面内平动纳米板振动特性的两类尺度效应分析  

Vibration characteristics analysis of two types of size effects on in-plane translational nanoplates

作　　者：王璟 于洋蓝 沈火明[3] 王宇星 戴小军[5] WANG Jing;YU Yanglan;SHEN Huoming;WANG Yuxing;DAI Xiaojun(School of Mechanical Engineering,Southwest Petroleum University,Chengdu 610500,China;State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation,Southwest Petroleum University,Chengdu 610500,China;School of Mechanics and Aerospace Engineering,Southwest Jiaotong University,Chengdu 611756,China;School of Mechanical Engineering,Southwest Jiaotong University,Chengdu 611756,China;School of Civil Engineering and Architecture,Southwest Petroleum University,Chengdu 610500,China)

机构地区：[1]西南石油大学机电工程学院,四川成都610500 [2]西南石油大学油气藏地质及开发工程全国重点实验室,四川成都610500 [3]西南交通大学力学与航空航天学院,四川成都611756 [4]西南交通大学机械工程学院,四川成都611756 [5]西南石油大学土木工程与测绘学院,四川成都610500

出　　处：《振动工程学报》2025年第3期653-662,共10页Journal of Vibration Engineering

基　　金：国家自然科学基金青年科学基金资助项目(12102373);四川省自然科学基金青年科学基金资助项目(2022NSFSC1938,2023NSFSC1300,2023NSFSC1296);中央高校基本科研业务费科技创新项目(2682022CX056);四川省自然科学基金面上项目(2022NSFSC0412)。

摘　　要：基于非局部应变梯度理论研究了具有轴向速度的二维纳米薄板的横向自由振动特性。根据广义哈密顿原理建立系统面内平动的振动控制方程,以四端简支情况为例,利用复模态分析法推导了纳米板的固有频率,通过控制方程的平衡解确定了系统的临界速度,并进一步对亚临界和超临界速度下前4阶模态函数的实部和虚部进行了分析。数值结果表明,尺度效应在微纳尺度下会导致系统自振频率发生改变,非局部参数和应变梯度参数分别对纳米板的等效刚度产生“软化”和“硬化”效应,从而影响了纳米板的固有频率和模态函数,高阶频率和振型受到尺度参数的影响更为显著。The transverse free vibration characteristics of a two-dimensional nanoplate with axial velocity are investigated based on the nonlocal strain gradient theory.The vibration control equations for the in-plane advection of the system are established according to the generalized Hamilton’s principle,and the intrinsic frequency of the nanoplate is derived by using complex modal analysis in the case of a four-ended simple support.The critical velocity of the system is determined by the equilibrium solution of the control equations,and the real and imaginary parts of the first-fourth-order modal functions are further analyzed for both the sub-critical and the supercritical velocities.The numerical results show that the scaling effect leads to a change in the self-oscillation frequency of the system at the micro-and nanoscale,and the nonlocal and strain gradient parameters have‘softening’and‘hardening’effects on the equivalent stiffness of the nanoplates,respectively,which affects the intrinsic frequency and the modal function of the nanoplates.This affects the intrinsic frequency and mode function of the nanoplates,and the higher order frequencies and vibration modes are more significantly affected by the size parameters.

关 键 词：纳米板 非局部应变梯度理论 尺度效应 临界速度 

分 类 号：TB383[一般工业技术—材料科学与工程] O326[理学—一般力学与力学基础]