本文選題：壓電層合結(jié)構(gòu) + 電壓激勵(lì)　； 參考：《中北大學(xué)》2015年碩士論文

【摘要】：壓電層合結(jié)構(gòu)在工程中已經(jīng)被廣泛地使用，其常被用在生產(chǎn)傳感器、轉(zhuǎn)換器、驅(qū)動(dòng)器等設(shè)備中。由于壓電智能層合結(jié)構(gòu)的應(yīng)用研究起步不久，為保證該類結(jié)構(gòu)在外激勵(lì)下安全可靠地工作，有許多基礎(chǔ)性力學(xué)問(wèn)題急需解決。以壓電層合梁、板為代表的分布式結(jié)構(gòu)成為高性能壓電元件設(shè)計(jì)的理想結(jié)構(gòu)形式，分析壓電層合梁、板結(jié)構(gòu)的動(dòng)力學(xué)問(wèn)題有著重要的應(yīng)用價(jià)值和理論意義。論文以壓電陶瓷-金屬-壓電陶瓷對(duì)稱層合結(jié)構(gòu)為研究對(duì)象，研究了其受電壓激勵(lì)時(shí)的響應(yīng)問(wèn)題。 首先闡述了論文的研究目的及意義，介紹了壓電材料的種類及性能，壓電方程及相關(guān)理論，國(guó)內(nèi)外研究現(xiàn)狀等。 其次基于Lagrange方程得到了等截面壓電層合對(duì)稱懸臂梁在橫向激振電壓下的強(qiáng)迫振動(dòng)微分方程。用ANSYS軟件對(duì)建立的相關(guān)有限元模型進(jìn)行動(dòng)力學(xué)仿真分析，仿真結(jié)果與理論值基本吻合，驗(yàn)證了理論的正確性。進(jìn)一步分析了阻尼對(duì)橫向位移響應(yīng)的影響，討論了速度、加速度隨時(shí)間的變化規(guī)律，分析了壓電懸臂梁的最大應(yīng)力出現(xiàn)位置及最大應(yīng)力值隨時(shí)間的關(guān)系。結(jié)果表明阻尼的大小對(duì)拍的形成及持續(xù)時(shí)間有一定的影響，振動(dòng)時(shí)最大應(yīng)力位置出現(xiàn)在靠近固定端的壓電陶瓷與基體材料的粘接處。 然后基于考慮了壓電材料的電致彈性和電致伸縮效應(yīng)的非線性本構(gòu)方程，依據(jù)VonKarman大撓度理論、Hamilton原理和Rayleigh-Ritz法推導(dǎo)出了電壓激勵(lì)下的壓電層合矩形薄板的非線性振動(dòng)方程。求得了壓電層合薄板主共振時(shí)幅頻響應(yīng)方程并通過(guò)算例驗(yàn)證了理論的正確性。證明了當(dāng)激勵(lì)電場(chǎng)較大時(shí)，壓電材料的非線性效應(yīng)不可忽略，說(shuō)明了本文層合薄板非線性振動(dòng)理論也適用于厚寬比小于0.2的壓電層合梁結(jié)構(gòu)。 最后對(duì)電壓激勵(lì)下壓電層合薄板進(jìn)行了主共振分析，討論了共振解的穩(wěn)定性，分析了電壓、阻尼、厚度比等參數(shù)對(duì)結(jié)構(gòu)主共振的影響；依據(jù)薄板的非線性振動(dòng)方程，探究了電壓、阻尼對(duì)薄板結(jié)構(gòu)的非線性分岔和混沌的影響。表明了薄板結(jié)構(gòu)會(huì)出現(xiàn)多值、跳躍、硬彈簧特性、分岔與混沌等非線性動(dòng)力學(xué)行為。
[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.
【學(xué)位授予單位】：中北大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：TQ174.1;TB34

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