梯度功能梁中一维非线性波的孤波解  

Solitary wave solutions to a one-dimensional nonlinear equation of wave propagation in a functionally graded beam

作　　者：孙丹[1] 罗松南[1] 

机构地区：[1]湖南大学力学与航空航天学院,长沙410082

出　　处：《振动与冲击》2009年第9期188-191,203,共5页Journal of Vibration and Shock

基　　金：高等学校博士学科点专项科研基金(20050532002);湖南省自然科学基金(06JJ2058)资助项目

摘　　要：在考虑有限变形并引入横向Poisson效应的情况下,利用Hamilton变分原理,推导出了梯度功能梁的一维非线性波动方程。运用行波约化法将非线性波动方程化为常微分方程,然后利用位移形函数的系数待定法求出了非线性波动方程的位移孤波解。通过实例分析了材料参数沿厚度方向指数形式变化和抛物线形式变化时,材料参数和波传播时的波速对孤波的波幅和波宽的影响。Considering finite deformation and cross Poisson effects,a new nonlinear wave equation in a functionally graded beam was derived by means of Hamilton principle. By using travelling wave reduced form method,the nonlinear partial differential equation of wave propagation in a functionally graded beam was transformed into an ordinary differential equation. The solitary wave solutions of displacement were obtained by using method of undetermined coefficient of displacement functions and the nonlinear differential equation of wave propagation was solved. Two cases of functionally graded materials,elastic modulus and mass density along the depth varying with exponentially and parabolic type,were analyzed by examples. The curves of displacement were presented and the influence of parameters of the functionally graded materials and velocity of wave propagation on amplitude and width of solitary wave were analyzed.

关 键 词：梯度功能梁 有限变形 非线性波 行波约化法 孤波解 

分 类 号：O347.41[理学—固体力学]