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.     

Theory and comparison of the effect of composite and shape memory alloy stiffeners on stability of composite shells and plates

The effects of composite and shape memory alloy stiffeners on stability of composite cylindrical shells and rectangular plates subjected to a compressive load are compared. The governing equations for reinforced cylindrical shells are developed based on the Love first approximation theory and smeared stiffeners technique. It is shown that composite stiffeners are more efficient in cylindrical shells, while shape memory alloy stiffeners may be preferable in plates or in long shallow shells. It is also proven that shape memory alloy stiffeners increase the upper and lower buckling loads, i.e. the linear buckling load and the minimum postbuckling load-carrying capacity of cylindrical shells modeled as single-degree-of-freedom systems by the same amount.     

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.     

Sound radiation from strip plates with longitudinal stiffeners using waveguide finite and boundary element methods

In this study, the vibration characteristics and sound radiation of strip plates with finite width and infinite length are investigated numerically in order to analyze the vibration and sound radiation of structures consisting of many stiffened and double-layered plates. The waveguide finite element approach, which is effective for waveguide structures, is applied as a numerical scheme. The sound power and radiation efficiencies for an unstiffened plate are calculated numerically via coupling boundary elements to the WFEs. Longitudinal stiffeners and additional upper plates are included in the plate model to investigate the effect of stiffeners and an upper plate on sound power and radiation efficiency. In this study, it is found that the stiffeners contribute differently to plate vibration and sound radiation, and that the radiation efficiencies of the stiffened and double plates are larger than those of the unstiffened plate due to the presence of the stiffeners.     

Active control of flow noise sources in turbulent boundary layer on a flat-plate using piezoelectric bimorph film

The piezoelectric bimorph film, which, as an actuator, can generate more effective displacement than the usual PVDF film, is used to control the turbulent boundary-layer flow. The change of wall pressures inside the turbulent boundary layer is observed by using the multi-channel microphone array flush-mounted on the surface when actuation at the non-dimensional frequency f_b⁺=0.008 and 0.028 is applied to the turbulent boundary layer. The wall pressure characteristics by the actuation to produce local displacement are more dominantly influenced by the size of the actuator module than the actuation frequency. The movement of large-scale turbulent structures to the upper layer is found to be the main mechanism of the reduction in the wallpressure energy spectrum when the 700v/u_τ-long bimorph film is periodically actuated at the non-dimensional frequency f_b⁺ =0.008 and 0.028. The biomorph actuator is triggered with the time delay for the active forcing at a single frequency when a 1/8″ pressuretype, pin-holed microphone sensor detects the large-amplitude pressure event by the turbulent spot. The wall-pressure energy in the late-transitional boundary layer is partially reduced near the convection wavenumber by the open-loop control based on the large amplitude event.     

压电智能悬臂梁结构振动主动控制仿真

为了提高LQR最优控制方法对压电类智能结构的振动控制效果,推导了表面离散分布压电元件的柔性悬臂梁结构的驱动和传感方程以及梁的弯曲振动方程,用模态分析方法对方程进行解耦和模型降阶,建立控制系统的状态空间方程。利用有限元分析方法来衡量压电元件对梁固有特性的影响,对状态空间方程的自振频率和振型函数进行修正,得到更为精确的数学模型。通过一悬臂梁的LQR最优控制仿真实例表明,经过模型修正后的最优振动控制效果更好。     

Damage identification in composite plates using two-dimensional B-spline wavelets

In this paper the construction of general order two-dimensional B-spline wavelets was presented and applied for damage identification in polymeric composite plates. At the very beginning the algorithm of one- and two-dimensional discrete wavelet transform and formulation of one- and two-dimensional B-spline wavelets with examples were presented. The fully clamped square layered composite plate was modeled using finite element-based software. Estimated natural modes of vibration with various damage configurations were analyzed using the two-dimensional sixth-order B-spline wavelet, and the method of damage identification was presented. The effective damage identification is based on the evaluation of the singularities in horizontal, vertical and diagonal details coefficients. Results obtained based on the numerical data were verified experimentally. Research results show the effectiveness of B-spline wavelets in application to the diagnostics and structural health monitoring.     

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.     

Semi-active vibration control using piezoelectric actuators in smart structures

The piezoelectric materials, as the most widely used functional materials in smart structures, have many outstanding advantages for sensors and actuators, especially in vibration control, because of their excellent mechanical-electrical coupling characteristics and frequency response characteristics. Semi-active vibration control based on state switching and pulse switching has been receiving much attention over the past decade because of several advantages. Compared with standard passive piezoelectric damping, these new semi-passive techniques offer higher robustness. Compared with active damping systems, their implementation does not require any sophisticated signal processing systems or any bulky power amplifier. In this review article, the principles of the semi-active control methods based on switched shunt circuit, including state-switched method, synchronized switch damping techniques, and active control theorybased switching techniques, and their recent developments are introduced. Moreover, the future directions of research in semi-active control are also summarized.     

