Natural Oscillations of an Elastic Half-Strip with a Different Arrangement of Fixation Areas of Its Edges

Eigenfrequencies and trapped modes are studied in an isotropic and homogeneous elastic half-strip. For different configurations of rigidly clamped and the traction-free zones, information was obtained about the absence or presence of eigenfrequencies below, and in some cases even above, the cutoff point of the continuous spectrum. Estimates of the multiplicity of the discrete spectrum are derived and various asymptotic representations of trapped modes and their frequencies are constructed.