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On the basis of classical linear theory on longitudinal, torsional and flexural waves in thin elastic rods, and taking finite deformation and dispersive effects into consideration, three kinds of nonlinear evolution equations are derived. Qualitative analysis of three kinds of nonlinear equations are presented. It is shown that these equations have homoclinic or heteroclinic orbits on the phase plane, corresponding to solitary wave or shock wave solutions, respectively. Based on the principle of homogeneous balance, these equations are solved with the Jacobi elliptic function expansion method. Results show that existence of solitary wave solution and shock wave solution is possible under certain conditions. These conclusions are consistent with qualitative analysis. 相似文献
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有限变形弹性杆中三种非线性弥散波 总被引:4,自引:2,他引:2
在一维弹性细杆拉压、扭转和弯曲波的经典线性理论基础上,分别计入有限变形和弥散效应,借助Hamilton变分原理,由统一的方法导出了3种非线性弥散波的演化方程.对3种演化方程进行了定性分析.结果表明,这些方程在相平面上存在同宿轨道或异宿轨道,分别相应于孤波解或冲击波解.根据齐次平衡原理,用Jacobi椭圆函数展开对这些演化方程进行了求解,在一定的条件下它们均可能存在孤立波解或冲击波解,这与方程的定性分析完全一致. 相似文献
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By using the energy criterion in[3],the impact torsional buckling for the rigid plastic cylindrical shell is studied.The linear dynamic torsional buckling equations for the rigid plastic shell is drived,and the critical impact velocity is given. 相似文献
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圆板振子超谐分岔和混沌运动的实验研究 总被引:9,自引:0,他引:9
设计了非线性圆板混沌实验振动台,就轴对称圆板在简谐载荷作用下的非线性动力学行为进行了较为系统的实验研究,理论分析和数值计算,对基础作简谐运动,周边固支圆板,进行了实验。通过测量时间-中心挠度的加速度曲线,进行快速傅立叶变换(FFT)分析,实验发现了对称破缺,超谐分岔,调幅调相等复杂现象;对基础作简谐运动,周边固支,中心加质量块的圆板,进行了实验,通过测量时间-周边应变曲线,进行FFT分析,实验发现了混沌,对称破缺和恢复及超谐分岔等复杂动力学行为。 相似文献
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The dynamic buckling of an elastic-plastic column subjected to an axial impact by a rigid body was discussed by using the energy law. The traveling process of elastic-plastic waves under impact action was analyzed by characteristics method. The equation of lateral disturbance used to analyze the problem was developed by taking into account the effect of elastic-plastic stress wave. The power series solution of this problem has been the power series approach. The buckling criterion of this problem was proposed by analyzing the characteristics of the solution. The relationship among critical velocity and impact mass, critical buckling length, hardening modulus was given by using theoretical analysis and numerical computation. 相似文献