Abstract: Analysis for the propagation of elastic waves in
arbitrary anisotropic plates is investigated, commencing with a
formal analysis of waves in a layered plate of an arbitrary anisotropic
media, the dispersion relations of elastic waves are obtained by
invoking continuity at the interface and boundary of conditions on
the surfaces of layered plate. The obtained solutions can be used for
material systems of higher symmetry such as monoclinic,
orthotropic, transversely isotropic, cubic, and isotropic as it is
contained implicitly in the analysis. The cases of free layered plate
and layered half space are considered separately. Some special cases
have also been deduced and discussed. Finally numerical solution of
the frequency equations for an aluminum epoxy is carried out, and
the dispersion curves for the few lower modes are presented. The
results obtained theoretically have been verified numerically and
illustrated graphically.
Abstract: In this article an isotropic linear elastic half-space with
a cylindrical cavity of finite length is considered to be under the
effect of a ring shape time-harmonic torsion force applied at an
arbitrary depth on the surface of the cavity. The equation of
equilibrium has been written in a cylindrical coordinate system. By
means of Fourier cosine integral transform, the non-zero
displacement component is obtained in the transformed domain. With
the aid of the inversion theorem of the Fourier cosine integral
transform, the displacement is obtained in the real domain. With the
aid of boundary conditions, the involved boundary value problem for
the fundamental solution is reduced to a generalized Cauchy singular
integral equation. Integral representation of the stress and
displacement are obtained, and it is shown that their degenerated
form to the static problem coincides with existing solutions in the
literature.