Closed-form vibration analysis of thick annular functionally graded plates with integrated piezoelectric layers

This paper employs an analytical method to analyze vibration of piezoelectric coupled thick annular functionally graded plates (FGPs) subjected to different combinations of soft simply supported, hard simply supported and clamped boundary conditions at the inner and outer edges of the annular plate on the basis of the Reddy's third-order shear deformation theory (TSDT). The properties of host plate are graded in the thickness direction according to a volume fraction power-law distribution. The distribution of electric potential along the thickness direction in the piezoelectric layer is assumed as a sinusoidal function so that the Maxwell static electricity equation is approximately satisfied. The differential equations of motion are solved analytically for various boundary conditions of the plate. In this study closed-form expressions for characteristic equations, displacement components of the plate and electric potential are derived for the first time in the literature. The present analysis is validated by comparing results with those in the literature and then natural frequencies of the piezoelectric coupled annular FG plate are presented in tabular and graphical forms for different thickness-radius ratios, inner-outer radius ratios, thickness of piezoelectric, material of piezoelectric, power index and boundary conditions.     

Dynamic characteristics of an eccentric crack in a functionally graded piezoelectric ceramic strip

The dynamic response of an eccentric Griffith crack in functionally graded piezoelectric ceramic strip under anti-plane shear impact loading is analysed using integral transform method. Laplace transform and Fourier transform are used to reduce the problem to two pairs of dual integral equations, which are then expressed to Fredholm integral equations of the second kind. We assume that the properties of the functionally graded piezoelectric material vary continuously along the thickness. The impermeable crack boundary condition is adopted. Numerical values on the dynamic stress intensity factors are presented for the functionally graded piezoelectric material to show the dependence of the gradient of material properties and electric loadings.     

Geometrically nonlinear vibration analysis of piezoelectrically actuated FGM plate with an initial large deformation

A theoretical model for geometrically nonlinear vibration analysis of piezoelectrically actuated circular plates made of functionally grade material (FGM) is presented based on Kirchhoff’s-Love hypothesis with von-Karman type geometrical large nonlinear deformations. To determine the initial stress state and pre-vibration deformations of the smart plate a nonlinear static problem is solved followed by adding an incremental dynamic state to the pre-vibration state. The derived governing equations of the structure are solved by exact series expansion method combined with perturbation approach. The material properties of the FGM core plate are assumed to be graded in the thickness direction according to the power-law distribution in terms of the volume fractions of the constituents. Control of the FGM plate’s nonlinear deflections and natural frequencies using high control voltages is studied and their nonlinear effects are evaluated. Numerical results for FG plates with various mixture of ceramic and metal are presented in dimensionless forms. In a parametric study the emphasis is placed on investigating the effect of varying the applied actuator voltage as well as gradient index of FGM plate on vibration characteristics of the smart structure. This paper was recommended for publication in revised form by Associate Editor Eung-Soo Shin Farzad Ebrahimi received his B.S. and M.S. degree in Mechanical Engineering from University of Tehran, Iran. He is currently working on his Ph.D. thesis under the title of “Vibration analysis of smart functionally graded plates” at Smart Materials and Structures Lab in Faculty of Mechanical Engineering of the University of Tehran. His research interests include vibration analysis of plates and shells, smart materials and structures and functionally graded materials.     

Dynamic analysis of laminated composite plates with piezoelectric sensor/actuator patches using the FSDT mesh-free method

This paper investigates the active control of laminated composite plates with piezoelectric sensor/actuator patches using an efficient mesh-free method, i.e. the element-free Galerkin (EFG) method. The formulation of the problem is based on the first-order shear deformation plate theory (FSDT) and the principle of virtual displacements. A simple control algorithm coupling the direct and converse piezoelectric effect is used to control the dynamic response of the laminate plate with distributed sensor/actuator patches through a closed control loop. Several example problems are studied to show the influence of stacking sequence and position of sensor/actuator patches on the dynamic responses of the laminate plate. These simulations provide us with the best location of the sensor/actuator patches for active control of the laminate plate.     

