Active damping of vibrations of plates subject to unknown pressure

An approach to the active damping of the forced resonant vibrations of orthotropic thermoviscoelastic plates with distributed sensors and actuators is proposed. The mechanical load is assumed unknown and is determined from the sensors’ indications. The problem of active damping of an isotropic thermoviscoelastic rectangular plate with hinged edges is solved as an example. A formula for the voltage to be applied to the actuator to damp the forced vibrations in the first mode is derived. The effect of the dimensions of the sensor and actuator and the dissipative properties of the materials on the effectiveness of active damping is studied     

界面特性对功能梯度智能梁静动态响应的影响研究

采用状态空间法分析了两边简支的含压电夹层的功能梯度梁的静力弯曲和自由振动问题．为了考虑中间压电层与上、下功能梯度层之间的粘结效果,采用线性弹簧模型以模拟界面性能．假设上下功能梯度层的材料参数沿厚度连续变化,而压电层则是均匀材料,并且它们都是正交各向异性的．由于功能梯度梁的不均匀性使得直接求解比较困难,文中用层合模型来进行近似．数值算例中,分别考虑了压电层用于传感器或作动器的情形,分析了粘结界面完美程度对组合梁静力弯曲和自由振动频率的影响．     

主动约束层阻尼圆柱壳体的振动特性研究

基于弹性、粘弹性和压电材料本构方程,应用能量法建立了主动约束层阻尼（ACLD）圆柱壳体的有限元动力学方程。通过对压电传感层自感电压的比例、微分反馈控制,对主动约束层阻尼（ACLD）圆柱壳体进行了主被动一体化振动控制,研究了复合圆柱壳体的动力学响应特性。讨论了主动约束层阻尼（ACLD）片体的位置、覆盖率、粘弹性层厚度及控制增益等关键参数对圆柱壳体振动特性的影响。研究表明：主动约束层阻尼（ACLD）片体的粘贴位置与模态有关,针对不同模态,应采用不同的粘贴位置;覆盖率、粘弹性层厚度及控制增益等直接影响到振幅衰减程度,通过对片体位置、覆盖率、粘弹性层厚度及控制增益等关键参数的优化,能有效降低主动约束层阻尼圆柱壳体的振动,具有十分重要的工程应用价值。     

Postbuckling of FGM cylindrical shells under combined axial and radial mechanical loads in thermal environments

A postbuckling analysis is presented for a shear deformable functionally graded cylindrical shell of finite length subjected to combined axial and radial loads in thermal environments. Heat conduction and temperature-dependent material properties are both taken into account. The temperature field considered is assumed to be a uniform distribution over the shell surface and varied in the thickness direction only. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The formulations are based on a higher order shear deformation shell theory with von Kármán–Donnell-type of kinematic nonlinearity. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of functionally graded cylindrical shells. A singular perturbation technique is employed to determine the interactive buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect cylindrical shells with two constituent materials subjected to combined axial and radial mechanical loads and under different sets of thermal environments. The results reveal that the temperature field and volume fraction distribution have a significant effect on the postbuckling behavior, but they have a small effect on the imperfection sensitivity of the functionally graded shell.     

Active control scheme for improving mass resolution of film bulk acoustic resonators

High mass resolution of sensors based on film bulk acoustic resonators (FBARs) is required for the detection of small molecules with the low concentration.An active control scheme is presented to improve the mass resolution of the FBAR sensors by adding a feedback voltage onto the driving voltage between two electrodes of the FBAR sensors. The feedback voltage is obtained by giving a constant gain and a constant phase shift to the current on the electrodes of the FBAR sensors. The acoustic energy produced by the feedback voltage partly compensates the acoustic energy loss due to the material damping and the acoustic scattering, and thus improves the quality factor and the mass resolution of the FBAR sensors. An explicit expression relating to the impedance and the frequency for an FBAR sensor with the active control is derived based on the continuum theory by neglecting the influence of the electrodes. Numerical simulations show that the impedance of the FBAR sensor strongly depends on the gain and the phase shift of the feedback voltage, and the mass resolution of the FBAR sensor can greatly be improved when the appropriate gain and the phase shift of the feedback voltage are used. The active control scheme also provides an effective solution to improve the resolution of the quartz crystal microbalance (QCM).     

