A hierarchy of high-order theories for symmetric modes in an elastic layer

A hierarchy of high-order theories for symmetric modes in an infinitely long elastic layer of the constant thickness is derived by means of the inertia-corrected polynomial approximations. For each member of the hierarchy, boundary conditions for layers of the finite length are formulated. The forcing problems at several approximation levels are solved with the use of the bi-orthogonality conditions. Accuracy of these approximations is assessed by comparison of results with the exact solution of the Rayleigh-Lamb problem. Special attention is paid to the power flow analysis in alternative modal excitation cases and to the applicability of the Saint-Venant׳s principle in stationary elasto-dynamics.