Estimates of errors in the frequency response of non-classically damped systems

Abstract This paper examines the vibration behaviour of non-classically damped systems in the frequency domain. Errors in the frequency response incurred by neglecting off-diagonal entries of a diagonally dominant modal damping matrix are assessed. The exact response is shown to be equivalent to an infinite Taylor’s series, and it is demonstrated that the commonly employed approximation of ignoring off-diagonal entries of the modal damping matrix is equivalent to retaining one term of the series. The frequency dependence of coupling of the non-classical modes is obtained.