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Vibrations of thin plate with piezoelectric actuator: Theory and experiments.

机译：压电致动器薄板的振动：理论和实验。

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摘要

Vibrations of flexible structures have been an important engineering study owing to its both deprecating and complimentary traits. These flexible structures are generally modeled as strings, bars, shafts and beams (one dimensional), membranes and plate (two dimensional) or shell (three dimensional). Structures in many engineering applications, such as building floors, aircraft wings, automobile hoods or pressure vessel end-caps, can be modeled as plates. Undesirable vibrations of any of these engineering structures can lead to catastrophic results. It is important to know the fundamental frequencies of these structures in response to simple or complex excitations or boundary conditions.After their discovery in 1880, piezoelectric materials have made their mark in various engineering applications. In aerospace, bioengineering sciences, Micro Electro Mechanical Systems (MEMS) and NEMS to name a few, piezoelectric materials are used extensively as sensors and actuators. These piezoelectric materials, when used as sensors or actuators can help in both generating a particular vibration behavior and controlling undesirable vibrations. Because of their complex behavior, it is necessary to model them when they are attached to host structures. The addition of piezoelectric materials to the host structure introduces extra stiffness and changes the fundamental frequency.The present study starts with modeling and deriving natural frequencies for various boundary conditions for circular membranes. Free and forced vibration analyses along with their solutions are discussed and simulated. After studying vibration of membranes, vibration of thin plates is discussed using both analytical and approximate methods. The method of Boundary Characteristic Orthogonal Polynomials (BCOP) is presented which helps greatly in simplifying computational analysis. First of all it eliminates the need of using trigonometric and Bessel functions as admissible functions for the Raleigh Ritz analysis and the Assumed Mode Method. It produces diagonal or identity mass matrices that help tremendously in reducing the computational effort. The BCOPs can be used for variety of geometries including rectangular, triangular, circular and elliptical plates. The boundary conditions of the problems are taken care of by a simple change in the first approximating function. Using these polynomials as admissible functions, frequency parameters for circular and annular plates are found to be accurate up to fourth decimal point.A simplified model for piezoelectric actuators is then derived considering the isotropic properties related to displacement and orthotropic properties of the electric field. The equations of motion for plate with patch are derived using equilibrium (Newtonian) approach as well as extended Hamilton's principle. The solution of equations of motion is given using BCOPs and fundamental frequencies are then found. In the final chapter, the experimental verification of the plate vibration frequencies is performed with electromagnetic inertial actuator and piezoelectric actuator using both circular and annular plates. The thesis is concluded with a summary of work and discussion about possible future work.
机译：柔性结构的振动由于其既具有折旧性又具有互补性而成为一项重要的工程研究。这些柔性结构通常建模为弦，杆，轴和梁（一维），膜和板（二维）或壳体（三维）。在许多工程应用中的结构，例如建筑地板，飞机机翼，汽车引擎盖或压力容器端盖，都可以建模为板。这些工程结构中的任何不期望的振动都可能导致灾难性的后果。了解这些结构响应简单或复杂激发或边界条件的基本频率非常重要.1880年发现压电材料后，压电材料已在各种工程应用中崭露头角。在航空航天，生物工程科学，微电子机械系统（MEMS）和NEMS中，压电材料被广泛用作传感器和致动器。这些压电材料用作传感器或执行器时，既可以帮助产生特定的振动行为，又可以控制不希望的振动。由于它们的行为复杂，当它们连接到宿主结构时，有必要对其建模。压电材料添加到主体结构中会引入额外的刚度并改变基频。本研究从建模和推导圆形膜各种边界条件的固有频率开始。对自由振动和强迫振动及其解决方案进行了讨论和仿真。在研究了膜的振动之后，使用解析和近似方法讨论了薄板的振动。提出了边界特征正交多项式（BCOP）方法，极大地简化了计算分析。首先，它消除了将三角函数和贝塞尔函数用作Raleigh Ritz分析和假定模式方法的允许函数的需要。它产生对角线或恒等式质量矩阵，极大地有助于减少计算量。 BCOP可用于各种几何形状，包括矩形，三角形，圆形和椭圆形的板。问题的边界条件可以通过简单地改变第一近似函数来解决。使用这些多项式作为允许函数，发现圆形和环形平板的频率参数在小数点后第四位都是准确的。然后，考虑到与电场的位移和正交各向异性有关的各向同性特性，得出了压电执行器的简化模型。使用平衡（牛顿）方法以及扩展的汉密尔顿原理推导了带有补片的板的运动方程。使用BCOP给出运动方程的解，然后找到基本频率。在最后一章中，使用圆形和环形板的电磁惯性执行器和压电执行器对板振动频率进行了实验验证。最后，本文对工作进行了总结，并对可能的未来工作进行了讨论。

著录项

  • 作者

    Mehta, Parikshit.;

  • 作者单位

    Clemson University.;

  • 授予单位 Clemson University.;
  • 学科 Engineering Mechanical.
  • 学位 M.S.
  • 年度 2009
  • 页码 160 p.
  • 总页数 160
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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