Analytical models of sandwich plates with piezoelectric strip-stiffeners

A theory of sandwich plates with composite-material facings and piezoelectric strip-stiffeners bonded to the surface or embedded in the facings is developed. The stiffeners bonded to the surfaces are modeled using either the plane stress assumption or a first-order shear deformable theory. The former approach is appropriate if the stiffeners represent thin strips, while the latter method can be used in the case where the stiffeners are relatively deep. The stiffeners embedded in the facings in the form of piezoelectric strips are considered using the plane stress assumption.     

Active robust vibration control of flexible composite beams with parameter perturbations

In this paper, a time domain approach is presented to treat the problem of active controlling simultaneously the bending and torsional vibration of flexible composite beams under both mode truncations and parameter perturbations. In the proposed approach, the residual model, which is known as unstructured uncertainty, is viewed as an additive perturbation to the controlled model. Based on a state space model, which incorporates both bending and torsional deformation effects, of the flexible composite beam with piezoelectric sensors and actuators, a robust stability condition is derived to guarantee that both bending and torsional vibration of the flexible composite beam, which is subject to both mode truncation and linear time-varying parameter perturbations, can be actively controlled by an observer-based controller. The proposed robust stability condition gives an insight into the relationship between the stability margins of the controlled and residual mode subsystems, spillover effects and additive time-varying parameter perturbations. Finally, an active robust vibration control problem of a cantilevered flexible composite beam with piezoelectric sensors and actuators is provided for illustration.     

Free vibration of laminated composite plates using two variable refined plate theory

Free vibration of laminated composite plates using two variable refined plate theory is presented in this paper. The theory accounts for parabolic distribution of the transverse shear strains through the plate thickness, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Equations of motion are derived from the Hamilton's principle. The Navier technique is employed to obtain the closed-form solutions of antisymmetric cross-ply and angle-ply laminates. Numerical results obtained using present theory are compared with three-dimensional elasticity solutions and those computed using the first-order and the other higher-order theories. It can be concluded that the proposed theory is not only accurate but also efficient in predicting the natural frequencies of laminated composite plates.     

Propagation behavior of SH waves in layered piezoelectric plates

In this study, the propagation of SH waves in a coupled plate consisting of a piezoelectric layer and an elastic layer is analytically investigated. The piezoelectric material is polarized in the z-axis direction and perfectly bonded to an elastic layer. The mathematical model of the SH wave propagation in this plate is based on the type of surface wave solution. Dispersion relations with respect to phase velocity are obtained for electrically open and mechanically free. Numerical examples are provided to illustrate graphically and compare the variations of the phase and group velocities versus the wave number for the different layers. The thickness ratio and the properties of the two layers have a significant effect on the propagation of SH waves. The conclusions are meaningful both theoretically and practically for the design of high-performance surface acoustic wave (SAW) devices.     

压电微夹钳的位移自感知反馈复合控制*

采用自感知方法获取压电微夹钳钳指位移,构成自感知反馈复合控制系统。根据反映钳指位移、表面电荷、夹持力、驱动电压之间关系的压电悬臂梁Smits方程,提出了基于电流积分的钳指位移自感知方法;引入死区算子对传统PI模型进行改进,建立了压电微夹钳钳指位移的迟滞模型;以对偏差的抛物线积分、对输出的先行微分分别代替常规PID控制器中的积分项和微分项,设计出了压电微夹钳的改进PID反馈控制器;将前馈控制器与PID反馈控制器相结合,并采用自感知反馈方式,设计出了压电微夹钳的闭环控制系统。实验结果表明:在自感知反馈复合控制作用下,压电微夹钳对5μm阶跃参考位移的响应时间为0.24 s,若不考虑噪声影响,稳态误差几乎为零;在最大位移为14.7μm的变幅值三角波参考位移以及最大位移为14.1μm的任意波形参考位移作用下,压电微夹钳的自感知反馈复合控制亦可取得良好的控制效果,其稳态误差中线在-0.02~0.04μm之间变化。自感知反馈控制的实验结果与传感器反馈控制基本相同,从而表明压电微夹钳的自感知反馈控制是有效的。     

Vibration analysis of delaminated composite beams and plates using a higher-order finite element

