FINITE ELEMENT FORMULATION AND ACTIVE VIBRATION CONTROL STUDY ON BEAMS USING SMART CONSTRAINED LAYER DAMPING (SCLD) TREATMENT

This work deals with the active vibration control of beams with smart constrained layer damping (SCLD) treatment. SCLD design consists of viscoelastic shear layer sandwiched between two layers of piezoelectric sensors and actuator. This composite SCLD when bonded to a vibrating structure acts as a smart treatment. The sensor piezoelectric layer measures the vibration response of the structure and a feedback controller is provided which regulates the axial deformation of the piezoelectric actuator (constraining layer), thereby providing adjustable and significant damping in the structure. The damping offered by SCLD treatment has two components, active action and passive action. The active action is transmitted from the piezoelectric actuator to the host structure through the viscoelastic layer. The passive action is through the shear deformation in the viscoelastic layer. The active action apart from providing direct active control also adjusts the passive action by regulating the shear deformation in the structure. The passive damping component of this design eliminates spillover, reduces power consumption, improves robustness and reliability of the system, and reduces vibration response at high-frequency ranges where active damping is difficult to implement. A beam finite element model has been developed based on Timoshenko's beam theory with partially covered SCLD. The Golla-Hughes-McTavish (GHM) method has been used to model the viscoelastic layer. The dissipation co-ordinates, defined using GHM approach, describe the frequency-dependent viscoelastic material properties. Models of PCLD and purely active systems could be obtained as a special case of SCLD. Using linear quadratic regulator (LQR) optimal control, the effects of the SCLD on vibration suppression performance and control effort requirements are investigated. The effects of the viscoelastic layer thickness and material properties on the vibration control performance are investigated.     

Active control of geometrically nonlinear transient vibration of composite plates with piezoelectric actuators

In this paper, the incremental finite element equations for geometric non-linear analysis of piezoelectric smart structures are developed using a total Lagrange approach by using virtual velocity incremental variational principles. A four-node first order shear plate element model with reduced and selective integration is also developed. Geometrically non-linear transient vibration response and control of plates with piezoelectric patches subjected to pulse loads are investigated. Active damping is introduced on the plates by coupling a self-sensing and negative velocity feedback algorithm in a closed control loop. The numerical results show that piezoelectric actuators can introduce significant damping and suppress transient vibration effectively. The effects of the number and locations of the piezoelectric actuators on the control system are also discussed.     

Vibration characteristics of a rotating flexible arm with ACLD treatment

In this paper, the vibration behavior and control of a clamped–free rotating flexible cantilever arm with fully covered active constrained layer damping (ACLD) treatment are investigated. The arm is rotating in a horizontal plane in which the gravitational effect and rotary inertia are neglected. The stress–strain relationship for the viscoelastic material (VEM) is described by a complex shear modulus while the shear deformations in the two piezoelectric layers are neglected. Hamilton's principle in conjunction with finite element method (FEM) is used to derive the non-linear coupled differential equations of motion and the associated boundary conditions that describe the rigid hub angle rotation, the arm transverse displacement and the axial deformations of the three-layer composite. This refined model takes into account the effects of centrifugal stiffening due to the rotation of the beam and the potential energies of the VEM due to extension and bending. Active controllers are designed with PD for the piezosensor and actuator. The vibration frequencies and damping factors of the closed-loop beam/ACLD system are obtained after solving the characteristic complex eigenvalue problem numerically. The effects of different rotating speed, thickness ratio and loss factor of the VEM as well as different controller gain on the damped frequency and damping ratio are presented. The results of this study will be useful in the design of adaptive and smart structures for vibration suppression and control in rotating structures such as rotorcraft blades or robotic arms.     

Analysis of energy conversion in two-mode vibration control using synchronized switch damping approach

The synchronized switch damping (SSD) approaches based on piezoelectric actuators have been successfully used in multimode vibration control of structures. By suppressing voltage inversion at some displacement extrema, the control performance of SSD approaches can be significantly improved. In this study, conversion of energy from mechanical to electrical in two-mode control is analyzed for different amplitude ratios and frequency ratios. The results show that the converted energy in two-mode control with voltage inversion at every extremum is smaller than the sum of the energies of the two modes in single-mode control, but the converted energy of the second mode in two-mode control may exceed that in single-mode control when the amplitude ratio of the second mode to the first mode is small enough. The influence of voltage threshold used to suppress voltage inversion on energy conversion of the system and each individual mode is also investigated. The converted energy of the first mode in two-mode control may be much larger than that in single-mode control when voltage inversion is suppressed suitably. The analytical results can successfully explain the phenomenon in the previous control experiments and can also be extended to multimode control.     

