摘要
在经典层合板理论的基础上,研究了四边简支和四边固支边界条件下的石墨烯增强复合材料板的自由振动。通过修正的哈尔平-蔡(Halpin-Tsai)模型来估测石墨烯增强复合材料板的等效杨氏模量,并根据混合准则确定复合材料板的等效质量密度和泊松比。利用哈密顿(Hamilton)原理对复合材料板的动力学方程进行了推导。研究了石墨烯的分布模式和质量分数、板的分层数及基体材料参数等对复合材料板固有频率的影响。结果表明:只在复合材料板的上下表层添加石墨烯小块的类夹芯分布模式增强效果最好。复合材料板的固有频率随着板的分层数和石墨烯质量分数的增加而增加。不同边界条件下石墨烯材料参数和基体材料参数对固有频率的影响规律均较为接近。在达到相同的增强效果时,环氧树脂基体材料比金属基体材料更加轻质化。
Based on the classic laminate theory, this paper studies the free vibration of graphene reinforced composite plates under the boundary conditions of simply supported on four sides and fixed on four sides. The modified Halpin-Tsai model is used to estimate the effective Young’s modulus of graphene reinforced composite plates, and the effective mass density and Poisson’s ratio of the composite plate are determined according to the rule of mixture. The Hamilton principle is used to derive the dynamic equation of the composite plate. The effects of graphene distribution pattern and weight fraction, the number of layers of the plate and parameters of the matrix material on the natural frequency of the composite plate are studied. The results show that the sandwich distribution pattern of adding small graphene nanoplatelets only on the upper and lower layers of the composite plate has the best enhancement effect. The natural frequency of the composite material plate increases with the increase of the number of layers of the plate and the weight fraction of graphene. The influence of graphene material parameters and matrix material parameters on the natural frequency under different boundary conditions are similar. When achieving the same reinforcement effect, the epoxy matrix material is lighter than the metal matrix material.
作者
陆文星
陈建恩
LU Wenxing;CHEN Jianen(Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control,Tianjin 300384,China;National Demonstration Center for Experimental and Electrical Engineering Education,Tianjin University of Technology,Tianjin 300384,China)
出处
《天津理工大学学报》
2022年第5期37-44,共8页
Journal of Tianjin University of Technology
基金
国家自然科学基金资助项目(11872274)。
关键词
石墨烯小块
固有频率
复合材料板
夹芯
graphene nanoplatelets
natural frequency
composite plate
sandwich
