A multiscale approach for the vibration analysis of heterogeneous materials: Application to passive damping

This paper presents a multiscale numerical technique for vibration analysis of heterogeneous materials. In this procedure, the unknown macroscopic constitutive relationship is searched by solving a local finite element problem at the microscale. Since the inertia effects are neglected at the microscopic level, this approach is limited to problems in which microstructure characteristic length is smaller than the wavelength. Numerical examples are limited to free vibration analysis of viscoelastic materials with a constant complex modulus. These examples allow one to validate the multiscale approach and to study the influence of different parameters on the passive damping of the structure. These parameters concern the morphology, the stiffness ratio and the inclusion volume fraction.