Infinite-Dimensional Control of Nonlinear Beam Vibrations by Piezoelectric Actuator and Sensor Layers

An infinite-dimensional approach for the active vibration control of a multilayered straight composite piezoelectric beam is presented. In order to control the excited beam vibrations, distributed piezoelectric actuator and sensor layers are spatially shaped to achieve a sensor/actuator collocation which fits the control problem. In the sense of von Kármán a nonlinear formulation for the axial strain is used and a nonlinear initial boundary-value problem for the deflection is derived by means of the Hamilton formalism. Three different control strategies are proposed. The first one is an extension of the nonlinear H-design to the infinite-dimensional case. It will be shown that an exact solution of the corresponding Hamilton–Jacobi–Isaacs equation can be found for the beam under investigation and this leads to a control law with optimal damping properties. The second approach is a PD-controller for infinite-dimensional systems and the third strategy makes use of the disturbance compensation idea. Under certain observability assumptions of the free system, the closed loop is asymptotically stable in the sense of Lyapunov. In this way, flexural vibrations which are excited by an axial support motion or by different time varying lateral loadings, can be suppressed in an optimal manner. A numerical example serves both to illustrate the design process and to demonstrate the feasibility of the proposed methods.     

Design of an Active Noise Control System Using a Distributed Actuator

A distributed acoustic actuator for active noise control, consisting of a piezoelectric PVDF film, bonded at each side of a carrier structure, is simulated and built. The piezoelements are driven in anti-phase, resulting in a bending motion of the actuator, and thus in the necessary out-of-plane displacement for sound radiation. An analytical model for the acoustic actuator is derived, relating the actuator's displacement to the applied voltage, taking into account the influence of the piezoelectric film on the actuator's stiffness. The model is used to optimise the specifications for the piezoelectric film and the carrier structure, resulting in the highest sound power output in a frequency range from 30–500 Hz. An analytical model for the behaviour of a double panel partition is derived. The analytical model is combined with the model for the acoustic actuator, describing an actively controlled double panel partition with a distributed acoustic actuator integrated in the cavity. A controller is added to the system to control the sound power transmitted through the double panel partition. Simulation results show that a substantial increase of transmission loss can be achieved in the low frequency region (30–500 Hz) with this configuration. This revised version was published online in July 2006 with corrections to the Cover Date.     

压电涂层-功能梯度压电界面层-基底结构的二维接触问题研究

在多层压电元件中,由于界面处材料成分和性质的突变,常常导致界面处应力集中,使得界面处出现开裂或蠕变现象,从而大大缩短了压电元件的使用寿命。功能梯度压电材料作为界面层,可有效的缓解界面材料不匹配导致的破坏。本文主要研究利用功能梯度压电材料界面层连接压电涂层和基底,分析三层结构在圆柱型压头作用下的力电响应。利用傅里叶积分变换技术,本文将压电涂层-功能梯度压电层-基底结构在刚性圆柱压头作用下的二维平面应变接触问题转化为带有柯西核的奇异积分方程。运用高斯-切比雪夫积分公式,将奇异积分方程转化为线性方程组并对其进行数值求解,得到压电涂层-功能梯度压电层-基底结构在圆柱形压头作用下的应力分布和电位移分布。数值结果表明,梯度压电材料参数的变化对结构中的力电响应具有重要的影响。本文研究结果对于利用功能梯度压电界面层消除界面处的应力不连续导致的界面破坏具有重要的理论指导意义,研究结果可为功能梯度压电材料界面层的设计提供帮助。     

Dynamic stability analysis of finite element modeling of piezoelectric composite plates

The dynamic stability of negative-velocity feedback control of piezoelectric composite plates using a finite element model is investigated. Lyapunov’s energy functional based on the derived general governing equations of motion with active damping is used to carry out the stability analysis, where it is shown that the active damping matrix must be positive semi-definite to guarantee the dynamic stability. Through this formulation, it is found that imperfect collocation of piezoelectric sensor/actuator pairs is not sufficient for dynamic stability in general and that ignoring the in-plane displacements of the midplane of the composite plate with imperfectly collocated piezoelectric sensor/actuator pairs may cause significant numerical errors, leading to incorrect stability conclusions. This can be further confirmed by examining the complex eigenvalues of the transformed linear first-order state space equations of motion. To overcome the drawback of finding all the complex eigenvalues for large systems, a stable state feedback law that satisfies the second Lyapunov’s stability criteria strictly is proposed. Numerical results based on a cantilevered piezoelectric composite plate show that the feedback control system with an imperfectly collocated PZT sensor/actuator pair is unstable, but asymptotic stability can be achieved by either bonding the PZT sensor/actuator pair together or changing the ply stacking sequence of the composite substrate to be symmetric. The performance of the proposed stable controller is also demonstrated. The presented stability analysis is of practical importance for effective design of asymptotically stable control systems as well as for choosing an appropriate finite element model to accurately predict the dynamic response of smart piezoelectric composite plates.     

