摘要
研究石墨烯片增强功能梯度(FG-GPLRC)梁在电场作用下的非线性动力响应.考虑介电效应,石墨烯片(GPL)含量沿梁厚度方向按照三种分布方式梯度变化,由有效介质理论计算等效弹性模量和等效介电常数.基于von Kármán非线性应变-位移关系,并利用拉格朗日方程推导获得非线性动力学控制方程组,引入位移近似函数将该方程组采用瑞利-里兹法转换为非线性常微分方程,并用龙格库塔法进行数值求解获得动力响应.讨论变电场作用下的FG-GPLRC梁的非线性动力响应分别与GPL体积分数、分布模式、GPL几何尺寸、预施加的拉应力、直流电压和交流电频率之间的关系.定量分析表明通过调整多个参数,可以对FG-GPLRC梁的动力响应进行设计.
The nonlinear dynamic response of graphene platelets reinforced functionally graded(FG-GPLRC)beams under electric field is studied.Considering the dielectric effect,the content of graphene platelets(GPL)varies gradiently along the thickness direction of the beam in three distribution modes,and the equivalent elastic modulus and equivalent dielectric constant are calculated by the effective medium theory.Based on the von Kármán nonlinear strain-displacement relationship,the nonlinear dynamic governing equations are derived by Lagrange equation.The displacement approximation function is introduced to convert the equations into nonlinear ordinary differential equations by the Rayleigh-Ritz method,and the dynamic response is obtained by numerical solution of the Runge-Kutta method.The relationships between the nonlinear dynamic response of the FG-GPLRC beam under variable electric field and GPL volume fraction,distribution mode,GPL geometric size,pre-applied tensile stress,DC voltage,and AC frequency are discussed.Quantitative analysis shows that the dynamic response of FG-GPLRC beams can be designed by adjusting multiple parameters.
作者
张靖华
陈争
ZHANG Jing-hua;CHEN Zheng(School of Science,Lanzhou University of Technology,Lanzhou 730050,China)
出处
《兰州理工大学学报》
北大核心
2026年第1期164-172,共9页
Journal of Lanzhou University of Technology
基金
国家自然科学基金(12362009)
甘肃省科技计划项目(23JRRA775)。
关键词
非线性动力响应
石墨烯片增强
功能梯度梁
介电效应
nonlinear dynamic response
graphene platelets reinforcement
functionally graded beam
dielectric effect
