FINITE AMPLITUDE AND FREE VIBRATIONS OF A BODY SUPPORTED BY INCOMPRESSIBLE, NONLINEAR VISCOELASTIC SHEAR MOUNTINGS

A constitutive equation for an incompressible. isotropic, nonlinear viscoelastic solid of differential type. a class which includes the Voigt-Kelvin solid of classical linear viscoelasticity. is applied to study the quasi-static response of the material in a simple shearing deformation superimposed on a given static homogeneous strain. The Cauchy stress is determined and general relations that characterize creep and recovery phenomena arc obtained. Specific equations are derived for a viscoelastic Mooney-Rivlin model. Then the finite amplitude, damped, free vibration of a rigid body supported symmetrically by viscoelastic Mooney-Rivlin shear mountings is examined, and solutions arc given for heavily damped and lightly damped motions. The effects of the primary static deformation on creep and recovery phenomena of the shear blocks. and its effects on the frequency, damping, and logarithmic decrement characteristic of the motion arc described analytically;and illustrated graphically. Effects Of the ultimate equilibrium shear induced by the load also arc described. Universal frequency and damping relations for viscoelastic Mooney-Rivlin;and neo-Hookean models arc noted. It is shown that the primary homogeneous deformation plays an important role in determination of all aspects air the mechanical response. General equations for the exact solution of the problem for free vibrations of a load on nonlinear. perfectly clastic shear mountings also are provided.