Abstract: The Vibration characteristic analysis of the weakly-viscoelastic material structures and the elastic-viscoelastic composite structres are mainly discussed. The basic equations of these viscoelastic structures are given. According to the strong stiffness and weakly-damping in their whole dynamic behaviors, the perturbation method for analysing their vibration characteristic is constructed, and the first three order perturbation formulas are derived. The perturbation method is also discussed when there exist the repeat-eigenvalues in their zero-order perturbation solutions. The method in this paper is simple and convenient, has high precision, and is suitable for different viscoelastic models.

Key words: viscoelasticity, perturbation method, vibration characteristic