Free Vibrations of Symmetrically Laminated Composite Plates.

Abstract

In the previous papers, the authors proposed a numerical approach for analyzing the vibration problem of combined systems. For the free vibration analysis, the approach consists of two steps. One is estimating Green's function for a static bending problem of the same plate and the other is to solve a frequency equation. First, this approach is applied to a symmetrically laminated FRP (fiber reinforced plastic) composite plate. Numerical calculations are carried out for a cantilevered plate and a clamped plate. Green's function of a cantilevered plate is estimated by the Ritz method and one of the clamped plate is obtained by Galerkin's method. Accuracy and convergency of natural frequencies of these plates are discussed. Next, it is an attempt to reduce the number of dimensions of the frequency equation, by assuming that the deflections of an adjacent 5 points in a straight line can be approximated as a parabolic function. This approximation reduces the number of dimensions of the frequency equation and the number of Green's functions. The improved approach was applied to a cantilevered plate. Numerical results showed that the computing time was reduced extensively by the approximation.