Coupling mechanisms of large-deformable beams and nonlinear acoustic waves in unbounded domains of heavy fluids

Abstract

The nonlinear vibration and acoustic radiation of large-deformable beams in light fluids have been studied to some extent, but the coupling effects in heavy fluids remain unclear. This paper aims to reveal the coupling mechanisms of large-deformable beams and nonlinear acoustic waves in heavy unbounded fluid domains. A partitioned strongly coupled nonlinear frequency-domain finite element method is established to solve the nonlinear beam and acoustic equations. The modal and harmonic components of beam displacement, acoustic pressure, excitation input energy, beam damping dissipation energy, and acoustic radiation energy are analyzed for elucidating the coupling mechanisms. The results show that, under the same external harmonic excitation conditions, compared to the frequency responses of beam displacement and acoustic pressure in air, those in water shift to lower frequencies, with larger amplitudes and stronger nonlinear effects. Due to the structural cubic geometric nonlinearity and large-amplitude excitation, super-harmonic resonances are observed in the frequency responses of beam displacement and acoustic pressure. Under super-harmonic resonance and low-order primary resonance conditions, the triple-frequency components of most modes account for a significant proportion of their total responses. Under high-order primary resonance conditions, compared to air, the beam vibration in water is more likely to excite low-order modes in the radiated acoustic field. Relatively high acoustic radiation efficiency can be witnessed in the first primary resonance in air and the high-order primary resonance in water. These results will help to understand the differences and connections in the coupling characteristics of vibration and radiated acoustic fields of large-deformable structures in light and heavy fluids.