Nonviscous Modes of Nonproportionally Damped Viscoelastic Systems

Author:

Lázaro Mario1

Affiliation:

1. Department of Continuum Mechanics and Theory of Structures, Universitat Politècnica de València, Valencia 46022, Spain e-mail:

Abstract

Nonviscously damped vibrating systems are characterized by dissipative mechanisms depending on the time-history of the response velocity, introduced in the physical models using convolution integrals involving hereditary kernel functions. One of the most used damping viscoelastic models is the Biot's model, whose hereditary functions are assumed to be exponential kernels. The free-motion equations of these types of nonviscous systems lead to a nonlinear eigenvalue problem enclosing certain number of the so-called nonviscous modes with nonoscillatory nature. Traditionally, the nonviscous modes (eigenvalues and eigenvectors) for nonproportional systems have been computed using the state-space approach, computationally expensive. In this paper, we address this problem developing a new method, computationally more efficient than that based on the state-space approach. It will be shown that real eigenvalues and eigenvectors of viscoelastically damped system can be obtained from a linear eigenvalue problem with the same size as the physical system. The numerical approach can even be enhanced to solve highly damped problems. The theoretical results are validated using a numerical example.

Publisher

ASME International

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Reference30 articles.

1. Dynamics of Viscoelastic Structures—A Time-Domain, Finite-Element Formulation;ASME J. Appl. Mech.,1985

2. Theory of Stress-Strain Relations in Anisotropic Viscoelasticity and Relaxation Phenomena;J. Appl. Phys.,1954

3. Variational Principles in Irreversible Thermodynamics With Application to Viscoelasticity;Phys. Rev.,1955

4. Biot, M., 1958, “Linear Thermodynamics and the Mechanics of Solids,” Proceedings of the Third U.S. National Congress on Applied Mechanics, Providence, RI, June 11–14, ASME, New York, pp. 1–18.

5. Viscoelasticity

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