Free vibration of partially supported plates and shells.

Abstract

First-order transverse shear-deformation Mindlin theory has been used to predict the free vibration frequencies and modal shapes for isotropic, laminated and composite plates or shells. A finite element model based on the small deflection linear theory has been developed to obtain numerical solutions for this class of problems. The results for some of the degenerate cases are compared with other results available in the literature. These analyses involve a wide number of variables, namely; material properties, aspect ratios, support conditions and also radius to base ratio. The cracked base plates, shells and blades are idealized as partially supported models with varying support lengths. The effects of the detached base length on natural frequencies, modal shapes and nodal lines of these types of structures are investigated. Although the expected decrease in frequency with increase in the detached base length is observed almost for all modes it is seen that this behavior is very pronounced for higher modes in both plates and shells. Analysis also showed that the variation of the detached base length has a small effect on the natural frequencies of plates and shells with large aspect ratios ( b/a > 2, r/a > 2).