The analysis of functionally graded shallow and non-shallow shell panels with piezoelectric layers under dynamic load and electrostatic excitation based on elasticity

Elasticity solution is presented for finitely long, simply-supported, functionally graded shallow and non-shallow shell panel with two piezoelectric layers under pressure and electrostatic excitation. The functionally graded panel is assumed to be made of many sub panels. Each sub panel is considered as an isotropic layer. Material’s properties in each layer are constant and functionally graded properties are resulted by suitable arrangement of layers in multilayer panel. In each interface between two layers, stress and displacement continuities are satisfied. The highly coupled partial differential equations (p.d.e.) are reduced to ordinary differential equations (o.d.e.) with variable coefficients for non-shallow panel and constant coefficients for shallow shell panel by means of trigonometric function expansion in circumferential and longitudinal directions. The resulting ordinary differential equations are solved by Galerkin finite element method and Newmark method is used to march in time. Numerical examples are presented for functionally graded shell panel with a piezoelectric layer as an actuator in external surface and a piezoelectric layer as a sensor in internal surface and the results of the shallow and non-shallow panels are discussed.     

Control of axisymmetric resonant vibrations and self-heating of shells of revolution with piezoelectric sensors and actuators

The coupled problem of forced vibrations and self-heating of thermoviscoelectroelastic shells of revolution with piezoceramic sensor and actuator under monoharmonic loading is solved. The temperature dependence of the complex characteristics of the passive and piezoactive materials is taken into account. The coupled nonlinear problem of thermoelectroelasticity is solved by time-marching integration, using discrete orhogonalization to integrate the equations of elasticity and explicit finite differencing to solve the heat conduction equation. The effect of the dimensions of the sensor and actuator and self-heating on the sensor voltage and on the active damping of forced vibrations of a circular plate under uniform monoharmonic transverse pressure is studied     

An exact solution for the steady-state thermoelastic response of functionally graded orthotropic cylindrical shells

We analyze the steady-state response of a functionally graded thick cylindrical shell subjected to thermal and mechanical loads. The functionally graded shell is simply supported at the edges and it is assumed to have an arbitrary variation of material properties in the radial direction. The three-dimensional steady-state heat conduction and thermoelasticity equations, simplified to the case of generalized plane strain deformations in the axial direction, are solved analytically. Suitable temperature and displacement functions that identically satisfy the boundary conditions at the simply supported edges are used to reduce the thermoelastic equilibrium equations to a set of coupled ordinary differential equations with variable coefficients, which are then solved by the power series method. In the present formulation, the cylindrical shell is assumed to be made of an orthotropic material, although the analytical solution is also valid for isotropic materials. Results are presented for two-constituent isotropic and fiber-reinforced functionally graded shells that have a smooth variation of material volume fractions, and/or in-plane fiber orientations, through the radial direction. The cylindrical shells are also analyzed using the Flügge and the Donnell shell theories. Displacements and stresses from the shell theories are compared with the three-dimensional exact solution to delineate the effects of transverse shear deformation, shell thickness and angular span.     

Postbuckling analysis of axially loaded functionally graded cylindrical panels in thermal environments

A postbuckling analysis is presented for a functionally graded cylindrical panel of finite length subjected to axial compression in thermal environments. Material properties are assumed to be temperature dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The governing equations of a functionally graded cylindrical panel are based on Reddy’s higher order shear deformation shell theory with a von Kármán–Donnell-type of kinematic nonlinearity and including thermal effects. Two cases of the in-plane boundary conditions are considered. The nonlinear prebuckling deformations and initial geometric imperfections of the panel are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of functionally graded cylindrical panels under axial compression. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of axially loaded, perfect and imperfect, functional graded cylindrical panels with two constituent materials and under different sets of thermal environments. The influences played by temperature rise, volume fraction distributions, the character of in-plane boundary conditions, transverse shear deformation, panel geometric parameters, as well as initial geometric imperfections are studied.     

Free vibration analysis of functionally graded laminated sandwich cylindrical shells integrated with piezoelectric layer

An analytical method for the three-dimensional vibration analysis of a functionally graded cylindrical shell integrated by two thin functionally graded piezoelectric (FGP) layers is presented. The first-order shear deformation theory is used to model the electromechanical system. Nonlinear equations of motion are derived by considering the von Karman nonlinear strain-displacement relations using Hamilton’s principle. The piezoelectric layers on the inner and outer surfaces of the core can be considered as a sensor and an actuator for controlling characteristic vibration of the system. The equations of motion are derived as partial differential equations and then discretized by the Navier method. Numerical simulation is performed to investigate the effect of different parameters of material and geometry on characteristic vibration of the cylinder. The results of this study show that the natural frequency of the system decreases by increasing the non-homogeneous index of FGP layers and decreases by increasing the non-homogeneous index of the functionally graded core. Furthermore, it is concluded that by increasing the ratio of core thickness to cylinder length, the natural frequencies of the cylinder increase considerably.     

