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Viscoelastic materials have the capability of dissipating vibrational energy which makes them very effective in the passive control of structural vibration and noise radiation. Efficient modeling-and simulation strategies for vibro-acoustic systems with these frequency-dependent damping materials are necessary. One way of doing that is to utilize the finite element (FE) method supported by a damping model that describes the frequency-dependency of the complex elastic modulus. However, in many applications, very large-scale FE models are required to obtain reliable predictions, which makes full-order system evaluation often intractable. Model order reduction (MOR), however, cannot be directly applied to models including viscoelastic materials due to the frequency-dependent property which exactly makes that the equations of motion are not of a standard second-order form as that for regular FE models. In this paper, a transformation technique based on Taylor’s theorem is introduced to treat the non-standard form of the equations of motion. After transforming the problem into a second-order system equation with an associated remainder term, an adaptive MOR procedure is applied to reduce the computational complexity of the vibro-acoustic systems. A numerical example is provided to demonstrate the simplicity and efficiency of the proposed approach.

An adaptive MOR method for vibro-acoustic analysis of dynamic systems with viscoelastic damping