【作者】 李向阳；

【导师】 于开平；

【作者基本信息】 哈尔滨工业大学 ， 一般力学与力学基础， 2019， 博士

【摘要】 夹层结构通常具有高比强度、高比刚度、优良的隔声与隔热等特性,目前已经被广泛应用于船舶、高速列车、航空航天等工程结构中。在极端的高温和噪声环境中,热应力、气动噪声与机械载荷叠加对整个飞行器结构产生巨大影响。因此深入研究夹层结构的动力学特性对结构设计具有深远意义。随着微电子机械系统、集成电路以及智能系统和结构的快速发展,使能量收集技术为低功耗微电子设备和无线传感网络提供能源成为一种可能。本文提出一种分段剪切变形理论,分析夹层结构的动力学性能,包括自由振动、振动声辐射、传声损失、后屈曲等特性;并根据新提出的分段剪切变形理论,设计出几种高效的夹层基振动能量收集器,用于从宽频、低频和低振幅振动源中获得能量。本文的主要研究内容如下:(1)现有的理论模型,有的精度低,难以准确预测夹层结构动力学特性;有的模型过于复杂,难以用来分析夹层结构的声振响应和后屈曲特性。本文提出一种简单、准确而又高效的分段剪切变形理论,可以方便的分析夹层结构在高温环境下的自由振动、振动声辐射、传声损失、后屈曲等动力学特性。根据哈密顿变分原理得到夹层板在高温环境下的振动控制方程,对四边简支边界条件下夹层板动力学特性进行理论求解,分析温度对夹层板固有频率、振动声辐射和传声损失的影响。(2)固支边界条件下板振动的精确理论解通常难以获得。本文研究夹层板在四边固支边界条件下振动、隔声等动力学特性。首先从简单的复合材料层合板入手,基于经典层合板理论和一阶剪切变形理论,利用假设模态法和伽辽金加权余值的思想,得到层合板自由振动的近似解析解;然后将这种方法推广到夹层板中,根据本文新提出的分段剪切变形理论,得到四边固支夹层板动力学响应的近似解析解;最后对四边固支边界条件下夹层板的自由振动特性、声振特性等进行了理论研究。(3)建立了夹层梁结构的分段剪切变形理论模型,对夹层梁热后屈曲和自由振动特性进行了理论研究,包括两边简支边界和两边固支边界两种工况。首先根据虚功原理得到了夹层梁的非线性控制方程,并利用其线性化方程推导出了夹层梁的固有频率和屈曲温度;然后利用非线性方程得到了夹层梁屈曲之后新的平衡位置,推导了当温度超过临界温度时,夹层梁屈曲后自由振动结果;最后详细分析了温度对屈曲和振动特性的影响。(4)设计了夹层基压电振动能量收集器,建立了夹层基振动能量收集器的分段剪切变形理论模型,采用拉格朗日方程得到了夹层基振动能量收集器的机电耦合方程。夹层基振动能量收集器与相同几何尺寸的传统振动能量收集器相比具有更低的共振频率,并且能输出更高的电压;如果以某一共振频率为设计目标,与传统振动能量收集器相比,夹层基振动能量收集器可以大幅度降低系统质量。详细地研究了材料属性和几何参数对能量收集器性能的影响。通过实验研究了不同芯层材料对夹层基振动能量收集器固有频率和输出电压的影响。(5)设计出多个夹层基多模态振动能量收集器,来证明夹层基振动能量收集器具有更好的可设计性。为了建立夹层基多模态振动能量收集器的理论模型,首先研究了传统的单层金属基础多模态振动能量收集器,建立了多模态振动能量收集器的理论模型。进而将这一理论推广到夹层基多模态振动能量收集器中。构造了一个含有两个内部支梁的夹层基多模态振动能量收集器,并完成实验测试。通过与实验结果和有限元仿真对比,验证了理论模型的有效性。通过参数优化和夹层基单模态能量收集器进行对比,说明了夹层基多模态振动能量收集器更适合从宽频、低频和低振幅振动源中获得能量。设计了一种内部含有三个悬臂梁的双压电片夹层基多模态振动能量收集器,通过改变内部悬臂梁几何参数和附加质量块大小,使前几阶固有频率充分接近,并均匀地分布在感兴趣的频率范围内,进一步说明了夹层基振动能量收集器具有灵活的设计性,可以适用于不同的振动环境中。更多还原

