A parametric model order reduction technique for inverse viscoelastic material identification

Abstract

Viscoelastic materials are mostly used to passively suppress structural vibrations. The theoretical analysis and design of such system require the knowledge of damping properties which are highly frequency-dependent and proper mathematical models for this dependency. The fractional derivative model is attractive as very few empirical parameters are required. These parameters can be identified through inverse procedures, either by fitting the frequency dependent constitutive properties from a dedicated dynamical mechanical analyzer experiment, or by fitting response curves, e.g. frequency response functions (FRFs) by using a dedicated numerical model. The optimization process requires frequently iterative prediction of the FRFs of large-scale full order model and furthermore each model inversion is expensive. To speed up numerical simulations, a parametric model order reduction technique is introduced. In the material parameter search space, quasi-random sequences are chosen and divided into two disjoint sets: a sample set is used to construct a reduced order model (ROM); while a validation set is used to assess its performance. A global orthonormal basis can then be constructed by non-weighted singular value decomposition on all local bases. Since the parameter- and frequency-dependency can be suitably preserved, the generated single ROM in conjunction with optimization algorithms is very useful to identify the material parameters of viscoelastic damping. The versatility and efficiency of the present procedure are demonstrated through a number of validation cases.