Transverse Vibrations Of Rectangular Plates Research Articles

Transverse vibrations of rectangular plates with thickness varying in two directions and with edges elastically restrained against rotation

The title problem is solved in the case of linear variation of the thickness in the x- and y- directions, a simple polynomial co-ordinate function being used. An approximate but quite convenient frequency equation is derived, by using the Rayleigh method. Apparently the open technical literature does not contain a previous analytical treatment of this problem which is as general and simple as that presented here.

A note on transverse vibrations of rectangular plates subject to in-plane normal and shear forces

To determine the fundamental frequency of transverse vibration of rectangular plates with edges elastically restrained against rotation and subjected to uniformly distributed in-plane normal and shear stresses, the plate displacement function is first expressed in terms of polynomial co-ordinate functions which identically satisfy the boundary conditions. A frequency equation is then generated by using a variational formulation. Numerical results for both the fundamental mode and the first fully antisymmetrical mode are given.

Transverse vibrations of rectangular plates with elastically restrained edges and subject to in-plane shear forces

Simple polynomial expressions and the Galerkin method are used in the present study. The results are in good agreement with values previously published in the open literature for the range of shear values used in this investigation. Consideration of in-plane, normal forces does not add any complications to the procedure.

Application of the extended Kantorovich method to the vibration of clamped rectangular plates

The transverse vibrations of rectangular plates are analysed by using the extended Kantorovich method of variational calculus. Several combinations of simply supported and clamped boundary conditions are discussed, and closed form solutions are obtained.

The Vibration of Rectangular Plates

In this paper are considered the free transverse vibrations of rectangular plates with all possible boundary conditions obtained by combining free, freely-supported, and fixed edges. The Rayleigh method, assuming waveforms similar to those of beams, is used to derive a simple approximate frequency expression for all modes of vibration. The terms in this expression depend on the nodal pattern and the boundary conditions; they are tabulated for fifteen boundary conditions—all four edges free, freely-supported, or fixed and the twelve cases in which some of the edges have one condition and the rest another. The expression can also be used to obtain frequencies for a plate which has a combination of all three boundary conditions. The effect on frequency of an edge being supported and partially restrained is discussed. For some boundary conditions it is possible to compare derived frequencies with those obtained by various methods of accurate analysis and by experiment; except for a few cases, the results from the approximate expression and accurate analysis agree closely. For rectangular plates and for most boundary conditions and modes of square plates, the nodal pattern consists of lines approximately parallel to the sides of the plate. The exceptions are discussed and the gradual transition from these non-parallel patterns characteristic of a square plate to those of a rectangular plate is traced. The frequencies of extensional vibrations of rectangular plates are derived for two boundary conditions.