The flexural vibration of welded rectangular plates

1981 ◽  
Vol 75 (2) ◽  
pp. 163-178 ◽  
Author(s):  
M.M. Kaldas ◽  
S.M. Dickinson
Keyword(s):  
Flexural Vibration ◽  
Rectangular Plates

Dynamic analysis of rectangular plates crossed by distributed moving loads

2017 ◽  
Vol 23 (9) ◽  
pp. 1291-1302 ◽  
Author(s):  
S Sorrentino ◽  
G Catania
Keyword(s):  
Coupling Effect ◽  
Ritz Method ◽  
Flexural Vibration ◽  
Analytical Form ◽  
Relative Magnitude ◽  
Transverse Displacement ◽  
Rectangular Plates ◽  
Moving Loads ◽  
Railway Bridges ◽  
Parallel Direction

This study investigates the dynamic behaviour of plates crossed by distributed moving gravitational and inertial loads, in the case in which the relative magnitude of the moving mass introduces a coupling effect with the structure, with possible applications to the vibration analysis of railway bridges. A rectangular Kirchhoff plate is considered, simply supported on two opposite edges and free on the other two edges, loaded by a partially distributed mass travelling in the parallel direction with respect to the free edges. The formulation includes damping, and it is accomplished by the Rayleigh–Ritz method, expressing the solution in semi-analytical form. The shape functions for describing the transverse displacement field of the plate are selected as tensor products of linearly independent eigenfunctions of homogeneous uniform beams in flexural vibration, yielding a low-order model with time-dependent coefficients. Numerical examples are then presented and discussed, aimed at investigating the effects of each of the model governing parameters.

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.

Flexural Vibration of In-Plane Loaded Plates with Straight Line/Curved Internal Supports

1993 ◽  
Vol 115 (4) ◽  
pp. 441-447 ◽  
Author(s):  
K. M. Liew ◽  
C. M. Wang
Keyword(s):  
Ritz Method ◽  
Flexural Vibration ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Internal Support ◽  
Straight Line ◽  
Contour Plots ◽  
Complete Set ◽  
Clamped Edge ◽  
Internal Line Supports

An investigation into the vibration analysis of a class of in-plane loaded rectangular plates with internal supports of arbitrary contour is conducted. Solutions to this vibration problem are obtained based on the pb-2 Rayleigh-Ritz method. The Ritz function for this method is defined as the product of (1) a two-dimensional polynomial function expanded in a new manner, (2) equations of the internal support and (3) equations of the boundary supports each raised to the power of either 0, 1, or 2 corresponding to a free, simply supported or clamped edge, respectively. A comparison study on the convergence between the proposed set of polynomials and mathematically complete set of polynomials is conducted. The simplicity and accuracy of the method are demonstrated by analyzing square plates with either two intersecting internal line supports or a central ring support. The influence of the in-plane loads on the natural frequencies will be studied. Note that this paper presents some first known solutions to in-plane loaded rectangular plates with internal supports of arbitrary contour. The mode shapes for these plates are also presented in contour plots.

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