A. Daveni et G. Muscolino, RESPONSE OF NONCLASSICALLY DAMPED STRUCTURES IN THE MODAL SUBSPACE, Earthquake engineering & structural dynamics, 24(9), 1995, pp. 1267-1281
The evaluation of the dynamic response of non-classically damped linea
r structures requires the solution of an eigenproblem with complex eig
envalues and modal shapes. Since in practice only a small number of co
mplex modes are needed, the complex eigenvalue problem is solved in th
e modal subspace in which the generalized damping matrix is not uncoup
led by classical real modes. It follows that the evaluation of the str
uctural response requires in both cases the determination of complex m
odes by numerical techniques, which are not as robust as techniques cu
rrently used for the solution of the real eigenvalue problem, and the
use of complex algebra. In the present paper an unconditionally stable
step-by-step procedure is presented for the response of non-classical
ly damped structures in the modal subspace without using complex quant
ities. The method is based on the evaluation of the fundamental operat
or in approximated form of the numerical procedure. In addition, the m
ethod can be easily modified to incorporate the modal superposition ps
eudo-static correction terms.