Computational method of underwater acoustic radiation from a spherical shell coupled with nonlinear systems

Abstract

During the continuous research and practical application of nonlinear vibration isolation systems, new problems arise for the vibro-acoustic calculation of underwater targets. The present frequency-domain analysis method can only deal with linear problems, so the acoustic radiation calculation of underwater targets coupled with nonlinear systems can only be performed in the time domain. When it comes to the real-time calculation, the huge computation cost will definitely bring challenges to the practical application. To solve this problem, a new calculation method is established for the underwater vibro-acoustic problems of structures coupled with nonlinear systems, taking elastic spherical shells as research objects in this paper. This method realizes the time-frequency domain conversion of the fluid-structure coupled vibration equation of an elastic spherical shell through the Fourier transform. The explicit difference method is further used to calculate the vibration response of the spherical shell, while the Newmark method is used to calculate the vibration response of the internal nonlinear system. An efficient integrated calculation of the two coupling parts is then achieved by considering boundary conditions at the connection point. Without the time-domain acoustic field solution, this method is able to calculate the vibration response of both the internal nonlinear system and the spherical shell, as well as the radiated acoustic power generated by the spherical shell vibration in real time. The calculation complexity and efficiency are radically improved. The nonlinear system discussed in this paper is a nonlinear mass-spring oscillator system installed at the bottom of a spherical shell. Finally, the correctness of the method described in this paper is verified through specific numerical examples, and a series of calculations and analyzes are carried out to explore the influence of nonlinear effects on the acoustic radiation of underwater structures. The calculation method described in this article is not limited to spherical shells, and is still applicable to general underwater targets.