On the flexural vibration of rectangular plates approached by using simple polynomials in the Rayleigh-Ritz method

1990 ◽  
Vol 143 (3) ◽  
pp. 379-394 ◽  
Author(s):  
C.S. Kim ◽  
P.G. Young ◽  
S.M. Dickinson
Keyword(s):  
Ritz Method ◽  
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.

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.

Flexural Vibration of Rectangular Plates with Stiffeners Parallel to the Edges

1963 ◽  
Vol 67 (634) ◽  
pp. 664-668 ◽  
Author(s):  
S. Mahalingam
Keyword(s):  
Natural Frequencies ◽  
Ritz Method ◽  
Flexural Vibration ◽  
Approximate Solutions ◽  
The Other ◽  
Rectangular Plates ◽  
Equivalent System ◽  
Simply Supported ◽  
Finite Difference Equations ◽  
Four Corners

SummaryThe basis of the procedure described in the paper is the replacement of the stiffeners by an approximately equivalent system of line springs. One of two methods may then be used to determine the natural frequencies. A rectangular plate with edge stiffeners, point-supported at the four corners, is used to demonstrate the application of the Rayleigh-Ritz method. Numerical results obtained are compared with known approximate solutions based on finite difference equations. A Holzer-type iteration is employed in the case of a plate with parallel stiffeners, where the two edges perpendicular to the stiffeners are simply supported, the other two edges having any combination of conditions.

Vibration of Rectangular Plates by the Ritz Method

1950 ◽  
Vol 17 (4) ◽  
pp. 448-453 ◽  
Author(s):  
Dana Young
Keyword(s):  
Ritz Method ◽  
Normal Modes ◽  
Approximate Solutions ◽  
The Other ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Modes Of Vibration ◽  
Ritz’S Method ◽  
Square Plate ◽  
Set Up

Abstract Ritz’s method is one of several possible procedures for obtaining approximate solutions for the frequencies and modes of vibration of thin elastic plates. The accuracy of the results and the practicability of the computations depend to a great extent upon the set of functions that is chosen to represent the plate deflection. In this investigation, use is made of the functions which define the normal modes of vibration of a uniform beam. Tables of values of these functions have been computed as well as values of different integrals of the functions and their derivatives. With the aid of these data, the necessary equations can be set up and solved with reasonable effort. Solutions are obtained for three specific plate problems, namely, (a) square plate clamped at all four edges, (b) square plate clamped along two adjacent edges and free along the other two edges, and (c) square plate clamped along one edge and free along the other three edges.

Sign in / Sign up

Export Citation Format

Share Document