The importance of the first and second symmetric Lamb modes in target identification of submerged elastic shells

Abstract

Resonances excited on any shell of constant thickness are one large resonance at a frequency inversely proportional to the shell thickness. Hence for thin shells it occurs at very high frequency. This effect occurs at the inception of the S1 resonance, which may be shown to be an amplitude-modulated wave at inception. Its critical frequency may be determined by the condition: ka=3.14 VLa/(2 daVW) or ka=3.14 VTa/(daVW) where VW, VT, VL, a, da, and k are the speed of sound in the ambient fluid, transverse and longitudinal velocities in the elastic material, largest dimension of the object, object thickness relative to a and the wave number in the fluid. If 2VT>VL the first condition defines the S1 critical frequency and the second that of the S2. The converse is true otherwise. The S2 resonance is not striking but may be identified as such. Thus, ratios of the two resonances lead to ratios of the bulk velocities and other considerations can isolate the shell thickness. This offers for any shell of constant thickness a means to determine the presence of certain submerged objects. We discuss the reasons for this and illustrate results in both time and frequency domains.