基于高精度位移传感器的减振平台

为了保证光学精密仪器工作基础的高稳定性,设计了一种新型的减振平台。该减振平台采用精度为10nm的位移传感器作为测量装置,通过位移传感器测量隔振平台支撑弹簧的长度变化,计算出支撑力的变化;然后,调整电磁驱动器的电磁力,使光学精密仪器受力平衡,达到减振的目的。理论及仿真分析表明,采用这种减振方式有很好的减振效果。同时,由于每级减振装置之间是彼此独立的,这种减振方式更有利于多级减振。实验结果显示,基座振幅为0.22mm时,减振台支撑面振幅为1.6μm;基座振幅为0.20mm时,减振台支撑面振幅为1.4μm;基座振幅0.18mm时,减振台支撑面振幅为1.2μm;基座振幅为0.15mm时,减振台支撑面振幅为1.0μm,表明该平台有效地起到了减振作用。     

Using a new generation of piezoelectric sensors for partial discharge detection

In this paper, we present the application potential for the on-line detection of partial discharges of a new generation of piezoelectric sensors (High Temperature Ultrasonic Transducers, HTUTs). Such a sensor was recently developed by Canada’s Industrial Materials Institute (IMI). Given its inherent features, it can be considered as an excellent economic alternative for partial discharge detection. A breadboard was designed to produce a specifically localized partial discharge source. Partial discharge measurements were taken simultaneously with piezoelectric sensors and with a standard detection circuit equipped with a capacitive coupler. This paper presents the correlation between the two measurement types.     

Three-dimensional vibration analysis of fluid-filled orthotropic FGM cylindrical shells

Based on the three-dimensional fundamental equations of anisotropic elasticity, a state equation with variable coefficients is derived in a unified matrix form. The free vibration of simply supported, fluid-filled cylindrically orthotropic functionally graded cylindrical shells with arbitrary thickness is then investigated. A laminate approximate model is employed which is suitable for an arbitrary variation of material constants along the radial direction. Numerical examples are presented and compared with existing results. The effects of related parameters on natural frequencies are discussed finally.     

Vibration analysis of submerged thin FGM cylindrical shells

This study gives a brief work on vibration characteristics of cylindrical shells submerged in an incompressible fluid. The shell is presumed to be structured from functionally graded material. The effect of the fluid is introduced by using the acoustic wave equation. Love’s first order thin shell theory is utilized in the shell dynamical equations. The problem is framed by combining shell dynamical equations with the acoustic wave equation. Fluid-loaded terms are associated with Hankel function of second kind. Wave propagation approach is employed to solve the shell problem. Some comparisons of numerical results are performed for the natural frequencies of simply supported-simply supported, clamped-clamped and clamped-simply supported boundary conditions of isotropic as well as functionally graded cylindrical shells to check the validity of the present approach. The influence of fluid on the submerged functionally graded cylindrical shells is noticed to be very pronounced.     

Impact force detection using an energy flow estimator with piezoelectric sensors

Currently, there are numerous methods for estimating impact locations. One is to find more detailed information because the system becomes complicated. Another method is to reduce energy, for which various autonomic energy harvesting methods have been developed. However, the occupied energy is still small. This paper proposes a simple, rapid, and low-powered impact estimation method based on energy flow direction estimation through a pair of piezoelectric sensors. The estimation energy flow is expressed by a Poynting vector subsequently linked to piezoelectric sensor voltage outputs. The presented approach is verified by numerical simulations and experiments.     

Impact force detection using an energy flow estimator with piezoelectric sensors

Currently, there are numerous methods for estimating impact locations. One is to find more detailed information because the system becomes complicated. Another method is to reduce energy, for which various autonomic energy harvesting methods have been developed. However, the occupied energy is still small. This paper proposes a simple, rapid, and low-powered impact estimation method based on energy flow direction estimation through a pair of piezoelectric sensors. The estimation energy flow is expressed by a Poynting vector subsequently linked to piezoelectric sensor voltage outputs. The presented approach is verified by numerical simulations and experiments.     

Stability and free vibration analysis of thick piezoelectric composite plates using spline finite strip method

In the present study, a spline finite strip with higher-order shear deformation is formulated for stability and free vibration analysis of piezoelectric composite plates. At each knot, the electric potentials on the surfaces and middle plane of each piezoelectric layer are taken as nodal degrees of freedom. However, if a continuous electrode is installed on the surface of the layer, the electric potential on the electrode is changed to structural degree of freedom, so that the equipotential condition on the electrode is automatically satisfied. The analysis can be conducted based on Reddy's third-order shear deformation theory, Touratier's “Sine” model, Afaq's exponential model or Cho's higher-order zigzag laminate theory. Consequently, the shear correction coefficients are not required in the analysis, and an improved accuracy for thick plates over the first-order shear deformation theory is achieved at only little extra computational cost.The numerical results obtained based on different shear deformation theories are presented in comparison with the three-dimensional solutions. The effects of length-to-thickness ratio, fiber orientation, boundary conditions and electrical conditions on the natural frequency and critical buckling load of piezoelectric composite plates are investigated through numerical examples.     