【Abstract】 Sandwich structure has properties such as high specific strength,high specific stiffness,excellent sound and heat insulation,etc.Thus,it has been widely used in ships,high-speed trains,aerospace and other engineering structures.In extreme high temperature and noise environment,the combination of thermal stress,aerodynamic noise and mechanical loading has a major impact on the aircraft structure.Therefore,studing dynamic characteristics of the sandwich structure is of significance for structural design.With the rapid development of MEMS,integrated circuit technology,and intelligent systems and structures,it is possible for energy harvesting technology to provide energy for low-power microelectronic devices and wireless sensor networks.In this dissertation,a piecewise shear deformation theory is proposed to analyze dynamic characteristics of sandwich structures,including free vibration,sound radiation,sound transmission loss,post-buckling,etc.Based on the proposed theory of piecewise shear deformation,several kinds of efficient energy harvesters are designed to harvesting energy from broadband,low-frequency and low-amplitude vibration sources.The main research contents of this dissertation are as follows:(1)Some of the existing theoretical models have low accuracy and are difficult to accurately predict the dynamic characteristics of sandwich structures.Some theoretical models are too complicated and can hardly analyze the vibro-acoustic and post-buckling characteristics of sandwich structures.In this dissertation,a simple,accurate and efficient piecewise shear deformation theory is proposed to conveniently analyze dynamic characteristics of sandwich structure such as free vibration,sound radiation,sound transmission loss and post-buckling in thermal environment.The governing equations in thermal environment are obtained based on Hamilton’s principle.For simply supported boundary condition,the analytical solution of sandwich plate is derived and the influence of temperature on the natural frequency,sound radiation and sound transmission loss is studied.(2)In general,it is difficult to obtain analytical solution of plate for clamped boundary conditions.To study dynamic characteristics such vibration and sound insulation of clamped sandwich plate,this dissertation starts from a simple composite laminated plate.The approximate analytic solution of the laminated plate is firstly obtained by assumed-mode method and Galerkin weighted residual method based on the classical laminated theory and first-order shear deformation theory.Then this modeling is extended to the sandwich plate and the approximate analytical solution of the clamped sandwich plate is obtained based on the proposed piecewise shear deformation theory.The free vibration and vibro-acoustic characteristics of clamped sandwich plate are finally studied theoretically.(3)The piecewise shear deformation theory of sandwich beam is proposed.Thermal post-buckling and free-vibration characteristics of the sandwich beam are studied theoretically,including simple supported boundary and clamped boundary conditions.The nonlinear governing equations of the sandwich beam are obtained based on the principle of virtual work.The natural frequency and buckling temperature of the sandwich beam are derived.The new equilibrium position of the sandwich beam after buckling is obtained using the nonlinear equations.The free vibration of the sandwich beam after buckling is obtained when the temperature exceeds the critical one.The influence of temperature on buckling and vibration characteristics is analyzed in detail.(4)The sandwich piezoelectric vibration energy harvester is designed,the piecewise shear deformation theroy of sandwdich vibtation energy harvester is proposed and electromechanical coupling equations are obtained using the Lagrangian equation.The proposed sandwich vibration energy harvester has lower resonant frequency and generates higher voltage output than the conventional vibration energy harvester with the same geometrical dimension.If designed for a certain resonant frequency,the proposed sandwich vibration energy harvester will be much smaller and lighter than the conventional vibration energy harvester.The influence of material properties and geometric parameters on the performance of the proposed sandwich vibration energy harvester is investigated in detail.A comparative study of different core materials for the sandwich vibration energy harvester is presented experimentally.(5)Several multi-mode sandwich piezoelectric vibration energy harvesters are designed and fabricated to validate the high design flexibility of sandwich piezoelectric vibration energy harvester.To derive the theoretical model of multi-mode sandwich piezoelectric vibration energy harvester,a conventional multi-mode vibration energy harvester is firstly designed and studied,and analytical modeling of the conventional multi-mode vibration energy harvester is proposed.Then this modeling is extended to the multi-mode sandwich vibration energy harvester.A multi-mode sandwich vibration energy harvester with two inner beams is designed,fabricated and tested.The good agreement with experimental and simulation results validates the accuracy of the theory.The parametric optimization and comparison with single-mode harvester presents that the sandwich multi-mode vibration energy harvester is more suitable to harvster energy from broadband,low-frequency and low-amplitude vibration sources.A multi-mode sandwich vibration energy harvester with three inner cantilevered beams is designed comprised of two patches of piezoelectric layer.The resonant frequencies of the energy harvester could be easily tuned to be sufficiently close and well distributed by varying the geometric parameters and the tip masses of the inner beams.This harvester further illustrates the excellent design flexibility of sandwich piezoelectric vibration energy harvester to work in various vibration environments.更多还原