Research on mode conversion of lamb wave at dip end face of elastic plate

Underwater target acoustic scattering is an important aspect of underwater acoustic research. Research on the elastic scattering wave is related to the wave dispersion curves and the exit angle, but the excited condition of a Lamb wave is rarely discussed in the context of elastic plates. The energy distribution for the reflected Lamb waves of several modes when Lamb waves of other anti-symmetric modes are formed by reflection at the end face of an elastic plate is also rarely discussed. However, the research concentrating on the excitation condition of Lamb waves and mode conversion at the end face of a submerged elastic plate can be the basis for target recognition. Based on R.D. Mindlin Hamilton's principle and using an orthogonal complete feature, the frequency dispersion equation of a Lamb wave is derived for an elastic plate in a vacuum; and water, phase velocity, attenuation coefficients and group velocity dispersion curves are obtained. Analysis of the energy ratio between each of two anti-symmetric mode backward Lamb waves resulting from mode conversion when an anti-symmetric Lamb wave is incident at the end face of the plate in single mode is derived. The scattering wave of a submerged elastic plate is measured experimentally, which shows that only the incident anti-symmetric Lamb wave at the critical angle of one mode can directly excite a Lamb wave of this mode in the elastic plate, Lamb waves of other anti-symmetric modes are formed by reflection at the end face of the elastic plate. There is also no energy change between a symmetric Lamb wave and an anti-symmetric Lamb wave, even with mode conversion, if the waves are reflected at the end of the elastic plate. Combined with radiation efficiency of submerged elastic plate energy ratio between each two anti-symmetric mode backward lamb waves resulted from mode conversion when anti-symmetric lamb wave incident at the end face of plate in single mode confirmed validity of the analysis results.