Dynamic contact problems for an orthotropic elastic half-plane and a composite plane

Abstract

The equivalence properties of certain boundary-value problems are studied for ortho- and isotropic elastic domains in stationary subsonic dynamics and statics. By using these properties, solutions obtained earlier in explicit form for dynamic contact problems for an isotropic half-plane with four, and a composite half-plane with six, kinds of boundary conditions /1/ are extended to the case of an orthotropic material whose characteristic equation has pure imaginary roots. An analogous problem is solved for an arbitrary orthotropic half-plane by constructing new complex potentials. The existence and uniqueness of the real root of the Rayleigh equation governing the rate of surface wave propagation in an orthotropic half-plane with a free boundary are proved. The problem of the breaking of a totally adherent stamp from an orthotropic half-plane is solved in terms of elementary functions. The existence of a single delamination section is proved its length is found, and the contact stresses are calculated.