NUMERICAL SOLUTION OF SOME VIBRATION PROBLEMS OF PLATES WITH VARIABLE THICKNESS

Abstract

The present work deals with the determination of first few frequencies and associated mode shapes for free transverse vibration of isotropic elastic plates of various geometries and variable thickness with different boundary conditions. The results for uniform thickness have been obtained as special cases. The use of elastic plates is very common in machine design, aeronautical engineering, nuclear reactor technology, naval structures, earthquake resistance structures, telephone industry etc. The whole range of the subject of study is covered in nine chapters which deal with the free transverse vibrations of isotropic circular, quarter circular, quarter elliptic, triangular, square, rectangular and skew plates. Classical plate theory has been assumed throughout the study. Rayleigh-Ritz method has been employed to compute the frequencies and associated mode shapes by working out several approximations to ensure convergence. The results are extensively tabulated. Mode shapes are plotted using computer graphics. Although these geometries have been studied extensively, a lot of information related to variable thickness is still missing in the existing literature. Further, some of the known results do not have the desired accuracy...........