兰州大学机构库 >土木工程与力学学院
杆梁类周期压电结构中的弹性波分析
Alternative TitleAnalysis of Elastic Waves in Periodically Piezoelectric Rod and Beam Structures
黎龙飞
Thesis Advisor郭永强
2017-05-01
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword杆梁类周期压电结构 高阶杆梁理论 修正的传递矩阵法 高频分析 被动和主动控制 弥散特性
Abstract

杆梁类周期结构由于具有通禁带特性而有望用于调制纵波、弯曲波的传播。然而,被动杆梁类周期结构具有的固定带隙的特性使其难以应用于多频率激励的工作环境,因此,能主动调控带隙大小和位置的杆梁类智能周期结构在振动控制领域中占有极其重要的地位。本文以杆梁类周期压电结构为研究对象,分析了此类结构中弹性波的带隙特性,具体工作包括:(1)利用Hamilton原理推导了任意各向异性Love压电杆(弹性杆)和Mindlin-Herrmann压电杆(弹性杆)的控制方程和本构关系,同时也建立了Timoshenko压电耦合梁结构的控制方程与本构关系,并将推导的杆梁理论与结合了回传射线矩阵法(MRRM)和传递矩阵法(TMM)的修正的传递矩阵法(MTMM)联立起来,分析杆梁类周期压电结构中弹性波的频带特性。(2)编制计算杆梁类周期压电结构中弹性波频带特性的Fortran程序,通过数值算例探究了被动控制(包括截面几何参数、电极厚度、采用的杆/梁理论以及结构构型)和主动控制(包括外接电容和外接电源反馈控制)对结构中弹性波频带的调制规律,同时利用相关物理量之间的关系得到了多种形式的弥散曲线。

研究发现:(1)本论文提出的修正的传递矩阵法在分析杆梁类周期压电结构中弹性波的频带特性时对低频和高频均适用。(2)在被动控制对结构频带曲线的影响中,改变基体杆(梁)面积和结构构型能有效调制结构的带隙特性,而电极厚度在一定范围内的变化却对结构带隙不产生明显影响。(3)在主动控制对结构频带曲线的影响中,电学闭路可作为外接电容和外接电源反馈控制之间的分界线,且可通过增大基于横向压电效应的外接电源反馈控制实现负电容效果。另外,除了周期压电梁在改变外接电容值时结构带隙几乎不发生变化外,其余电学边界对结构的频带曲线均有明显的调制效果。(4)多种形式的弥散曲线各自从不同角度综合地反映了结构中弹性波的传播规律和频带特性。

Other Abstract

The periodical rod and beam structures are expected to tune the propagation of the longitudinal waves and flexural waves due to its bandgap characteristics. However, the characteristics of the fixed bandgap for the passively periodical rod and beam structure hardly meet the requirements of the working environment with variable frequency, therefore, the intelligently periodical rod and beam structures which can actively control the position and size of bandgap are vastly important in vibration control realm. In this paper, the object of study is periodically piezoelectric rod and beam structures aforementioned and the bandgap characteristics of elastic wave in it are analyzed, and the concrete work includes:(1) The governing equations and constitutive relations of anisotropic Love piezoelectric rod (elastic rod) and Mindlin-Herrmann piezoelectric rod (elastic rod) are deduced by Hamilton theory. At the same time, the counterparts of the Timoshenko piezoelectric composite beam are also be derived. The modified transfer matrix method that uses the derived rod and beam theory and combines the method of reverberation-ray matrix with the transfer matrix method analyzes the elastic wave bandgap characteristics in periodically piezoelectric rod and beam structures.(2) A Fortran program is programmed to calculate the characteristics of the elastic wave in periodically piezoelectric rod and beam structures. The influences of passive control (including the geometric parameters of the section, the thickness of the electrode, the rod/beam theory and the structure configuration) and active control (including external capacitance and external power feedback control) on the elastic wave band in the structure are studied by numerical examples. Meanwhile the diverse dispersion curves based on relationships between physical quantities are obtained.

These results show that: (1) The modified transfer matrix method proposed in this paper is valid both in low and high frequencies for analysis of the frequency band characteristics of the elastic wave in the periodically piezoelectric rod and beam structures. (2) In the influence of the passive control on the frequency band curve, the change of host rod (beam) and structure’s configuration can efficiently model the bandgap characteristics, while the change of electrode’s thickness within a certain range cannot cause visible influence on bandgap. (3) In the influence of the active control on the frequency band curve, electric-short can be used as the boundary between the applied electric capacity and applied feedback control, and the effect of applied negative electric capacity can be realized by increasing the applied feedback control based on transverse piezoelectric effect. In addition, all electrical boundary conditions can obviously tune the band gap of periodically piezoelectric rod and beam structures except applied capacity for periodically piezoelectric beam. (4) The variously formal dispersion curves comprehensively reflect the propagation law and bandgap characteristics of the elastic wave in the structure from different views.

URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/226469
Collection土木工程与力学学院
Recommended Citation
GB/T 7714
黎龙飞. 杆梁类周期压电结构中的弹性波分析[D]. 兰州. 兰州大学,2017.
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