Rectangular plate with velocity feedback loops using triangularly shaped piezoceramic actuators: experimental control performance

This paper presents experimental results on the implementation of decentralized velocity feedback control on a new smart panel in order to produce active damping. The panel is equipped with 16 triangularly shaped piezoceramic patch actuators along its border and accelerometer sensors located at the top vertex of the triangular actuators. The primary objective of this paper is to demonstrate the vibration and sound radiation control using the new smart panel. Narrow frequency band experimental results highlight that the 16 control units can produce reductions up to 15 dB at resonance frequencies between 100 and 700 Hz in terms of both structural vibration and sound power radiation.     

Dynamic Modeling and Analysis of Wind Turbine Blade of Piezoelectric Plate Shell

This paper presents a theoretical analysis of vibration control technology of wind turbine blades made of piezoelectric intelligent structures. The design of the blade structure, which is made from piezoelectric material, is approximately equivalent to a flat shell structure. The differential equations of piezoelectric shallow shells for vibration control are derived based on piezoelectric laminated shell theory. On this basis, wind turbine blades are simplified as elastic piezoelectric laminated shells. We establish the electromechanical coupling system dynamic model of intelligent structures and the dynamic equation of composite piezoelectric flat shell structures by analyzing simulations of active vibration control. Simulation results show that, under wind load, blade vibration is reduced upon applying the control voltage.     

Finite element modelling of piezolaminated smart structures for active vibration control with distributed sensors and actuators

Finite element modelling of laminated structures with distributed piezoelectric sensor and actuator layers and control electronics is considered in this paper. Beam, plate and shell type elements have been developed incorporating the stiffness, mass and electromechanical coupling effects of the piezoelectric laminates. The effects of temperature on the electrical and mechanical properties and the coupling between them are also taken into consideration in the finite element formulation. The piezoelectric beam element is based on Timoshenko beam theory. The plate/shell element is a nine-noded field-consistent element based on first order shear deformation theory. Constant-gain negative velocity feedback, Lyapunov feedback as well as a linear quadratic regulator (LQR) approach have been used for active vibration control with the structures subjected to impact, harmonic and random excitations. The influence of the pyroelectric effects on the vibration control performance is also investigated. The LQR approach is found to be more effective in vibration control with lesser peak voltages applied in the piezo actuator layers as in this case the control gains are obtained by minimizing a performance index. The application of these elements in high-performance, light-weight structural systems is highlighted.     

Active control of low-frequency sound radiation by cylindrical shell with piezoelectric stack force actuators

A novel active control method of sound radiation from a cylindrical shell under axial excitations is proposed and theoretically analyzed. This control method is based on a pair of piezoelectric stack force actuators which are installed on the shell and parallel to the axial direction. The actuators are driven in phase and generate the same forces to control the vibration and the sound radiation of the cylindrical shell. The model considered is a fluid-loaded finite stiffened cylindrical shell with rigid end-caps and only low-frequency axial vibration modes are involved. Numerical simulations are performed to explore the required control forces and the optimal mounting positions of actuators under different cost functions. The results show that the proposed force actuators can reduce the radiated sound pressure of low-frequency axial modes in all directions.     

MODELLING DYNAMICS OF A CONTINUOUS STRUCTURE WITH A PIEZOELECTRIC SENSORACTUATOR FOR PASSIVE STRUCTURAL CONTROL

This paper presents the concept of a vibration control system in which motions of a continuous structure with piezoelectric sensors/actuators can be suppressed (or activated) through transforming mechanical energy to electrical one and vice versa. The study is focused on distributed parameter structures, in which electromechanical variables are spatially dependent, and therefore traditional methods of design of piezoelectric transformers do not apply. In this case, a different approach is necessary to account for the spatial dependency of the variables. To examine the feasibility of the proposed vibration control system, we have performed the vibration suppression analysis of the cantilevered beam with piezoelectric sensors/actuators subjected to an exciting force/moment(s). The experimental results indicate that the damping of the composite system increases by 8-10 times in comparison with the mechanical system.As a result, the paper significantly expands the concept of passive damping mechanism for structural systems to take into account the dynamics of a continuous elastic structure piezoelectrically coupled to electrical network.     

