基于非局部理论的轴向运动黏弹性纳米板的参数振动及其稳定性

发布时间：2018-12-26 07:01

【摘要】：研究了轴向运动黏弹性二维纳米板结构的非局部横向参数振动及其稳态响应。利用哈密顿原理推导了问题模型的控制方程,应用多尺度法分析了带有周期脉动成分的变速运动黏弹性纳米板的失稳现象。根据边界条件及复模态法可确定模态函数的表达,讨论了其特例匀速运动时固有频率与小尺度参数的关系,重点探讨了当脉动频率为两阶固有频率之和或者为某阶固有频率二倍时所发生的和型组合参数共振及主参数共振。结果表明,小尺度参数的存在使得轴向运动黏弹性纳米板的弯曲刚度及固有频率减小,并导致组合参数共振失稳区域减小但主参数共振区域增大,同时削弱了黏弹性系数对主参数共振区域的影响。同等条件下,黏弹性系数对组合共振区域的影响更为明显。
[Abstract]:The nonlocal transverse parametric vibration and its steady state response of axially moving viscoelastic two-dimensional nanoplate structures are studied. The governing equation of the problem model is derived by using the Hamiltonian principle and the instability of the variable velocity viscoelastic nanoplates with periodic pulsating components is analyzed by using the multi-scale method. According to the boundary condition and complex mode method, the expression of modal function can be determined, and the relation between the natural frequency and the small scale parameter in the uniform motion of its special case is discussed. When the pulsating frequency is the sum of the two natural frequencies or twice the natural frequency of a certain order, the sum combined parameter resonance and the principal parameter resonance are discussed. The results show that the bending stiffness and natural frequency of axially moving viscoelastic nanoplates are reduced by the existence of small scale parameters, and the resonant instability region of composite parameters decreases but the resonance region of main parameters increases. At the same time, the influence of viscoelastic coefficient on the resonance region of main parameter is weakened. Under the same conditions, the influence of viscoelastic coefficient on the combined resonance region is more obvious.
【作者单位】：苏州大学城市轨道交通学院;
【基金】：国家自然科学基金(11572210) 江苏省自然科学基金(BK20130303) 苏州市科技计划项目(SYG201537) 苏州大学“东吴学者”计划项目(R513300116)
【分类号】：O327

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