基于非局部弹性理论的纳米板横向振动

发布时间：2018-03-19 14:56

本文选题：非局部弹性理论　切入点：纳米板　出处：《力学季刊》2016年03期 　论文类型：期刊论文

【摘要】：本文利用非局部弹性理论研究了单层石墨烯的纳米板的横向自由振动响应.通过迭代法推导了非局部应力表达,进一步通过哈密顿原理推导了纳米板的控制方程,应用纳维解法得到四边简支纳米板振动固有频率的数值解,并将本文研究结果与已有文献结果进行对比,进一步讨论了小尺寸效应,以及纳米板的三维尺寸和半波数对振动频率的影响.结果表明:非局部效应的存在使得纳米板的等效刚度和固有频率降低;半波数的增加则使得纳米板的固有频率提高.相关分析结果对基于二维纳米材料的新设备的设计和优化具有重要意义.
[Abstract]:In this paper, the lateral free vibration response of graphene monolayer nanoplates is studied by using the nonlocal elastic theory. The nonlocal stress expression is derived by iterative method, and the governing equation of the nanoplate is derived by the Hamiltonian principle. The numerical solution of the vibration natural frequency of simply supported nanoplates with four edges is obtained by using the method of Navier. The small size effect is further discussed by comparing the results of the present study with those obtained in previous literatures. The effect of 3D size and half wave number on the vibration frequency is also discussed. The results show that the effective stiffness and natural frequency of the nanoplate are reduced due to the existence of nonlocal effect. The increase of half-wave number will increase the natural frequency of nanoplate. The results of correlation analysis are of great significance for the design and optimization of new equipment based on two-dimensional nanomaterials.
【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(11572210,51406128) 苏州市科技计划项目(SYG201537) 江苏省自然科学基金(BK20140342) 苏州大学“东吴学者”计划(R513300116)
【分类号】：O326

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