弹性地基内充液压力管道中的非线性波

NONLINEAR WAVE IN A FLUID-FILLED THIN ELASTIC TUBE BURIED INSIDE ELASTIC FOUNDATION

  • 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_0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.

     

    Abstract: Propagation of nonlinear waves in a fluid-filled thinelastic foundation is studied in this paper. The material of the tube isassumed to be linear elastic, the reaction of foundation is calculatedbased on Winkler model, and the fluid is incompressible and inviscid.Initially, the tube subjected to a uniform inner pressure P_0 is in astate of static equilibrium. The dynamic displacement field and thevariations of inner pressure and fluid velocity are considered as adisturbance superimposed on this static deformation. The nonlinearequations of motion are obtained by considering the massconservation and the balance of linear momentum. With the reductiveperturbation method, the KdV equation is derived in the longwaveapproximation. It is shown that the system can have a solitary wave solution.

     

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