Description of the high-order lamb waves resonances in scattering problem for a cylindrical shell

The steady-state problem of a high-frequency plane acoustic wave scattering by an empty elastic cylindrical shell is considered. Resonances of the high-order Lamb waves are investigated. The explicit asymptotic formulas for the damping factor are proposed for the first resonances of the symmetric and antisymmetric. Lamb waves in the case of a circular cylindrical shell. The formulas are obtained in the assumption that the relative thickness of a shell and the relative impedance of a liquid are small. The asymptotic formulas show that the damping factor (the resonances width) depends significantly on a shell vibrations type in the resonance thickness vicinities. The resonances width of quasitransversal vibrations is greater than the width of corresponding resonances of quasi-tangential vibrations. The resonances width for quasi- transversal vibrations does not depend on their number. For quasi-tangential vibrations the resonances width increases as n2 with the increase of their number n.