双功能梯度石墨烯片增强金属-陶瓷基圆柱壳的行波振动分析

Traveling wave vibration analysis of dual-functional gradient metal-ceramic matrix rotatingcylindrical shell reinforced by graphene sheets

采用Halpin-Tsai微观力学模型和传递矩阵方法,开展了旋转态双功能梯度石墨烯片增强复合材料圆柱壳体的行波振动特性研究。描述了金属-陶瓷功能梯度基体和5种石墨烯片分布模式的材料属性,基于Love壳理论和传递矩阵方法,考虑转速影响推导了任一截面状态向量的常微分方程和整体传递矩阵关系。以固支-自由(悬臂)边界条件为主,对动力学微分方程进行求解计算,验证了分析方法的合理性。结果表明:低阶模态以轴向半波数为1和周向模态的振动为主,转速引起的科氏力使行波曲线出现分离现象;行波频率随着石墨烯质量分数的增加而增大,分布模式对振型顺序的影响较小,基体体积分数指数对振动特性的影响较大,而石墨烯片层数对振动特性的影响很小,不同倍频激励对共振特性的影响不同。

Here,using Halpin-Tsai micromechanical model and transfer matrix method,traveling wave vibration characteristics of a dual-functional gradient metal-ceramic matrix rotating cylindrical shell reinforced by graphene sheets were studied.Material properties of metal-ceramic functionally gradient matrix and 5 graphene sheet distribution modes were described.Based on Love shell theory and transfer matrix method,considering effects of rotating speed,dynamic differential equations of a typical shell cross-section’s state vector and shell overall transfer matrix were derived.Taking fixed-free(cantilever)boundary condition as an example,the rationality of the analysis method was verified by solving dynamic differential equations and calculating transfer matrix.The results showed that lower order modes mainly are vibrations with axial half wave number 1 and vibrations of circumferential modes;Coriolis force caused by rotating speed causes separation of traveling wave curves;traveling wave frequencies increase with increase in graphene weight fraction;graphene sheet distribution mode has a smaller impact on sequence of vibration modes;shell matrix’s volume fraction index affects vibration characteristics more largely,while layer number of graphene sheets has a very small impact on vibration characteristics;different frequency-doubling excitations have different effects on resonance characteristics.