The eigenfrequencies of a slightly curved isotropic strip clamped between absolutely rigid profiles

The propagation of elastic waves along an isotropic homogeneous strip, distorted on a finite part and clamped without friction and detachment between two absolutely rigid profiles, is investigated. It is established that, by choosing the shape of the curved sides one can obtain eigenfrequencies, accompanied by trapping of the elastic wave. The result is based on an asymptotic analysis of an auxiliary object – an augmented scattering matrix, which was previously constructed exclusively for scalar problems.