ABSTRACT
A mathematical description of the general deformation wave problem is based on both nonlinear elasticity theory and nonlinear wave theory in condensed matter, in particular, the theory of solitons. Guided waves in a hyperelastic material may be short or long, providing either small finite or large deformations in dependence of (in)compressibility of the material, not to say about unior bidirectional propagation in oneor two-dimensional wave guide. Consider the problem of longitudinal deformation wave’s propagation in the homogeneous isotropic infinite nonlinear elastic plate. The derivation of the system of equations is based also on M. F. Hamilton’s variational principle and on the assumption that the deformation of the material is described by relationships of the nonlinear theory of elasticity of either incompressible or compressible medium. The chapter discusses the statement of the problem and provides some basic equations to describe the influence of the energy transfer through the lateral surface of a rod on a nonlinear guided wave.
