高次非线性弹性杆纵向振动方程的摄动分析

Perturbation analysis for higher order equation of longitudinal oscillation of a nonlinear elastic rod

对在计入横向惯性效应后的非线性弹性杆纵向波动方程进行了分析.通过建立非线性双曲方程组,在n≥2和小振幅、长波长的一般情况下,根据远方场简单波理论,采用向量摄动法,将方程化为变形KdV方程,并给出了方程的解析解.

The nonlinear wave equation of longitudinal oscillaton of a nonlinear elastic rod with transverse inertia is discussed.The nonlinear hyperbolic equations are established in the case of n ≥2,small amplitude and long wave line.Based on far field and simple waves theory,using vectorial perturbation method,are the equations transferred into KdV equations of transformation and obtained analytical solutions.