Dynamics of structural systems with various frequency-dependent damping models

Abstract

The aim of this paper is to present the dynamic analyses of the system involving various damping models. The assumed frequency-dependent damping forces depend on the past history of motion via convolution integrals over some damping kernel functions. By choosing suitable damping kernel functions of frequency-dependent damping model, it may be derived from the familiar viscoelastic materials. A brief review of literature on the choice of available damping models is presented. Both the mode superposition method and Fourier transform method are developed for calculating the dynamic response of the structural systems with various damping models. It is shown that in the case of non-deficient systems with various damping models, the modal analysis with repeated eigenvalues are very similar to the traditional modal analysis used in undamped or viscously damped systems. Also, based on the pseudo-force approach, we transform the original equations of motion with nonzero initial conditions into an equivalent one with zero initial conditions and therefore present a Fourier transform method for the dynamics of structural systems with various damping models. Finally, some case studies are used to show the application and effectiveness of the derived formulas.

Hybrid vibration control of a Two-Link Flexible manipulator

“…The damping factors have been obtained using half power bandwidth method. Li et al [13] have presented the dynamic analyses of the system using various damping models. The damping forces are frequency dependent and depend upon the past history of motion.…”

“…In Eqs. (12) and (13), σ = stress within the viscoelastic element of length dx and area dA, ϵ = strain within the viscoelastic element, η = dynamic viscosity of the viscoelastic material and A = total cross-sectional area of the 12and (13) and the principle of minimum potential energy used for finite element formulation [48], the stiffness matrix for viscoelastic material can be formulated as given in Eq. (9).…”

A free interface component mode synthesis method for viscoelastically damped systems

“…The equations of motion describing an N degree-of-freedom (DOF) linear viscoelastic system with various damping models can be expressed by [46] …”

“…Also, some researchers studied the frequency-dependent damping functions via fractional derivative models [51][52][53][54] (see e.g., references [46,55] for further reading). The eigenvalue problem of Eq.…”

Direct Time-Domain Integration Approach for Viscoelastic Systems Involving Various Damping Models

“…Although the exponential damping model, Biot model, GHM model and ADF model are physically different, they can be mathematically represented by a friction formula of rational polynomials [31]. The uniform way to express damping models can simplify the theoretical analysis of dynamic responses and be applied conveniently in multiple damping models.…”