Investigation on the Design of Piezoelectric Actuator/Sensor for Damage Detection in Beam with Lamb Waves

Piezoelectric wafer type actuator/sensor is widely used to generate and sense Lamb waves for Structural Health Monitoring (SHM). However, multiple Lamb waves modes are generally excited with this type of transducer. As a result, there is some difficulty in using Lamb waves for damage detection. To selectively generate a single A₀/S₀ Lamb mode, the tuned excitation of Lamb waves has been studied by some researchers. This paper investigates the design of the PZT actuator/sensor bonded to beam-like structure for generating single A₀/S₀ Lamb mode. In the study it is found that some factors, including the bonding layer, the unknown material properties and dynamical characteristics of the beam, will influence the design of PZT actuator/sensor. Piezoelectric impedance technique is introduced to facilitate the design of PZT actuator/sensor. Crack detection in beam using the tuned A₀/S₀ Lamb waves is performed.     

Vibroacoustic responses of a heavy fluid loaded cylindrical shell excited by a turbulent boundary layer

A fully coupled structural–acoustic model of a cylindrical shell under external turbulent boundary layer excitation is herein developed. The numerical process requires computation of the wall pressure cross spectral density function as well as sensitivity functions for the fluid-loaded cylindrical shell. A semi-empirical model from literature is used to describe the wall pressure field induced by the turbulent boundary layer in the wavenumber–frequency domain. An analytical expression of the wall pressure field for a flat surface is adapted to describe the wall pressure field for a cylindrical surface. Circumferential sensitivity functions are derived using a wavenumber-point reciprocity principle. Results for the near-field and far-field acoustic pressure spectra are presented. Contributions of individual circumferential modes to the acoustic pressure spectra are examined, showing distinct trends below and above the ring frequency. The proposed method is computationally efficient and provides an effective approach to investigate vibroacoustic responses for maritime platforms.     

层叠式PVDF压电作动器及圆柱壳的振动主动控制

设计了一个层叠式PVDF压电作动器用于壳结构的振动控制。考虑压电层、粘接层、壳体耦合关系,推导了表面局部粘贴层叠式PVDF压电作动器的圆柱壳的振动控制方程,给出了作动力与压电层和粘接层层数、厚度之间的关系以及作动力与作动器粘贴位置之间的关系。针对一端固定、另一端自由的圆柱壳,进行了振动控制仿真。结果表明层叠式PVDF压电作动器作动力与作动器层数近似成线性关系,增大作动器层数能有效增大作动力,在低控制电压下能显著抑制圆柱壳振动,作动器周向不完全粘贴时,在径向产生的径向作动力对壳体横向振动控制非常有利。说明了层叠式PVDF压电作动器是一种可用于壳体结构振动并具有良好作动效果的作动器。     

Postbuckling of piezoelectric FGM plates subject to thermo-electro-mechanical loading

In this paper, we examine the postbuckling behavior of functionally graded material FGM rectangular plates that are integrated with surface-bonded piezoelectric actuators and are subjected to the combined action of uniform temperature change, in-plane forces, and constant applied actuator voltage. A Galerkin-differential quadrature iteration algorithm is proposed for solution of the non-linear partial differential governing equations. To account for the transverse shear strains, the Reddy higher-order shear deformation plate theory is employed. The bifurcation-type thermo-mechanical buckling of fully clamped plates, and the postbuckling behavior of plates with more general boundary conditions subject to various thermo-electro-mechanical loads, are discussed in detail. Parametric studies are also undertaken, and show the effects of applied actuator voltage, in-plane forces, volume fraction exponents, temperature change, and the character of boundary conditions on the buckling and postbuckling characteristics of the plates.     

Active damping of a stiff beam-like structure with acceleration feedback

This paper describes a local control scheme using acceleration feedback and a colocated proof-mass actuator for active damping of structures. The closed-loop system is unconditionally stable. The control law is implemented digitally on a stiff beam (f ₁=68 Hz) representative of an optical test bench. The modal damping ratio is improved from below 0.2 percent to above 4 percent.     

ACTIVE CONTROL OF THE PIEZOELASTIC LAMINATED CYLINDRICAL SHELL''''S VIBRATION UNDER HYDROSTATIC PRESSURE

IntroductionDuetotheintrinsicdirectandconversepiezoelectriceffects,piezoelectricmaterialscanbeeffectivelyusedtoproducesensorsoractuatorsfortheactiveshapeorvibrationcontrolostructures.Therefore,theuseofpiezoelectricmaterialsinintelligentstructuresattractedmanyattentionsinrecentyears.Thedesignofsuchactivesystemsrequiresgoodunderstandingofthemechanical_electricinteractionbetweenthestructuresandpiezoelectricmaterials.Manyinvestigationshavebeendoneinthisfield[1].However,mostofthesestudiesarebasedo…