复合材料点阵夹芯板非线性组合共振特性研究  

Research on Nonlinear Combination Resonance Characteristics of Composite Lattice Sandwich Piate

作　　者：马婷[1] 张伟[2] Ma Ting;Zhang Wei(College of Mechanical Engineering,Beijing University of Technology,Beijing 100124,China;School of Civil Engineering and Architecture,Guangxi University,Nanning 530004,China)

机构地区：[1]北京工业大学材料与制造学部,北京100124 [2]广西大学土木建筑工程学院,南宁530004

出　　处：《动力学与控制学报》2024年第4期23-29,共7页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(11832002,12072201)。

摘　　要：复合材料点阵夹芯板在1:3内共振和外部组合共振同时发生时的非线性共振问题被研究.首先,基于哈密顿原理和分层位移场理论建立了复合材料夹芯板的振动偏微分方程,然后利用多尺度方法求解了伽辽金离散后的常微分方程,并得到了内共振和组合共振同时存在下夹芯板的协调方程.最后利用数值方法得到了协调方程稳态平衡解随系统参数变化的分岔图.研究了不同点阵芯子胞元构型,外激励频率以及外激励幅值对复合材料点阵夹芯板非线性组合共振特性所产生的影响.The nonlinear resonance problem of composite lattice sandwich panels is studied when both 1:3 internal resonance and external combined resonance occur simultaneously.Firstly,based on Hamiltonian principle and layered displacement field theory,the vibration partial differential equation of composite sandwich panels was established.Then,the ordinary differential equation obtained by Galerkin discretization was solved using multi-scale method,and the modulation equation of the sandwich panel was obtained in the presence of both internal and combination resonances.Finally,the bifurcation diagram of the steady-state equilibrium solution of the modulation equation with changes in system parameters was obtained using numerical methods.The effects of different lattice core cell configurations,external excitation frequencies,and external excitation amplitudes on the nonlinear combined resonance characteristics of composite lattice sandwich panels is studied.

关 键 词：夹芯板 组合共振 点阵 非线性 内共振 

分 类 号：O322[理学—一般力学与力学基础]