Levy-type solution for the analysis of nonuniform plates

Abstract

The Levy-type solution for the static and dynamic response of an elastically restrained rectangular plate, resting on a nonuniform elastic Winkler foundation is presented. Both the flexural rigidity of the plate and the stiffness of the elastic foundation considered are uniform along the y-axis and variable along the x-axis. The static deflection and forced dynamic response of the plate are derived in Green's function form and expressed in terms of the four normalized fundamental solutions of the system. The frequency equation for the free vibration of the system is obtained from letting the denominator of the corresponding Green's function equal zero. If the coefficients of the governing characteristic different equation are in arbitrarily polynomial form, then the exact fundamental solutions in terms of power series can be obtained by the method of Frobenius. Finally, several examples are given to illustrate the analysis and the results are compared with those in the existing literature.