压电材料在机敏结构振动控制中的应用

采用压电传感器与控制实现机敏结构的振动控制是当前振动工程的一个研究热点。本文在阐述其基本原理的基础上,对该领域的研究现状进行了简要回顾了,并指出了今后研究中一些亟待解决的问题。     

Dynamic propagation of a finite eccentric crack in a functionally graded piezoelectric ceramic strip

The dynamic propagation of an eccentric Griffith crack in a functionally graded piezoelectric ceramic strip under anti-plane shear is analyzed using the integral transform method. A constant velocity Yoffe-type moving crack is considered. Fourier transform is used to reduce the problem to a pair of dual integral equations, which is then expressed in a Fredholm integral equation of the second kind. We assume that the properties of the functionally graded piezoelectric material vary continuously along the thickness. The impermeable crack boundary condition is adopted. Numerical values on the dynamic stress intensity factors are presented for the functionally graded piezoelectric material to show the dependence of the gradient of material properties, crack moving velocity, and eccentricity. The dynamic stress intensity factors of a moving crack in functionally graded piezoelectric material increases when the crack moving velocity, eccentricity of crack location, material property gradient, and crack length increase. This paper was recommended for publication in revised form by Associate Editor Hyeon Gyu Beom Jeong Woo Shin received a B.S. and M.S. degree in Mechanical Engineering from Yonsei University in Seoul, Korea in 1998 and 2000, respectively. A major field of Mr. Shin is fracture mechanics. He is currently working on the KARI (Korea Aerospace Research Institute) as a senior researcher. He conducted load analysis of fixed wing aircraft and full scale airframe static test at the KARI. He is now developing landing gear in the KHP (Korea Helicopter Program) as a performance engineer.     

透镜式压电陶瓷激波发生器压电分析及试验研究

在压电方程基础上,对所设计的透镜式激波发生器建立了进行压电分析的数学模型,利用有限元ANSYS对激波发生器厚度模式的谐振频率进行了计算,并与阻抗分析仪测试的结果进行了对比.实验表明:实验测量模态结果与有限元结果基本吻合,为激波发生器性能的研究提供了有效的分析工具.还进一步分析了透镜厚度对激波发生器谐振频率的影响,这对激波发生器的设计和制作具有指导意义.     

FSDPT based study for vibration analysis of piezoelectric coupled annular FGM plate

The vibration behavior of a piezoelectrically actuated thick functionally graded (FG) annular plate is studied based on first order shear deformation plate theory (FSDPT). A consistent formulation that satisfies the Maxwell static electricity equation is presented so that the full coupling effect of the piezoelectric layer on the dynamic characteristics of the annular FG plate can be estimated based on the free vibration results. The differential equations of motion are solved analytically for various boundary conditions of the plate. The analytical solutions are derived and validated by comparing the obtained resonant frequencies of the composite plate with those of an isotropic core plate. As a special case, assuming that the material composition of core plate varies continuously in the direction of the thickness according to a power law distribution, a comprehensive study is conducted to show the influence of functionally graded index on the vibration behavior of smart structure. Also, the good agreement between the results of this paper and those of the finite element (FE) analyses validates the presented approach. This paper was recommended for publication in revised form by Associate Editor Eung-Soo Shin Farzad Ebrahimi received his B.S. and M.S. degree in Mechanical Engineering from University of Tehran, Iran. He is currently working on his Ph.D. thesis under the title of “Vibration analysis of smart functionally graded plates” at Smart Materials and Structures Lab in Faculty of Mechanical Engineering of the University of Tehran. His research interests include vibration analysis of plates and shells, smart materials and structures and functionally graded materials.     

Modeling and analysis of curved beams with debonded piezoelectric sensor/actuator patches

In this paper, a mathematical model for thin-walled curved beams with partially debonded piezoelectric actuator/sensor patches is presented for investigating the effect of debonding of the actuator/sensor on their open- and closed-loop behaviors. The actuator equations and the sensor equations of the curved beam in perfectly bonded and debonded regions are derived. In the perfect bonding region, the adhesive layer is modeled to carry constant peel and shear stresses; while in the debonding area, it is assumed that there is no peel and shear stress transfer between the host beam and the piezoelectric layer. Both displacement continuity and force equilibrium conditions are imposed at the interfaces between the bonded and debonded regions. Based on the model and the sensing equation of the sensor, a closed-loop vibration control for the curved beams is performed. To obtain the frequency response from the presented model, a solution scheme for solving the complex governing equations is given. Using this model and the solution scheme, the effects of the debonding of actuator and sensor patches on open- and closed-loop control are investigated through an example. The results show that edge debonding of the piezoelectric patch has a significant side effect on the closed-loop control of the curved beams.     

