Reduction of Structural Dynamics Models Having Nonlinear Damping

Abstract

The purpose of this work has been to explore the suitability of significantly reduced order structural dynamics models for simulation of nonlinear response of structures. In this paper oscillator chains having nonlinear damping and linear stiffness are considered. Both non-smooth and smooth nonlinear damping will be discussed for the case of isolated nonlinear damping and for the case of many equal nonlinear damping elements distributed throughout the structure. Most of the results to be shown will address the accuracy with which significantly reduced order models (e.g., 5, 10 and 20 DOF reduced models of a 1,000 DOF system) simulate the free oscillation decay caused by the nonlinear damping. The model reduction employed utilizes an “exact-for-the-linear-case” linear state transformation to eliminate slave coordinates, yielding a reduced model containing only specified master degrees of freedom. The ultimate objective of this work is to develop efficient, sufficiently accurate models that can be integrated numerically to determine response of very large nonlinear structures in situations for which numerical integration over reasonably long times is needed. The results obtained here are promising: even drastically reduced models provide accurate simulation of the oscillation decay for both smooth and non-smooth nonlinearity.