Abstract
The free transverse vibrations of thin nonhomogeneous rectangular plates of variable thickness have been studied using boundary characteristic orthogonal polynomials in the Rayleigh-Ritz method. Gram-Schmidt process has been used to generate these orthogonal polynomials in two variables. The thickness variation is bidirectional and is the cartesian product of linear variations along two concurrent edges of the plate. The nonhomogeneity of the plate is assumed to arise due to linear variations in Young's modulus and density of the plate material with the in-plane coordinates. Numerical results have been computed for four different combinations of clamped, simply supported and free edges. Effect of the nonhomogeneity and thickness variation with varying values of aspect ratio on the natural frequencies of vibration is illustrated for the first three modes of vibration. Three dimensional mode shapes for all the four boundary conditions have been presented. A comparison of results with those available in the literature has been made.
Highlights
Plates of various geometries are widely used as structural components in various technological situations ranging from household goods such as mixer, grinder etc. to modern space technology
Numerous studies have been made by researchers on free vibrations of rectangular plates with different types of thickness variations and boundary conditions
Keeping in view the above fact, a study dealing with nonhomogeneous rectangular plates of varying thickness using two dimensional boundary characteristic orthogonal polynomials in the Rayleigh-Ritz method is presented employing classical plate theory
Summary
Plates of various geometries are widely used as structural components in various technological situations ranging from household goods such as mixer, grinder etc. to modern space technology. In many practical situations, in modern missile technology and microelectronics, plate type structural components have to work under high temperature conditions, which cause nonhomogeneity For such type of situations, it is more appropriate to take the variation in the mechanical properties of the material as the function of two variables instead of one. Keeping in view the above fact, a study dealing with nonhomogeneous rectangular plates of varying thickness using two dimensional boundary characteristic orthogonal polynomials in the Rayleigh-Ritz method is presented employing classical plate theory. These orthogonal polynomials may be generated either by Gram-Schmidt process [28] or using the recurrence relation [29].
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