TOWARDS IDENTIFICATION OF A GENERAL MODEL OF DAMPING

Characterization of damping forces in a vibrating structure has long been an active area of research in structural dynamics. In spite of a large amount of research, understanding of damp-ing mechanisms is not well developed. A major reason for this is that unlike inertia and stiffness forces it is not in general clear what are the state variables that govern the damping forces. The most common approach is to use ‘viscous damp-ing ’ where the instantaneous generalized velocities are the only relevant state variables. However, viscous damping by no means the only damping model within the scope of linear analysis. Any model which makes the energy dissipation func-tional non-negative is a possible candidate for a valid damping model. This paper is devoted to develop methodologies for identification of such general damping models responsible for energy dissipation in a vibrating structure. The method uses experimentally identified complex modes and complex natural frequencies and does not a-priori assume any fixed damping model (eg., viscous damping) but seeks to determine param-eters of a general damping model described by the so called ‘relaxation function’. The proposed method and several re-lated issues are discussed by considering a numerical exam-ple of a linear array of damped spring-mass oscillators. NOMENCLATURE M mass matrix K stiffness matrix G(τ) matrix of kernel functions y(t) generalized coordinates ωj,xj j-th undamped frequency and mode λj, zj j-th complex frequency and mode ûj, v̂j real and imaginary parts of zj µ relaxation parameter of damping C damping coefficient matrix <(•),=(•) real and imaginary parts of (•) (•) ∗ complex conjugation ˆ(•) measured quantity of (•)