Numerical analyses of nonlinear acoustic wave radiation behaviors of vibrational objects immersed in infinite fluid

Abstract

This paper is concerned with numerical analyses of radiated sound behaviors of dynamic systems containing nonlinear vibrational objects immersed in a compressible and inviscid fluid of infinite extent. The vibrational solids are modelled by the Lagrangian description of motion, while the fluid surrounding the vibrational objects is formulated by the two-dimensional linearized Euler equations (LEEs). The nonlinear dynamic responses of the vibrational solids are computed by both the harmonic balance method (HBM) and direct time integration method. A fourth-order dispersion-relation-preserving (DRP) scheme is implemented on a fixed Cartesian grid to solve the governing equations of the fluid. A constrained moving least-squares sharp-interface immersed boundary method is adopted to impose the compatibility conditions on the common boundaries of the vibrational objects and the fluid. Selective filters are employed to suppress the spurious short waves appearing in numerical computations. Several numerical tests are carried out to confirm the validity of the developed vibro-acoustic coupling computational model by comparing the present solutions with the exact solutions. Nonlinear acoustic wave responses of vibrational objects with smooth and non-smooth nonlinearities are examined, including rigid cylinder-shaped oscillators resting on nonlinear mounts, ellipse-shaped objects suspended on nonlinear torsional springs, and rigid isolators with frictions and clearances. It is found that for vibrational objects containing nonlinearities, the amplitude-frequency responses of radiated sound pressure exhibit shifting resonance frequencies, secondary resonances and jump phenomenon. The intermittent collisions of the vibrational objects with clearances can result in abrupt fluctuations and distortions of the radiated acoustic waves in fluid. In addition, the radiation efficiency of high-order harmonics of nonlinear acoustic waves induced by stick/slip transitions of friction interfaces can reach to maximum with the friction coefficient.