The Natural Frequencies of Thin Skew Plates

Abstract

Summary Using Rayleigh's principle, the natural frequencies of thin isotropic rhombic plates, with three possible combinations of boundary conditions obtained by combining clamped-clamped and clamped-supported edge conditions, are determined in Part I of this paper. To introduce constant limits of integration, non-orthogonal co-ordinate systems are used and the wave shape for the vibrating plate is approximated by using normal functions representing mode shapes of corresponding bars. To estimate the accuracy of these eigenvalues, Kato's theorem is used and the lower bounds for the natural frequencies are determined in Part II of the paper. It is also shown that normal beam functions are not generally suitable for the determination of eigenfrequencies of skew plates with large skew angles.