Dynamic stiffness and response analysis

Abstract

The dynamic stiffness method enables one to model an infinite number of natural modes by means of a finite number of degrees of freedom. The method has been extended to frame structures with uniform or non-uniform, straight or curved, damped or undamped beam members. An orthonormal condition is suggested here for the natural modes resulting from the dynamic stiffness method; modal analysis in the classical sense is then made possible. Modes corresponding to repeated natural frequencies are discussed in detail. An expansion theorem for expanding from a finite number of degrees of freedom by means of an infinite number of modes is validated by means of the frequency-dependent shape functions. Distributed modal participation factors are introduced for distributed excitations.