Modelling and simulation of acoustic pulse interaction with a fluid-filled hollow elastic sphere through numerical Laplace inversion

A detailed study is undertaken to analyze the non-steady interaction of plane progressive pressure pulses with an isotropic, homogeneous, fluid-filled and submerged spherical elastic shell of arbitrary wall thickness within the scope of linear acoustics. The formulation is based on the general three dimensional equations of linear elasticity and the wave equation for the internal and external acoustic domains. The Laplace transform with respect to the time coordinate is invoked, and the classical method of separation of variables is used to obtain the transformed solutions in the form of partial-wave expansions in terms of Legendre polynomials. The inversion of Laplace transforms have been carried out numerically using Durbin’s approach based on Fourier series expansion. Special convergence enhancement techniques are invoked to completely eradicate spurious oscillations (Gibbs’ phenomenon), and obtain uniformly convergent solutions. Detailed numerical results for the transient and vibratory responses of water-submerged steel shells of selected wall thickness parameters with various internal fluid loadings under an exponential wave excitation are presented. Many of the interesting dynamic features in the transient shell–shock interaction such as shock transparency, shell-radiated negative pressure waves, formation of triple points, and focusing of the reflected waves are examined using appropriate 2D images of the internal pressure field. Also, the temporal behavior of the specularly-reflected, the lowest symmetric S0- and antisymmetric A0-Lamb waves, as well as appearance of the Franz’s creeping waves are discussed through proper visualization of the external scattered field. Likelihood of cavitation is addressed and regions proned to cavitation are identified. Moreover, the effects of internal fluid impedance in addition to shell wall thickness on the dynamic stress concentrations induced within the shell are analyzed. Limiting cases are considered and fair agreements with well-known solutions are established.