FGP梁非线性振动的谱几何⁃增量谐波平衡解法  

Spectral geometry-incremental harmonic balance solutions for nonlinear vibrations of FGP beams

作　　者：钟锐 王瑞华 王青山 ZHONG Rui;WANG Ruihua;WANG Qingshan(College of Mechanical and Electrical Engineering,Central South University,Changsha 410083,China;State Key Laboratory of Precision Manufacturing for Extreme Service Performance,Central South University,Changsha 410083,China)

机构地区：[1]中南大学机电工程学院,湖南长沙410083 [2]中南大学极端服役性能精准制造全国重点实验室,湖南长沙410083

出　　处：《振动工程学报》2025年第4期731-738,共8页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(52075554);中南大学中央高校基本科研业务费专项资金资助项目(2021zzts0138);湖南省研究生科研创新项目(CX20210214)。

摘　　要：针对含几何非线性因素的功能梯度多孔(FGP)梁动力学问题,提出一种谱几何⁃增量谐波平衡法(SGM⁃IHBM)研究其非线性振动特性。根据von Karman理论获得梁结构的几何非线性应变⁃位移关系,基于Timoshenko理论推导FGP梁的拉格朗日能量泛函。使用谱几何级数表征梁结构的各位移分量,并引入线性模态分量建立FGP梁的非线性降阶方程,进而采用增量谐波平衡(IHB)法追踪FGP梁降阶模型的动力学响应解。通过SGM⁃IHBM解与文献解的对比验证了本文非线性模型的正确性,进而分析了孔隙率、厚度、激励幅值等对FGP梁非线性振动特性的影响。A spectral geometry-incremental harmonic balance method(SGM-IHBM)is proposed to study the nonlinear vibration characteristics of functionally graded porous(FGP)beams with geometric nonlinearities.The geometrically nonlinear strain-displacement relationship of the beam structure is obtained according to the Von-Karman theory,and the Lagrange energy function of the FGP beam is derived based on the Timoshenko theory.The spectral geometric series are used to characterize each displacement component of the beam structure,and the linear modal components are introduced to establish the nonlinear reduced-order equations of the FGP beams,and then the incremental harmonic balance(IHB)method is used to trace the dynamical response solution of the reduced-order model of the FGP beams.The correctness of the nonlinear model in this paper is verified by comparing the SGM-IHBM solution with the literature solution,and then the effects of porosity,thickness,and excitation amplitude on the nonlinear vibration characteristics of FGP beams are analyzed.

关 键 词：非线性振动 FGP梁 谱几何 增量谐波平衡法 

分 类 号：O322[理学—一般力学与力学基础]