Modeling of Linear Viscoelastic Space Structures

Abstract

The GHM Method provides viscoelastic finite elements derived from the commonly used elastic finite elements. Moreover, these GHM elements are used directly and conveniently in second-order structural models jut like their elastic counterparts. The forms of the GHM element matrices preserve the definiteness properties usually associated with finite element matrices—namely, the mass matrix is positive definite, the stiffness matrix is nonnegative definite, and the damping matrix is positive semi-definite. In the Laplace domain, material properties are modeled phenomenologically as a sum of second-order rational functions dubbed mini-oscillator terms. Developed originally as a tool for the analysis of damping in large flexible space structures, the GHM method is applicable to any structure which incorporates viscoelastic materials.

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

“…As a result, there has been an increasing demand in recent years on nonviscous damping models with the purpose of describing dissipative forces in a more general and accurate manner compared to the limited scope offered by the viscous damping model. Majority of the nonviscous damping models, like Biot model [2,3], GollaHugher-McTavish (GHM) model [4,5], Anelastic Displacement Field (ADF) model [6,7], are presented considering the entire velocity history via convolution integrals over some kernel functions.…”

“…In recent years, researchers have considered the dynamic responses of nonviscous damping models. Some authors developed exact state-space approaches [4][5][6][7][8][9][10][11][12] based on internal variables. Others proposed approximated approaches [13][14][15][16][17][18][19][20] and model reduction methods [21][22][23][24][25][26] to solve the eigenproblem for the exponential-like damping models.…”

Explicit solution for the natural frequency of structures with partial viscoelastic treatment

“…Relaxation material model. Constitutive relations for viscoelastic materials are conveniently described by linear models, where the stress components are governed by a convolution integral with a decaying exponential kernel representing strain relaxation [22,23]. In the frequency domain, with angular frequency ω, these linear relaxation characteristics imply real-valued material stiffness in both the low-and high-frequency limits.…”

Experimental Identification of GHM and ADF Parameters for Viscoelastic Damping Modeling

“…One alternative is the GHM (Golla-Hughes-McTavish) model [24,25] which assumes the material modulus function sG(s) represented in terms of a series of mini-oscillator terms (Table 1),…”

“…Thus, to account for the frequency dependent material properties, iterative versions of the MSE have been used successfully for moderate damping values [22]. Time domain models, relying on internal variables (see [23]), such as the Golla-Hughes-McTavish (GHM) [24,25] and anelastic displacement fields (ADF) [26,27], or others [28,29], utilizing additional dissipation variables, have been successfully utilized and yield good damping estimates. Alternatively, the use of fractional calculus (FC) [30,31] models, based upon the use of fractional derivatives, has the drawback of generating a "non-standard" finite element (FE) formulation, with a more complex characteristic solution procedure, but yielding also good damping estimates.…”