Waves generated by a vibrating rigid sphere with an elastic shell submerged in a fluid(a))

An analytical solution for the sound and elastic waves generated by a rigid sphere with a shell made of elastic material submerged in an infinite fluid is introduced. The sphere oscillates up and down at a fixed frequency and generates elastic waves (both longitudinal and transverse) in the shell, which are then transmitted to the fluid. The effects of the acoustic boundary layer are included (thus, no implicit arbitrary “slip” on the surface as in the usual fluid acoustic model is present). An example of a 1 mm radius sphere with an elastic shell is analyzed in detail for several conditions to understand the physical phenomena involved in such a system.