On the Approximate Solution of Nonclassically Damped Linear Systems

Abstract

A common procedure in the solution of a nonclassically damped linear system is to neglect the off-diagonal elements of the associated modal damping matrix. For a large-scale system, substantial reduction in computational effort is achieved by this method of decoupling the system. In the present paper, the error introduced by disregarding the off-diagonal elements is evaluated, and a quadrature formula for the approximation error is derived. A tight error bound is then obtained. In addition, an effective scheme to improve the accuracy of the approximate solution is outlined.