非线性弹性地基内预应力梁中的非线性波  

Nonlinear Waves of a Prestressed Beam in Nonlinear Elastic Foundation

作　　者：贺媛媛[1] 刘志芳[1] 张善元[1] 

机构地区：[1]太原理工大学应用力学与生物医学工程研究所,太原030024

出　　处：《科学技术与工程》2011年第11期2409-2413,共5页Science Technology and Engineering

基　　金：国家自然科学基金(10772129)资助

摘　　要：研究了埋置于非线性弹性地基内预应力梁中非线性弯曲波的传播特性。同时考虑了梁中的预应力和非线性弹性地基对梁中非线性弯曲波的传播特性的影响。利用Hamilton变分原理导出了梁中非线性弯曲波传播的支配方程。借助多重尺度法将非线性弯曲波动方程简化为非线性Schr dinger方程,并给出了包络孤立子解。研究结果表明,在一定条件下,非线性弹性地基内预应力梁中存在包络孤立波。The propagation characteristic of nonlinear flexural wave in a prestressed beam buried inside nonlinear elastic foundation is studied.Using Hamilton variational principle,a nonlinear flexural wave propagation equation of motion considering the prestressing force and the nonlinear elastic foundation to the propagation characteristic of nonlinear flexural wave in the prestressed beam are derived.By means of multiple scale method a nonlinear Schrdinger equation is obtained from the nonlinear flexural wave equation.It follows that under certain conditions the existence of the envelope soliton in the prestressed beam in nonlinear elastic foundation is possible.

关 键 词：非线性弹性地基 预应力梁 多重尺度法 包络孤立子 

分 类 号：O347.4[理学—固体力学]