Abstract :
Starting from a fundamental, continuum mechanical, constitutive material damping
description, the augmented Hooke’s law (AHL) introduced by Dovstam povstam, K. (1995).
Augmented Hooke’s law in frequency domain. A three-dimensional, material damping formulation.
International Journal of Solids and Structures 32, 2835-28521, a linear three-dimensional damped
vibration response model for isotropic material is proposed. The derivations, valid for a restricted
but important class of cases, are based on general, continuous, elastic vibration modes, Gurtin
[Gurtin, M. E. (1972). The linear theory of elasticity. In Encyclopedia of Physics, vol. Via/2,
Mechanics of Solids II (eds Fltigge, S. and Truesdell, C.). Springer, Berlin]. Material damping is
represented by two complex, frequency dependent, damping functions defined directly by constitutive
parameters in the isotropic AHL. Alternatively, for isotropic, tiscoelastic solids, the damping
functions are derived from two stress relaxation ftinctions. Modal damping functions, which define
overall “structural” damping in terms of elastic, modal parameters and the two material damping
functions, are introduced in the response model. It is shown that the modal damping functions,
indirectly, depend on the geometry and boundary conditions of the piece of material under investigation.
Introduced are also new, elastic modal parameters which determine the quantitative
contribution to the modal damping functions from the two isotropic, material damping functions.
The new modal parameters are easily computed using, slightly modified, standard finite element
code, and elastic modes resulting from standard finite element eigenvalue analyses. A close agreement
between direct linite element calculations and responses predicted using the proposed modal model
is obtained for a studied three-dimensional cantilever test plate. 0 1997 Elsevier Science Ltd.
