含黏弹性夹芯FG-GRC后屈曲梁的低速冲击响应  

LOW-VELOCITY IMPACT RESPONSES OF FG-GRC SANDWICH BEAMS WITH VISCOELASTIC CORES

作　　者：金其多 任毅如[1,2] 胡绚 蒋宏勇[1,2] Jin Qiduo;Ren Yiru;Hu Xuan;Jiang Hongyong(College of Mechanical and Vehicle Engineering,Hunan University,Changsha 410082,China;State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body,Hunan University,Changsha 410082,China)

机构地区：[1]湖南大学机械与运载工程学院,长沙410082 [2]湖南大学汽车车身先进设计与制造国家重点实验室,长沙410082

出　　处：《力学学报》2021年第1期194-204,共11页Chinese Journal of Theoretical and Applied Mechanics

基　　金：工信部基础产品创新科研项目(237099000000170008);国家自然科学基金项目(11402011)资助。

摘　　要：研究了含黏弹性夹芯的功能梯度石墨烯增强复合材料(functionally graded graphene reinforced composite,FG-GRC)后屈曲梁在低速跌落冲击下的跳跃振荡行为.采用修正Halpin-Tsai细观模型预测FG-GRC的材料宏观属性.使用赫兹点接触模型确定冲击器和梁之间的接触力.提出了考虑轴向预应力的复合材料层本构关系和阻尼层的Kelvin型黏弹性本构.通过一种广义高阶剪切变形锯齿梁模型建立夹芯梁的非线性位移场.基于Hamilton能量变分原理,推导了动力学控制方程组.通过两步分析,首先获得弹性后屈曲平衡路径作为冲击问题的初始状态.随后,结合四阶龙格库塔法,拓展了两步摄动−伽辽金法计算接触力的时程曲线以及后屈曲梁的位移时程曲线.研究了后屈曲梁在单次和两次撞击下双稳态大幅振荡过程的动力学特征.讨论了轴向载荷、冲击速度、黏弹性阻尼特性、冲击器材料等因素对于碰撞接触力以及后屈曲梁动力响应的影响规律.结果表明,接触力仅对冲击速度较为敏感,一定的结构碰撞参数设计可以在接触力变化不大的情况下,使得后屈曲梁由单势能阱运动转变为双阱大幅振荡.The dynamic snap-through and oscillation behaviors are studied of a post-buckled functionally graded graphene reinforced composite(FG-GRC)beam with a viscoelastic core under low-velocity impact.The modified Halpin Tsai meso-mechanical model is used to predict the material properties of FG-GRC.The Hertz point contact model is used to calculate the contact force between the impactor and the post-buckled beam.Considering the axial prestress,the constitutive relations of the composite layer and the Kelvin type viscoelastic constitutive model of the damping layer are proposed.A generalized higher-order shear deformation zig-zag beam theory is utilized to model the nonlinear displacement fields.Based on the Hamilton energy variational principle,the governing equations of dynamics are derived.Through two-step analysis,the post-buckling equilibrium paths are obtained as the initial state condition for the impact problem analysis.Further,combined with the fourth-order Runge Kutta method,the two-step perturbation-Galerkin method is extended to simulate the time history curves of the contact force and the dynamic response curves of the postbuckled beams.Compared with the results based on other beam models,the correctness of the material model,theoretical model and computation method is validated.The dynamic characteristics of bi-stable large amplitude vibration of the post-buckled beams under single and two collisions are studied.The effects of axial load,impact velocity,viscoelastic damping characteristics and impactor materials on the contact force and the deflection time history curves of the postbuckled beams are discussed.The results suggest that the contact force is only sensitive to the impact velocity.A certain structural collision parameter design can change the response of the post-buckled beam from single potential energy trap motion to double trap large oscillation,and the contact force is approximately unchanged.The results of this work can be of reference significance for the design of bi-stable energy capture

关 键 词：低速冲击 后屈曲梁 FG-GRC 跳跃振荡 黏弹性 

分 类 号：O347.1[理学—固体力学]