Additive Property of Modal Density for a Composite Structure

Abstract

It has been postulated that the modal density for a composite structure is equivalent to sum of the modal densities of the idealized substructures. A demonstration of the validity of this postulate for a particular composite is given by analyzing a structure consisting of two beams joined at right angles to form an L-shaped frame. The frequency equation for the composite and its asymptotic representation are utilized to determine the cumulative number of modes for the structure as a function of frequency. Modal density is determined from a graphical presentation of these results and compared with the sum of the modal densities of the two substructures. Consistent agreement is obtained for all frequencies giving rise to the additive property of modal density for the structure analyzed. [Work supported by NASA.]