Vibrations of neo-Hookean elastic wedge

This paper considers small amplitude vibrations superimposed upon large planar deformations of an infinite wedge composed of a neo-Hookean elastic material. It is shown herein that even though the static deformation of the entire wedge and the vibrations of the wedge faces are planar, out-of-plane vibrational modes must necessarily be excited in the wedge interior even to first order in an asymptotic expansion of the motion with small parameter being the amplitude of the vibration applied to the wedge faces. In addition, it is demonstrated that this result is fundamentally due to the non-linearity of the problem by demonstrating that the corresponding problem for an incompressible, isotropic, homogeneous linear elastic wedge does not exhibit the same behavior.