Free vibrations of a rectangular plate carrying a distributed mass

Abstract

In this paper, an analytical method is presented to find the eigenfrequencies of a rectangular plate carrying a uniformly distributed mass. Using the standard Galerkin procedure, the equation of motion is reduced to a set of ordinary differential equations. From this set, the frequency equation is obtained. This polynomial equation is solved numerically. Due to the significance of the fundamental frequency of the system, its variation with respect to the non-dimensional parameters associated with the location, the area density and the distribution area of the mass attached to the plate, is investigated. Furthermore, it is shown by a numerical example that the method can be used to study plates with concentrated mass as a special case. Finally, an analysis to obtain the modal surfaces and the related nodal lines is carried out. It is demonstrated that the location of the attachment significantly affects the nodal lines, and modal interchanges may occur.