In order to analyze the vibration response of delaminated composite plates of moderate thickness, a FEM model based on a simple higher-order plate theory, which can satisfy the zero transverse shear strain condition on the top and bottom surfaces of plates, has been proposed in this paper. To set up a C⁰-type FEM model, two artificial variables have been introduced in the displacement field to avoid the higher-order derivatives in the higher-order plate theory. The corresponding constraint conditions from the two artificial variables have been enforced effectively through the penalty function method using the reduced integration scheme within the element area. Furthermore, the implementation of displacement continuity conditions at the delamination front has been described using the present FEM theory. Various examples studied in many previous researches have been employed to verify the justification, accuracy and efficiency of the present FEM model. The influences of delamination on the vibration characteristic of composite laminates have been investigated. Especially the variation of ‘curvature of vibration mode’ (i.e., the second-order differential of deflections in vibration mode) caused by delamination has been studied in detail to provide valuable information for the possible identification of delamination. Furthermore, two approaches have been investigated to detect a delamination in laminates by employing this information.     

Local surface defects of composite plates

A static three-dimensional model of an elasticoplastic solid is considered, with the dependence of the material’s parameters on temperature taken into account. The effects of maximum indentation depth and its in-plane sizes are investigated, as are those of plate thickness and temperature on deformations and stresses at each plate’s point, in order to discover heating patterns that would enable operation of the plates without degradation.     

Thermally induced vibration control of cylindrical shell using piezoelectric sensor and actuator

Shell type components and structures are very common in many mechanical and structural systems. Modeling and analysis of adaptive piezothermoelastic shell laminates represent a high level of sophistication and complexity. In this paper a finite element model is developed for the active control of thermally induced vibration of laminated composite shells with piezoelectric sensors and actuators. The present model takes into account the mass, stiffness and thermal expansion of the piezoelectric patches. A C_o continuous nine-node degenerated shell element is implemented to model the structure. The piezoelectric sensing layer senses the structural vibration and a suitable voltage applied in the piezoelectric actuator layer suppresses the oscillation. Actuator and sensor are coupled together with a control algorithm so as to actively control the dynamic response of the structure in a close loop. Numerical results are generated for a cylindrical shell and it is observed that thermally induced vibration of a laminated cylindrical shell can be suppressed through the application of piezoelectric sensor and actuator. Effects of variation in control gain and piezoelectric layer area coverage (PAC) have been studied. Higher control gain is more effective in damping out the vibration. Although the damping is enhanced by increase in PAC, increase beyond a certain level may not be useful in view of smaller efficacy and increased weight.     

Robust observer-based OMF vibration control of flexible linkage mechanisms using piezoelectric films

Based on the state-space model of the flexible linkage mechanism equipped with piezoelectric films, a robust control methodology for actively suppressing the elastodynamic responses of the high-speed flexible linkage mechanism with linear structured time-varying parameter perturbations by employing an observer-based optimal model-following (OMF) controller is presented. The advantage of the proposed robust observer-based OMF control methodology is that it not only can avoid the problem of how to choose the appropriate weighting matrices in the quadratic cost function of the linear-quadratic/linear-quadratic-Gaussian (LQ/LQG) control method but also can make the controlled closed-loop system to have the specified system response characteristics. Besides, in order to guarantee that the designed observer-based OMF controller can make the controlled flexible linkage mechanism system to avoid the possibilities of both spillover-induced instability and time-varying-parameter-perturbation-induced instability, a robust stability criterion is also presented in this paper. The control method, presented in this paper, can not only make the controlled closed-loop system to have the specified system response characteristics, but also guarantee the controlled closed-loop system to have robust stability properties by using the proposed robust stability criterion; while those control methods reported recently do not have these above-mentioned merits. Finally, an active robust vibration control problem of a slider-crank mechanism is provided for illustrating the applicability of the proposed method.     

CFD study of pressure loss characteristics of multi-holed orifice plates using central composite design

The study on the use of multi-holed orifice plate for measuring flow rate is a growing area of research. As compared to standard orifice plate, multi-holed orifice plates (MO) have number of advantages, such as, these plates require minimum straight piping at the upstream without compromising the pressure losses and provide better accuracy in the measurement of flow rates. In this study, a systematic methodology is adopted for investigating the effect of different geometrical parameters on pressure loss coefficient and values of parameters under investigation varied using central composite design. The geometrical parameters chosen for the study are: (a) Number of holes; (b) Multi-hole Diameter ratio and (c) Compactness of holes. Commercial computational fluid dynamics code (ANSYS Fluent) is employed to perform simulations for 15 different settings of these parameters to analyze their effect on pressure loss coefficient and flow development length at downstream of multi-holed orifice plates. It is found that values of pressure loss coefficient is a strong function of multi-hole diameter ratio, whereas, the flow conditioning properties are strongly affected by the number of holes.