中文摘要：

研究了埋置于弹性地基内充液压力管道中非线性波的传播.假设管壁是线弹性的,地基反力采用Winkler线性地基模型,管中流体为不可压缩理想流体.假定系统初始处于内压为P_O的静力平衡状态,动态的位移场及内压和流速的变化是叠加在静力平衡状态上的扰动.基于质量守恒和动量定理,建立了管壁和流体耦合作用的非线性运动方程组;进而用约化摄动法,在长波近似情况下得到了KdV方程,表征着系统有孤立波解.

英文摘要：

Propagation of nonlinear waves in a fluid-filled thin elastic foundation is studied in this paper. The material of the tube is assumed to be linear elastic, the reaction of foundation is calculated based on Winkler model, and the fluid is incompressible and inviscid. Initially, the tube subjected to a uniform inner pressure P0 is in a state of static equilibrium. The dynamic displacement field and the variations of inner pressure and fluid velocity are considered as a disturbance superimposed on this static deformation. The nonlinear equations of motion are obtained by considering the mass conservation and the balance of linear momentum. With the reductive perturbation method, the KdV equation is derived in the longwave approximation. It is shown that the system can have a solitary wave solution.