基于压电悬臂梁的驱动器与传感器性能分析的精确解析模型

三层压电梁结构在电场作用下发生变形后会产生诱发电势,进而改变材料整体电势分布,本文考虑此变形和电势耦合效应,基于欧拉-伯努利梁变形理论,推导出能够准确预测压电智能悬臂梁传感器与驱动器性能的解析表达式。考虑压电梁结构弯曲变形后产生的电场影响,建立了三层压电梁结构的控制方程;建立了压电梁作为驱动器时端部输出位移、驱动力矩与输入电压之间联系的解析表达式,以及作为传感器时输出电压与端部作用力之间联系的解析表达式。通过与ANSYS有限元模拟结果以及传统的驱动器和传感器性能表达式的对比,验证了所推导的解析表达式的准确性。     

Vibration control of smart hull structure with optimally placed piezoelectric composite actuators

Active vibration control to suppress structural vibration of the smart hull structure was investigated based on optimized actuator configurations. Advanced anisotropic piezoelectric composite actuator, Macro-Fiber Composite (MFC), was used for the vibration control. Governing equations of motion of the smart hull structure including MFC actuators were obtained using the Donnell-Mushtari shell theory and Lagrange's equation. The Rayleigh-Ritz method was used to obtain the dynamic characteristics of the smart hull structure. Experimental modal tests were conducted to verify the proposed mathematical model. In order to achieve high control performance, optimal locations and directions of the MFC actuators were determined by genetic algorithm. Optimal control algorithm was then synthesized to suppress structural vibration of the proposed smart hull structure and experimentally implemented to the system. Active vibration control performances were evaluated under various modes excitations. Vibration tests revealed that optimal configurations of MFC actuators improved the control performance of the smart hull structure in case of the limited number of actuators available.     

Vibration analysis of multi-supported curved panel using the periodic structure approach

This papers deals with the radial vibration of a row of cylindrical panels of finite length using the concept of wave propagation in periodic structures. For this study, the structure is considered as an assemblage of a number of identical cylindrically curved panels each of which will be referred to as a periodic element. For a given geometry dispersion curves of the propagation constant versus (non-dimensional) natural frequency have been drawn corresponding to the circumferential wave propagation. New conclusions that have emerged from this study are as follows. It is shown that by a proper choice of the periodic element the bounding frequencies and the corresponding modes in all the propagation bands can be determined. These have been shown to correspond to a single curved panel with all its edges simply supported. It is noted that there are no attenuation gaps in the entire frequency spectrum beyond the lowest bounding frequency. This is a unique feature of circumferential wave propagation around circular cylindrical shells and panels, as opposed to the wave propagation of periodically supported beams and rectangular panels without curvature. The natural frequency corresponding to every circumferential mode of the complete shell has been identified on the propagation constant curve. It has been observed that the natural frequencies of a cylindrically curved panel of a given curvature and length but of different circumferential arc length (corresponding to different angles subtended at the centre of any circular cross-section) may also be identified on the same propagation constant curve. Finally, it is shown that the same propagation constant curve may also be used to determine all the natural frequencies of a finite row of curved panels with the extreme edges simply supported. Wherever possible the numerical results have been compared with those obtained independently from finite element analysis and/or results available in the literature. Flutter analysis of multi-span curved panels using a wave approach is the ultimate objective of this work.     

“Y”形流管无阀压电泵模拟与试验研究

为了对“Y”形流管无阀压电泵的工作特性有更深入的了解,使其更好地满足输血、输液等工作的需要,对“Y”形流管无阀压电泵内部流场及泵流量特性进行了模拟及试验研究。采用CFX软件对“Y”形流管无阀压电泵泵腔内的流场特性进行了模拟分析。结果表明：“Y”形流管无阀压电泵工作时泵腔内的压强变化很小,涡旋对流体传输活体细胞及长链大分子基本无影响。实际制作了“Y”形流管无阀压电泵,并通过改变“Y”形流管的几何尺寸,研究了压电泵进出口端压差的变化规律。试验结果表明压差随支管夹角增大而减小,并且当两支管宽的和接近主管宽时,压差值达到最小,当支管夹角为5°,宽为1.2mm时,压差达到最大的74mm水柱。