电压激励下压电层合结构的动力学分析

发布时间：2018-04-20 14:12

本文选题：压电层合结构 + 电压激励　；参考：《中北大学》2015年硕士论文

【摘要】：压电层合结构在工程中已经被广泛地使用，其常被用在生产传感器、转换器、驱动器等设备中。由于压电智能层合结构的应用研究起步不久，为保证该类结构在外激励下安全可靠地工作，有许多基础性力学问题急需解决。以压电层合梁、板为代表的分布式结构成为高性能压电元件设计的理想结构形式，分析压电层合梁、板结构的动力学问题有着重要的应用价值和理论意义。论文以压电陶瓷-金属-压电陶瓷对称层合结构为研究对象，研究了其受电压激励时的响应问题。首先阐述了论文的研究目的及意义，介绍了压电材料的种类及性能，压电方程及相关理论，国内外研究现状等。其次基于Lagrange方程得到了等截面压电层合对称悬臂梁在横向激振电压下的强迫振动微分方程。用ANSYS软件对建立的相关有限元模型进行动力学仿真分析，仿真结果与理论值基本吻合，验证了理论的正确性。进一步分析了阻尼对横向位移响应的影响，讨论了速度、加速度随时间的变化规律，分析了压电悬臂梁的最大应力出现位置及最大应力值随时间的关系。结果表明阻尼的大小对拍的形成及持续时间有一定的影响，振动时最大应力位置出现在靠近固定端的压电陶瓷与基体材料的粘接处。然后基于考虑了压电材料的电致弹性和电致伸缩效应的非线性本构方程，依据VonKarman大挠度理论、Hamilton原理和Rayleigh-Ritz法推导出了电压激励下的压电层合矩形薄板的非线性振动方程。求得了压电层合薄板主共振时幅频响应方程并通过算例验证了理论的正确性。证明了当激励电场较大时，压电材料的非线性效应不可忽略，说明了本文层合薄板非线性振动理论也适用于厚宽比小于0.2的压电层合梁结构。最后对电压激励下压电层合薄板进行了主共振分析，讨论了共振解的稳定性，分析了电压、阻尼、厚度比等参数对结构主共振的影响；依据薄板的非线性振动方程，探究了电压、阻尼对薄板结构的非线性分岔和混沌的影响。表明了薄板结构会出现多值、跳跃、硬弹簧特性、分岔与混沌等非线性动力学行为。
[Abstract]:Piezoelectric laminated structures have been widely used in engineering. They are often used in the production of sensors, converters, actuators and other equipment. Since the application research of piezoelectric intelligent laminated structures has started soon, in order to ensure the safety and reliability of the structures under external excitation, there are many basic mechanical problems need to be solved. The distributed structure represented by piezoelectric laminated beam and plate is an ideal structure for the design of high performance piezoelectric elements. It is of great application value and theoretical significance to analyze the dynamic problems of piezoelectric laminated beam and plate structure. In this paper, the symmetrical laminated structure of piezoelectric ceramics-metal-piezoelectric ceramics is studied, and the response of piezoelectric ceramics to voltage excitation is studied. Firstly, the purpose and significance of this paper are described, and the kinds and properties of piezoelectric materials, piezoelectric equations and related theories, and the research status at home and abroad are introduced. Secondly, based on Lagrange equation, the differential equation of forced vibration of piezoelectric laminated symmetric cantilever beam with constant cross section under transverse excitation voltage is obtained. The dynamic simulation analysis of the relevant finite element model is carried out by using ANSYS software. The simulation results are in good agreement with the theoretical values, and the correctness of the theory is verified. The influence of damping on lateral displacement response is further analyzed. The variation of velocity and acceleration with time is discussed. The position of maximum stress and the relationship between maximum stress and time of piezoelectric cantilever beam are analyzed. The results show that the damping has a certain influence on the formation and duration of the beat, and the maximum stress position during vibration occurs near the bond between the piezoelectric ceramics and the substrate material near the fixed end. Then, based on the nonlinear constitutive equations considering the electro-elastic and electrostrictive effects of piezoelectric materials, the nonlinear vibration equations of piezoelectric laminated rectangular thin plates under voltage excitation are derived based on VonKarman's large deflection theory and Rayleigh-Ritz 's method. The amplitude-frequency response equation of piezoelectric laminated thin plate at main resonance time is obtained, and the correctness of the theory is verified by an example. It is proved that the nonlinear effect of piezoelectric material can not be ignored when the excited electric field is large. The nonlinear vibration theory of laminated thin plates is also applicable to piezoelectric laminated beam structures with thickness to width ratio less than 0.2. Finally, the main resonance analysis of piezoelectric laminated thin plate subjected to voltage excitation is carried out, and the stability of resonance solution is discussed, the influence of voltage, damping and thickness ratio on the main resonance of the structure is analyzed, and the nonlinear vibration equation of thin plate is presented. The effects of voltage and damping on nonlinear bifurcation and chaos of thin plate structures are investigated. It is shown that nonlinear dynamical behaviors such as multi-value, jump, hard spring, bifurcation and chaos will occur in thin plate structure.
【学位授予单位】：中北大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：TQ174.1;TB34

【参考文献】