摘要
基于非局部应变梯度理论和Mindlin板理论,研究了热‐力‐电多场耦合下轴对称压电纳米圆板的振动特性。通过Hamilton原理推导了非局部应变梯度本构框架内的运动方程,采用微分求积法数值求解了理论模型微分方程组,分析了压电纳米圆板的振动固有频率受内尺度参数与外场参数的影响。压电纳米圆板的固有频率随着非局部参数的增大而减小,随着应变梯度特征参数的增大而增大。当非局部参数小于应变梯度特征参数时,纳米圆板表现出刚度硬化行为;当非局部参数大于应变梯度特征参数时,表现出刚度软化行为。当非局部参数等于应变梯度特征参数时,纳米圆板的刚度退化为相应的经典连续介质理论结果。此外,固有频率随着径向压力和正电压的增大而减小,随着径向拉力和负电压的增大而增大,随着温差的增加而小幅减小。特别地,研究发现当径向载荷和电压增大到一定程度时,纳米圆板出现了振动失稳现象,并分析了非局部参数与应变梯度特征参数对失稳临界径向载荷及临界电压的影响。
The coupling vibration performances of axisymmetric piezoelectric circular nanoplates under thermo-electro-mechanical fields are studied based on the nonlocal strain gradient theory and Mindlin plate theory.Hamilton’s principle is used to develop the equations of motion in the framework of nonlocal strain gradient constitutive relations,and the differential quadrature method is ad‐opted to solve differential equations describing the theoretical model.The influences of internal scale parameters and external field parameters on natural frequencies of piezoelectric circular nanoplates are analyzed.It shows that the natural frequency of piezoelec‐tric circular nanoplate decreases with an increase of the nonlocal parameter,and increases with an increase of the strain gradient characteristic parameter.When the nonlocal parameter is less than the strain gradient characteristic parameter,the circular nano‐plate demonstrates a hardening behavior.When the nonlocal parameter is greater than the strain gradient characteristic parameter,it demonstrates a softening behavior.When the nonlocal parameter is equal to the strain gradient characteristic parameter,the stiff‐ness degenerates into the corresponding result of classical continuum theory.Additionally,it indicates that the natural frequencies decrease with an increase of the radial compressive load and positive voltage,and increase with an increase of the radial tensile load and negative voltage.The natural frequency decreases slightly with an increase of the temperature.In particular,it is found that while increasing the radial load and voltage to a certain value,the vibration instability occurs.The effects of the nonlocal parameter and strain gradient characteristic parameter on the critical radial load and critical voltage are analyzed accordingly.
作者
罗秋阳
李成
LUO Qiu-yang;LI Cheng(Department of Vehicle Engineering,School of Rail Transportation,Soochow University,Suzhou 215131,China;School of Automotive Engineering,Changzhou Institute of Technology,Changzhou 213032,China)
出处
《振动工程学报》
EI
CSCD
北大核心
2022年第5期1118-1129,共12页
Journal of Vibration Engineering
基金
国家自然科学基金资助项目(11972240,12272064)。