Optimal locations and orientations of piezoelectric transducers on cylindrical shell based on gramians of contributed and undesired Rayleigh–Ritz modes using genetic algorithm

In this study, the active vibration control and configurational optimization of a cylindrical shell are analyzed by using piezoelectric transducers. The piezoelectric patches are attached to the surface of the cylindrical shell. The Rayleigh–Ritz method is used for deriving dynamic modeling of cylindrical shell and piezoelectric sensors and actuators based on the Donnel–Mushtari shell theory. The major goal of this study is to find the optimal locations and orientations of piezoelectric sensors and actuators on the cylindrical shell. The optimization procedure is designed based on desired controllability and observability of each contributed and undesired mode. Further, in order to limit spillover effects, the residual modes are taken into consideration. The optimization variables are the positions and orientations of piezoelectric patches. Genetic algorithm is utilized to evaluate the optimal configurations. In this article, for improving the maximum power and capacity of actuators for amplitude depreciation of negative velocity feedback strategy, we have proposed a new control strategy, called “Saturated Negative Velocity Feedback Rule (SNVF)”. The numerical results show that the optimization procedure is effective for vibration reduction, and specifically, by locating actuators and sensors in their optimal locations and orientations, the vibrations of cylindrical shell are suppressed more quickly.     

Modeling and analysis of laminate composite plates with embedded active-passive piezoelectric networks

The objective of this work is to present the finite element modeling of laminate composite plates with embedded piezoelectric patches or layers that are then connected to active-passive resonant shunt circuits, composed of resistance, inductance and voltage source. Applications to passive vibration control and active control authority enhancement are also presented and discussed. The finite element model is based on an equivalent single layer theory combined with a third-order shear deformation theory. A stress-voltage electromechanical model is considered for the piezoelectric materials fully coupled to the electrical circuits. To this end, the electrical circuit equations are also included in the variational formulation. Hence, conservation of charge and full electromechanical coupling are guaranteed. The formulation results in a coupled finite element model with mechanical (displacements) and electrical (charges at electrodes) degrees of freedom. For a Graphite-Epoxy (Carbon-Fibre Reinforced) laminate composite plate, a parametric analysis is performed to evaluate optimal locations along the plate plane (xy) and thickness (z) that maximize the effective modal electromechanical coupling coefficient. Then, the passive vibration control performance is evaluated for a network of optimally located shunted piezoelectric patches embedded in the plate, through the design of resistance and inductance values of each circuit, to reduce the vibration amplitude of the first four vibration modes. A vibration amplitude reduction of at least 10 dB for all vibration modes was observed. Then, an analysis of the control authority enhancement due to the resonant shunt circuit, when the piezoelectric patches are used as actuators, is performed. It is shown that the control authority can indeed be improved near a selected resonance even with multiple pairs of piezoelectric patches and active-passive circuits acting simultaneously.     

Enhanced switching law for synchronized switch damping on inductor with bimodal excitation

Piezoelectric shunt damping is an emerging field of research. In recent years, a multitude of different electrical circuits have been developed aiming to increase the damping performance and robustness. Synchronized switch damping on inductor (SSDI) is a semi-active control technique that utilizes a passive inductance to build-up a voltage on the piezoceramics that is synchronized with the mechanical vibration. For a single mode excitation the voltage inversion should occur at the moments of maximum deformation, but for multimodal vibrations such a switching law may not be optimal.In this paper a novel switching law for bimodal vibrations is presented using a modal observer. An enhanced voltage build-up is generated by utilizing the vibration energy of the second mode. The amplification of dissipated energy is calculated in an analytical way using normalized parameters, yielding a general result which includes the influence of the frequency and amplitude ratio of the excitation signal. Measurements on a clamped beam test rig are conducted in order to validate the proposed method. An increase of nearly 350 percent in energy dissipation compared to the classical SSDI has been achieved. Furthermore, the increase in energy dissipation is higher than for a previously suggested, comparable switching law.     

