Modified, More Rapidly Converging Modal Series Representation for Mechanical Admittance

Abstract

The standard modal series representation of mechanical admittance may be slowly convergent, especially at antiresonance, for structures that may exhibit a spatially localized response to a spatially localized excitation, e.g., beams on elastic foundation as well as plates and shells. A William's modal acceleration approach is used to arrive at a modified, faster converging, modal series representation for the displacement admittance of a general, finite, linear elastic structure which contains damping. A freely supported, damped, circular cylindrical shell, driven by a radial point force, is employed as an example for a comparison of the modified and the standard modal representations for driving-point and transfer displacement admittance in various frequency bands. At a shell antiresonance, the convergence of the modified driving-point admittance representation is very rapid in comparison to that of the standard modal representation. This is particularly true for that shell antiresonance that lies between the two most widely separated shell resonances. As one proceeds from the case of very light to intermediate shell damping, the convergence, at antiresonance, of both types of admittance representation improves considerably.