功能梯度压电层合板的强迫振动分析

发布时间：2018-01-12 06:20

本文关键词：功能梯度压电层合板的强迫振动分析　出处：《中北大学》2017年硕士论文　论文类型：学位论文

【摘要】：功能梯度压电材料是一种新型智能材料,在航天、航空、化工、电动控制、机械系统等领域发挥着重要作用。近年来,其力学行为上的研究出现了一些成果,但仍存在许多急需解决的难题,尤其是振动问题已成为国内外研究的热点。文章首先对论文的研究背景和意义做了阐述,简要介绍了功能梯度材料、压电材料、功能梯度压电材料及其国内外研究现状。通过建立功能梯度层合板的几何模型,利用哈密顿原理推导出机械力作用下功能梯度层合板的非线性动力学方程。利用Matlab软件对薄板进行非线性主共振分析,主要讨论了层合板在不同边界条件下对主共振的影响,其次分析了阻尼、幂率指数、机械力等参数越大对系统动力响应越明显,越容易发生跳跃现象,使系统处于不稳定状态。最后以功能梯度压电层合板结构为研究对象,基于压电材料和功能梯度材料的应力应变方程,推导出电压激励下功能梯度压电层合板的非线性动力学方程,然后利用多尺度法推导出幅频响应方程;通过改变简谐电压、系统阻尼、功能梯度板的幂率指数和功能梯度板的厚度等参数的大小,分析这些参数与主共振之间的联系;最后分析了电压和阻尼对系统分岔与混沌的影响,并绘制出系统的相图。
[Abstract]:Functionally graded piezoelectric (FGM) is a new type of intelligent material, which plays an important role in the fields of aerospace, aviation, chemical industry, electric control, mechanical system and so on. In recent years, some achievements have been made in the study of its mechanical behavior. However, there are still many difficult problems that need to be solved, especially the vibration problem has become a hot spot at home and abroad. Firstly, the research background and significance of this paper are described, and the functionally graded materials and piezoelectric materials are briefly introduced. The research status of functionally graded piezoelectric materials at home and abroad. The geometric model of functionally graded laminated plates is established. The nonlinear dynamic equations of functionally graded laminated plates under mechanical force are derived by using Hamiltonian principle. The nonlinear principal resonance analysis of thin plates is carried out by using Matlab software. This paper mainly discusses the influence of laminated plates on the main resonance under different boundary conditions. Secondly, the larger the damping, the exponent and the mechanical force, the more obvious the dynamic response of the system is, and the more easy to jump. Finally, the structure of functionally graded piezoelectric laminates is taken as the research object, based on the stress-strain equations of piezoelectric materials and functionally graded materials. The nonlinear dynamic equations of functionally graded piezoelectric laminates under voltage excitation are derived, and the amplitude-frequency response equations are derived by using the multi-scale method. By changing the parameters of harmonic voltage, system damping, power ratio exponent of functionally gradient plate and thickness of functional gradient plate, the relationship between these parameters and the main resonance is analyzed. Finally, the effects of voltage and damping on the bifurcation and chaos of the system are analyzed, and the phase diagram of the system is drawn.
【学位授予单位】：中北大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TB381

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