石墨烯片增强功能梯度介电梁的非线性动力响应

兰州理工大学学报 ›› 2026, Vol. 52 ›› Issue (1): 164-172.

• 数理科学 • 上一篇

石墨烯片增强功能梯度介电梁的非线性动力响应

张靖华^*, 陈争

兰州理工大学理学院, 甘肃兰州 730050

收稿日期:2024-01-07 出版日期:2026-02-28 发布日期:2026-03-05
通讯作者: 张靖华(1979-),甘肃渭源人,博士,教授,博导.Email:zjhhrb@163.com
基金资助:
国家自然科学基金(12362009),甘肃省科技计划项目(23JRRA775)

Nonlinear dynamic response of graphene platelets reinforced functionally graded dielectric beams

ZHANG Jing-hua, CHEN Zheng

School of Science, Lanzhou University of Technology, Lanzhou 730050, China

Received:2024-01-07 Online:2026-02-28 Published:2026-03-05

摘要/Abstract

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.

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

Abstract: 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.

Key words: nonlinear dynamic response, graphene platelets reinforcement, functionally graded beam, dielectric effect

中图分类号:

O343

张靖华, 陈争. 石墨烯片增强功能梯度介电梁的非线性动力响应[J]. 兰州理工大学学报, 2026, 52(1): 164-172.

ZHANG Jing-hua, CHEN Zheng. Nonlinear dynamic response of graphene platelets reinforced functionally graded dielectric beams[J]. Journal of Lanzhou University of Technology, 2026, 52(1): 164-172.

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石墨烯片增强功能梯度介电梁的非线性动力响应

Nonlinear dynamic response of graphene platelets reinforced functionally graded dielectric beams

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