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.
Few men in this century have had as great an impact on engineedng mechanics and engineering education as St~phen P. Timoshenko. Through his research and his writing he contributed remarkably to the advancement of his profession, and through his teaching and his contagious enthusiasm inspired thousands of his students and colleagues.Professor Timoshenko started his career in Russia during the turbulellt years before and d1ll'ing the Communist Revolution.
A general method of solution for rectangular plates with clamped edges and any kind of loading has been developed by Professor S. P. Timoshenko. The present paper gives the results of calculations using this method for the maximum deflection, moment, and edge shears for rectangular plates of various proportions with all four edges clamped and loaded by a single concentrated load at the centre. Similar data for a clamped rectangular plate with a uniformly distributed load have been given by I. A. Wojtaszak and also T. H. Evans. A report of an experimental investigation of this problem with some analytical results has been given by R. G. Sturm and R. L. Moore.
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