【摘要】 分别采用四阶精度和六阶精度的中心差分格式 ,限定扰动 (振幅 )的取值在 1 0 -3 m以内 ,进行了一维固体中非线性纵波传播的数值模拟 ,并通过两种格式对比性研究来保证差分格式的稳定性和收敛性 .讨论了边界所输入正弦波的振幅、频率及介质非线性系数对非线性波的影响 .模拟结果与位于生存周期之内近似解析解相符 ,并证实非线性波在传播过程中会发生波形畸变、产生倍频效应及谐波能量积累 ,而且这些非线性波动特征随输入振幅、频率和介质非线性系数 (绝对值 )的增大而增强更多还原

【Abstract】 Two finite difference of centered schemes with different accuracy orders of spac e sampling step Δx(fourth order and sixth order respectively) were used in order to study the 1-D nonlinear P-wave propagation in the nonlinear solid med ia by numerical method. As known by all, in the numerical treatment to nonlinear partial differential equation several difficulties may arise, due to problems o f stability and convergence, since the classical stability analysis is valid onl y for linear systems. However, the stability of finite difference scheme can be assured if the product of the absolute value of nonlinear coefficient and the va lue of u/x is small, that is, the value of βu/x is much smaller than 1. Two schemes with different accuracy orders were studied at the same time, which can explain the convergence and stability of the numerical method. Sereval results were founded, in the numerical study of nonlinear P-wav e propagation, that is, the waveform will change with time and distance, the fre quency spectrum become wider than that of the linear wave, multiple-frequency a nd lower-frequency components of the initial wave form, the energy of the multi ple-frequency components become larger with longer distance. At the same time, we know from the study, for the nonlinear wave, the energy of the initial freque ncy component will transfer to the multiple-frequency and lower-frequency comp onents.更多还原