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非齐次边界条件下轴向运动梁的非线性振动

张登博 唐有绮 陈立群

张登博, 唐有绮, 陈立群. 非齐次边界条件下轴向运动梁的非线性振动[J]. 力学学报, 2019, 51(1): 218-227. doi: 10.6052/0459-1879-18-189
引用本文: 张登博, 唐有绮, 陈立群. 非齐次边界条件下轴向运动梁的非线性振动[J]. 力学学报, 2019, 51(1): 218-227. doi: 10.6052/0459-1879-18-189
Zhang Dengbo, Tang Youqi, Chen Liqun. NONLINEAR VIBRATIONS OF AXIALLY MOVING BEAMS WITH NONHOMOGENEOUS BOUNDARY CONDITIONS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(1): 218-227. doi: 10.6052/0459-1879-18-189
Citation: Zhang Dengbo, Tang Youqi, Chen Liqun. NONLINEAR VIBRATIONS OF AXIALLY MOVING BEAMS WITH NONHOMOGENEOUS BOUNDARY CONDITIONS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2019, 51(1): 218-227. doi: 10.6052/0459-1879-18-189

非齐次边界条件下轴向运动梁的非线性振动

doi: 10.6052/0459-1879-18-189
基金项目: 1) 国家自然科学基金重点项目(11232009)和国家自然科学基金项目(11672186,11502147, 11602146, 11572182)资助.
详细信息
    作者简介:

    作者简介: 2) 张登博,博士研究生,主要研究方向:非线性动力学与振动控制. E-mail:zhangdengbo2009@163.com;

    通讯作者:

    张登博,唐有绮,陈立群

    张登博,唐有绮,陈立群

    张登博,唐有绮,陈立群

  • 中图分类号: O323;

NONLINEAR VIBRATIONS OF AXIALLY MOVING BEAMS WITH NONHOMOGENEOUS BOUNDARY CONDITIONS

  • 摘要: 轴向运动系统的横向非线性振动一直是国内外研究的热点课题之一.目前相关研究大都是针对齐次边界条件的.但是在工程实际中,非齐次边界条件更为常见,而针对非齐次边界条件的研究相对较少.为深入研究非齐次边界条件对轴向运动系统横向非线性振动的影响,本文以轴向变速运动黏弹性Euler梁为例,引入由黏弹性引起的非齐次边界条件,同时还引入由轴向加速度引起的径向变化张力,建立梁横向振动的积分-偏微分型运动方程,并导出了相应的非齐次边界条件.采用直接多尺度法分析了梁的次谐波参数共振.由可解性条件得到了梁的稳态响应,并根据Routh-Hurvitz判据确定了系统稳态响应的稳定性.通过数值例子讨论了黏弹性系数,轴向运动速度,轴向速度脉动幅值和非线性系数对幅频响应的影响,并详细对比分析了非齐次边界条件和齐次边界条件对幅频响应的影响.结果表明:随着黏弹性系数的增大,非齐次边界条件下的零解失稳区域和稳态响应幅值比齐次边界条件下的失稳区域和幅值大,非齐次边界条件对高阶次谐波参数共振的影响更加显著.最后,引入微分求积法来验证直接多尺度法的近似解结果.

     

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  • 刊出日期:  2019-01-18

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