Design sensitivity analysis for transient responses of viscoelastically damped systems using model order reduction techniques.

Design sensitivity analysis (DSA) of transient responses, which are indispensable in gradient-based time domain optimization, often requires excessive computational resources for viscoelastically damped systems to directly differentiate and integrate the full-order model (FOM). In this paper, an efficient model-order reduction (MOR)–based DSA framework is developed for capturing the 1st- and 2nd-order derivatives of the transient responses and response functions for viscoelastically damped systems. The damping force is represented by a non-viscous damping model, which depends on the past history of motion via convolution integrals over suitable kernel functions. The direct differentiation method (DDM) is used to derive the DSA. Three robust modal reduction bases, namely multi-model (MM) method, modal strain energy modified by displacement residuals (MSER) method and improved approximation method (IAM) are introduced to reduce the system dimension. Based on a generalized damping model in expression of fraction formula, a reduced state-space formulation without convolution integral term is derived. The 1st- and 2nd-order derivatives of the transient responses and response functions are calculated using a modified precise integration method and the DDM on the reduced stage. The computational efficiency and accuracy of the presented methods are illustrated and compared by two examples. The results indicate that the computational time is significantly reduced by the proposed MOR methods maintaining fairly good accuracy. Among these methods, the MM method represents the most compromise between precise and efficiency and would be the best candidate to be the reduction basis for calculating the time domain DSA of large-scale viscoelastically damped systems. [ABSTRACT FROM AUTHOR]