NATURAL FREQUENCIES OF A RECTANGULAR PLATE CARRYING A DISTRIBUTED MASS

Abstract

In this paper, an analytical method is presented to find the eigenfrequencies of a plate carrying an attachment which consist of a uniformly distributed mass. The frequency equation of polynomial type is obtained by applying the standard Galerkin procedure to the equation of motion. The nondimensional parameters which are associated with the location, the area density and the distribution of the mass, are defined in order to make the analysis results generally applicable. Then, the variation of the three lowest frequencies, especially of the fundamental frequency due to its significance, with respect to these nondimensional parameters 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, the effects of the location and the mass of such an attachment on the modal surfaces and nodal lines of a plate are investigated