大振幅简正波

本文将简正波理论推广到大振幅声场,计及声场内的非线性效应。这涉及非线性偏微分方程的固有振动解的问题。简正波具有驻波性质,基本已反映在一阶近似解中。高阶近似解只是非线性引致参量的局部变化或修正,并不影响分布。根据这个概念解决了过去的数学困难,求得了大振幅简正函数,为线性商正函数及其谐频项,此外还有常数项,代表辐射压,与经典辐射压值作了比较。

Finite-amplitude normal modes

Conception of normal modes of vibration is generalized to finite-amplitude sound fields in enclosures,taking into acount of the nonlinear effects.This includes the solution the wave equation in the from of nonlinear partial differential equations,for the natural vibrations in the closed space.In doing sos the standing wave nature of the solution is emphasized.The first order solution is taken as the basic solution of the problem,and all the higher order solutions but the modification or correction at various points on basic waveform due to the nonlinearity and do not change the standing wave nature of the solution.In this way,the finite-amplitude normal function is derived for the first time,containing the basic solution,the same normal function as in linear acoustics,and its harmonics.And besides,time-independent terms exist in the complete solution,representing the radiation pressure in the finite-amplitude sound field