Generation of symmetric Lamb waves by non-uniform excitations

The plane strain response of a semi-infinite, elastic strip to harmonic, symmetric, and non-uniform end excitation is investigated analytically. The solution is obtained as a series expansion of the Rayleigh–Lamb modes of the strip. The variation of the energy partition among the propagating modes with the frequency of the end excitation was found for mixed end conditions prescribed at the excited end (load and displacement types). The bi-orthogonality relation was employed in deriving the relative amplitudes of each mode to the given excitation. It was found that the far-field response of the strip is largely indifferent to whether the excitation is a displacement or stress type. The previously reported phenomenon of the existence of one dominating wave in uniform excitation is shown to extend to moderately non-uniform excitations as well. The phenomenon of complete dominance of one mode for generally non-uniform excitations was exposed.