RESPONSE OF NONCLASSICALLY DAMPED STRUCTURES IN THE MODAL SUBSPACE

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.