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A new nonlinear wave equation of a finite deformation elastic circular rod simultaneously introducing transverse inertia and shearing strain was derived by means of Hamilton principle. The nonlinear equation includes two nonlinear terms caused by finite deformation and double geometric dispersion effects caused by transverse inertia and transverse shearing strain. Nonlinear wave equation and corresponding truncated nonlinear wave equation were solved by the hyperbolic secant function finite expansion method. The solitary wave solutions of these nonlinear equations were obtained. The necessary condition of these solutions existence was given also. 相似文献
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研究了梁中的非线性弯曲波的传播特性,同时考虑了梁的大挠度引起的几何非线性效应和
梁的转动惯性导致的弥散效应,利用Hamilton变分法建立了梁中非线性弯曲波的波动方程.
对该方程进行了定性分析,在不同的条件下,该方程在相平面上存在同宿轨道或异宿轨道,
分别对应于方程的孤波解或冲击波解. 利用Jacobi椭圆函数展开法,对该非线性方程进行
求解,得到了非线性波动方程的准确周期解及相对应的孤波解和冲击波解,讨论了这些解存
在的必要条件,这与定性分析的结果完全相同. 利用约化摄动法从非线性弯曲波动方程中导
出了非线性Schr\"{o}dinger方程,从理论上证明了考虑梁的大挠度和转动惯性时梁中存在
包络孤立波. 相似文献
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利用Ham ilton变分原理,导出了计及有限变形和横向Possion效应的弹性杆中非线性纵向波动方程.利用Jacob i椭圆正弦函数展开和第三类Jacob i椭圆函数展开法,对该方程和截断的非线性方程进行求解,得到了非线性波动方程的两类准确周期解及相应的孤波解和冲击波解,讨论了这些解存在的必要条件. 相似文献
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In the present paper the propagation property of nonlinear waves in a thin viscoelastic tube filled with incom-pressible inviscid fluid is studied.The tube is considered to be made of an incompressible isotropic viscoelastic material described by Kelvin-Voigt model.Using the mass conservation and the momentum theorem of the fluid and radial dynamic equilibrium of an element of the tube wall,a set of nonlinear partial differential equations governing the prop-agation of nonlinear pressure wave in the solid-liquid coupled system is obtained.In the long-wave approximation the nonlinear far-field equations can be derived employing the reductive perturbation technique (RPT).Selecting the expo-nent α of the perturbation parameter in Gardner-Morikawa transformation according to the order of viscous coefficient η,three kinds of evolution equations with soliton solution,i.e.Korteweg-de Vries (KdV)-Burgers,KdV and Burgers equations are deduced.By means of the method of traveling-wave solution and numerical calculation,the propagation properties of solitary waves corresponding with these evolution equations are analysed in detail.Finally,as a example of practical application,the propagation of pressure pulses in large blood vessels is discussed. 相似文献
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对钢质和铜质金属圆柱壳的轴向冲击动力响应进行了实验研究,记录了两种不同材料圆柱壳在大质量低速冲击下的冲击力时程曲线,得到其屈曲模态。采用高速摄像及模拟技术给出了钢质圆柱壳渐进屈曲的全过程,为理解钢质圆柱壳的屈曲机理提供了直观的结果。黄铜质圆柱壳在大质量低速冲击下, 出现整个壳面滿布屈曲波纹的塑性动力屈曲现象,说明高速冲击不是产生塑性动力屈曲的充要条件。像铜这样具有高密度的韧性材料,在大质量低速冲击下,会在轴向产生持续的压缩塑性流作用而出现塑性动力屈曲现象。 相似文献
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