SOME EXACT DYNAMIC SOLUTIONS IN NONLINEAR ELASTICITY

We show that the solutions of Rajagopal and Wineman [Int. J. Engng Sci. 23, 217 (1985)], describing combined torsion and shearing of a slab of Mooney-Rivlin material, may be generalized to dynamic elasticity. In these motions, each of a family of planes is undistorted, but undergoes a rotation and an in-plane translation. When the twist and angular speed are uniform, the transverse displacements may be any solutions to certain linear partial differential equations. The dispersion and stability of wavelike solutions are discussed. So also are time-harmonic motions. It is shown also that, for neo-Hookean and certain other special cases of Mooney-Rivlin materials, exact solutions can be found in which the twist and angular speed are nonuniform.