Research On The Characteristics Of Nonlinear Acoustics In Air

In this thesis, numerical studies of the nonlinear propagation characteristics with acoustic wave in air are presented. The Finite-Difference Time-Domain Method (FDTD) is implemented to simulate finite-amplitude acoustics wave propagating in 1D/2D air.The equation, Westervelt equation, which describes the nonlinear acoustic model, was derived from the basic equations of fluid mechanics and thermodynamics for a thermoviscous fluid.The FDTD was introduced. The difference expression to Westervelt equation was given, and a program for nonlinear acoustic field solver was written in FORTRAN.The nonlinear acoustic waves, exited by plane circular piston in air, were simulated. The waveform is distorted as it propagates until weak shock is formed. The frequency characteristics were investigated, and the detail of second harmonic generation is given.The interaction of finite-amplitude acoustics were simulated, including: the interaction of the plane circular piston of different frequencies, the interaction of nonlinearity and absorption, the finite-amplitude inverse Shock-Wave propagation and focusing source using arrays. The results show that: 1) The sub or the difference frequencies was generated due to the interaction effect; 2) Because of the generation of high frequencies harmonic, the absorption effect increases, and competes with the nonlinear effect; specifically, the absorption effect may influence the forming of weak shock; 3) The investigation of the finite-amplitude inverse Shock-Wave propagation indicates the discontinuity distance could be maximized or the formation could be totally avoided; 4) The studying of focusing using arrays indicates that the nonlinear effect degrades the line array focusing performance.