Vibrations of a body supported by shear mountings of incompressible material with memory

Constitutive equations of materials with memory are applied in the study of mechanical response of rubber-like materials in a simple shearing deformation superimposed on a static longitudinal stretch. The Cauchy stress is assumed to be the sum of the contribution of internal elastic forces derived from a strain energy and internal dissipative forces, which depend on previous deformations with an effective memory that is governed by two parameters: the modulus and the time of relaxation. Creep and recovery processes are analyzed for incompressible isotropic materials with various strain energies (Mooney-Rivlin, quadratic, Gent). The finite amplitude vibrations (free and forced with sinusoidal excitation) of a rigid body supported by incompressible simple shearing mountings are investigated. The governing equations have non-linear terms due to the elastic part of the Cauchy stress tenser. Then it is always possible to determine the equivalent. discrete model with spring and dashpot. The more relevant features, in the case of cubic nonlinearity, which corresponds to the quadratic strain energy, are obtained by numerical integration and perturbation methods. The influence of the relaxation time is shown in the frequency response curves and in the related backbone curve, which presents a forked shape. As already observed by Fosdick et al. (Int. J. Solids Struct. 35(5-6) (1998a) 403-420; Int. J. Nonlinear Mech. 33(3) (1998b) 447-459), in their linear analysis of axial vibrations, this behavior suggests potential applications as adaptive damping devices. Indeed, several experimental results show that the values of the internal damping parameters are affected by changes in temperature and by action of electric fields. (C) 2001 Elsevier Science Ltd. All rights reserved.