Isotropic Plates

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Supun Jayasinghe ◽  
Seyed M. Hashemi
Keyword(s):  
Exact Solution ◽  
Free Vibration ◽  
Free Vibration Analysis ◽  
Flexural Vibration ◽  
Coefficient Matrix ◽  
Dynamic Coefficient ◽  
Rectangular Plates ◽  
Various Boundary Conditions ◽  
Unique Method ◽  
Benchmark Solutions

The free flexural vibration of thin rectangular plates is revisited. A new, quasi-exact solution to the governing differential equation is formed by following a unique method of decomposing the governing equation into two beam-like expressions. Using the proposed quasi-exact solution, a Dynamic Coefficient Matrix (DCM) method is formed and used to investigate the free lateral vibration of a rectangular thin plate, subjected to various boundary conditions. Exploiting a special code written on MATLAB®, the flexural natural frequencies of the plate are found by sweeping the frequency domain in search of specific frequencies that yield a zero determinant. Results are validated extensively both by the limited exact results available in the open literature and by numerical studies using ANSYS® and in-house conventional FEM programs using both 12- and 16-DOF plate elements. The accuracy of all methods for lateral free vibration analysis is assessed and critically examined through benchmark solutions. It is envisioned that the proposed quasi-exact solution and the DCM method will allow engineers to more conveniently investigate the vibration behaviour of two-dimensional structural components during the preliminary design stages, before a detailed design begins.

scholarly journals A dynamic coefficient matrix method for the free vibration of thin rectangular isotropic plates

2021 ◽  
Author(s):  
Supun Jayasinghe ◽  
Seyed M. Hashemi
Keyword(s):  
Exact Solution ◽  
Free Vibration ◽  
Free Vibration Analysis ◽  
Flexural Vibration ◽  
Coefficient Matrix ◽  
Dynamic Coefficient ◽  
Rectangular Plates ◽  
Various Boundary Conditions ◽  
Unique Method ◽  
Benchmark Solutions

The free flexural vibration of thin rectangular plates is revisited. A new, quasi-exact solution to the governing differential equation is formed by following a unique method of decomposing the governing equation into two beam-like expressions. Using the proposed quasi-exact solution, a Dynamic Coefficient Matrix (DCM) method is formed and used to investigate the free lateral vibration of a rectangular thin plate, subjected to various boundary conditions. Exploiting a special code written on MATLAB, the flexural natural frequencies of the plate are found by sweeping the frequency domain in search of specific frequencies that yield a zero determinant. Results are validated extensively both by the limited exact results available in the open literature and by numerical studies using ANSYS and in-house conventional FEM programs using both 12- and 16-DOF plate elements. The accuracy of all methods for lateral free vibration analysis is assessed and critically examined through benchmark solutions. It is envisioned that the proposed quasi-exact solution and the DCM method will allow engineers to more conveniently investigate the vibration behaviour of two-dimensional structural components during the preliminary design stages, before a detailed design begins.

On Free Vibration of Functionally Graded Mindlin Plate and Effect of In-Plane Displacements

2013 ◽  
Vol 29 (2) ◽  
pp. 373-384 ◽  
Author(s):  
A. Hasani Baferani ◽  
A.R. Saidi ◽  
H. Ehteshami
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Mindlin Plate ◽  
Rectangular Plates ◽  
Various Boundary Conditions ◽  
Aspect Ratios

AbstractIn this paper, free vibration analysis of functionally graded rectangular plate is investigated based on the first order shear deformation theory and the effect of in-plane displacements on the natural frequencies of such plate is studied. The governing equations of motion are obtained, which are five coupled partial differential equations, without any simplification. Some mathematical manipulation leads us to decouple the equations. The decoupled equations are solved by the Levy's method for various boundary conditions. As the results show, in some boundary conditions the in-plane displacements cause a drastic change of frequencies. In other words, neglecting the in-plane displacement, which is assumed in some papers, is not proper for these boundary conditions. However, in the other boundary conditions, the natural frequencies are not significantly affected by the in-plane displacements. The results for various boundary conditions are discussed in detail and some interpretations for these differences are provided. Besides to the comparisons, the accurate natural frequencies of the plate for six different boundary conditions with several aspect ratios, thickness-length ratios and power law indices are presented. The natural frequencies of Mindlin functionally graded rectangular plates with considering the in-plane displacements are reported for the first time and can be used as benchmark.

Vibration Analysis of Laminated Composite Rectangular Plates With General Boundary Conditions

2018 ◽  
Author(s):  
Yu Fu ◽  
Jianjun Yao ◽  
Zhenshuai Wan ◽  
Gang Zhao
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Laminated Composite ◽  
Free Vibration Analysis ◽  
Geometric Parameters ◽  
General Boundary ◽  
Rectangular Plates ◽  
General Boundary Conditions ◽  
Benchmark Solutions

In this investigation, the free vibration analysis of laminated composite rectangular plates with general boundary conditions is performed with a modified Fourier series method. Vibration characteristics of the plates have been obtained via an energy function represented in the general coordinates, in which the displacement and rotation in each direction is described as an improved form of double Fourier cosine series and several closed-form auxiliary functions to eliminate any possible jumps and boundary discontinuities. All the expansion coefficients are then treated as the generalized coordinates and determined by Rayleigh-Ritz method. The convergence and reliability of the current method are verified by comparing with the results in the literature and those of Finite Element Analysis. The effects of boundary conditions and geometric parameters on the frequencies are discussed as well. Finally, numerous new results for laminated composite rectangular plates with different geometric parameters are presented for various boundary conditions, which may serve as benchmark solutions for future research.

Theoretical Study on Space Coupling Free Vibration Analysis of Self-Anchored Cable-Stayed Suspension Bridge

2014 ◽  
Vol 501-504 ◽  
pp. 1107-1111
Author(s):  
Miao Feng
Keyword(s):  
Free Vibration ◽  
Strain Energy ◽  
Coupling Effect ◽  
Longitudinal Vibration ◽  
Free Vibration Analysis ◽  
Flexural Vibration ◽  
Suspension Bridge ◽  
Large Displacement ◽  
Generalized Variational Principle ◽  
Suspension Bridges

Based on Large-displacement Non-linear Elastic Generalized Variational Principle, coupling effect of axial and flexural action, shearing strain energy, torsional strain energy of stiffening girder were considered, the large-displacement incomplete generalized potential energy functional of space coupling free vibration of a three-span self-anchored cable-stayed suspension bridge was presented. By constraint variation, fundamental differential equations of vertical flexural vibration, lateral flexural vibration, longitudinal vibration and torisional vibration were formulated, also presented the equations for the main tower with respect to longitudinal and lateral vibration. The linear free vibration differential equation was obtained when the nonlinear items were discarded. This approach provides theoretical basis for analysis of natural vibration character of self-anchored cable-stayed suspension bridges.

Sign in / Sign up

Export Citation Format

Share Document