Forced torsional oscillations of multilayered solids

Abstract

A new approach is proposed for obtaining the dynamic elastic response of a multilayered elastic solid caused by a forced torsional oscillation inside the solid. The elastodynamic Green’s function of the center of rotation and a point load method are used to solve the problem. The solution of the center of rotation for multilayered solids is obtained by solving a set of simultaneous linear algebraic equations using the boundary conditions for the singularity and for the layer interfaces. The solution of the forced torsional oscillation is formulated by integrating the Green’s function over the contact area with unknown surface traction. The dual integral equations of the unknown surface traction are established by considering the boundary conditions on the contact surface of the multilayered solid, which can be converted into a Fredholm integral equation of the second kind and solved numerically.