Independent modal control for nonlinear flexible structures: An experimental test rig

This paper investigates the use of independent modal control to suppress the vibration of nonlinear flexible structures. In recent years technological improvements in the mechanical field have led to high-performance systems with low weight and, as a consequence, high flexibility and low damping. Here active control quickly bettered the traditional passive damping systems. The structure investigated in this paper is a multi-body flexible boom moved by hydraulic actuators. The nonlinear system dynamic was numerically reproduced and a control strategy, based on the use of the same actuators, was developed. Finally a test rig was created to validate the proposed approach experimentally.     

Quality factors for the nano-mechanical tubes with thermoelastic damping and initial stress

The Quality factors (Q-factor) are defined as the ratio of the kinetic and potential energy to dissipation for various damping mechanisms of structures. Therefore, improvement in the Q-factors is an important issue in micro- and nano-resonator applications for the high performance. Also, it is well known that the thermoelastic damping is more crucial than the other damping factors in a device. Thus, the vibration of nano-mechanical circular tube is investigated with thermoelastic damping and initial stress effects in this work. To simplify the shell equations for the transverse displacement-dominated problems, the Donnell-Mushtari-Vlasov (DMV) approach is adopted. Applying the stress function, the equations of motion for deflection, compatibility equation and heat conduction equation are derived. Using an iterative scheme, the natural frequencies and the Q-factors under the initial stress are obtained, and the influences of the dimensions of the shell, the mode numbers and initial stress are discussed in detail.     

Active control of cylindrical shell with magnetostrictive layer

This paper analyses the damping characteristics of a titanium shell with a magnetostrictive layer bonded to it. The magnetostrictive layer produces an actuating force required to control vibration in the shell, based on a negative velocity feedback control law. The control input is the current to the solenoid surrounding the shell. In the present study, a finite element formulation, physically consistent with the problem has been developed. Vibration reduction in the shell by changing the position of the magnetostrictive layer and its current carrying actuating coil pair along the shell is investigated.     

Partial pole placement in structures by the method of receptances: Theory and experiments

The theory and practical application of the receptance method for vibration suppression in structures by multi-input partial pole placement is described. Numerous advantages of the receptance method over conventional matrix methods such as state-space control based on finite elements have been demonstrated, in particular there is no need to know or to evaluate the structural matrices M, C, K and in practical experimentation the measurement of ‘receptance’ may be generalised so that explicit modelling of actuator dynamics becomes unnecessary. Active vibration control is demonstrated experimentally using two test rigs. In the first set of experiments partial pole placement is applied to a lightweight glass-fibre beam using macro fibre composite (MFC) actuators and sensors. In the second set of experiments active vibration control is implemented on a heavy modular test structure representative of systems of differing dynamic complexity using electromagnetic actuators and piezoelectric (ICP) accelerometers. It is demonstrated that chosen poles may be assigned to predetermined values without affecting the position of other poles of interest.     

Active modal control simulation of vibro-acoustic response of a fluid-loaded plate

Active modal control simulation of vibro-acoustic response of a fluid-loaded plate is presented. The active modal control of the vibro-acoustic response is implemented using piezoelectric actuators/sensors. The active modal damping is added to the coupled system via negative velocity feedback. The feedback gain between the piezoelectric actuators/sensors for the modal control is obtained using the in-vacuo modal matrix and the incompressible fluid-loaded modal matrix. The modal control performance of structural vibration and acoustic radiation of a baffled plate is numerically studied. It is shown that the proposed method increases the modal damping ratio and achieves reduction in the mean square velocity and the sound power for given modes of the fluid-loaded plate.     

微机械薄膜变形镜自适应光学系统实验研究

为求出自适应光学系统的最优校正电压, 提出了一种基于改进奇异值分解的闭环迭代控制算法。该算法可通过调节控制参量g1,g2和w,优化模式的收敛速度, 使控制信号快速收敛到一个可靠的局部最优解。搭建基于微机械薄膜变形镜(MMDM)的自适应光学系统, 测量光学影响函数并验证单个电极电压和镜面变形之间的准平方线性关系, 以及各个驱动器电极响应之间的线性叠加性。分别采用模拟眼和人眼出射波前作为原始波前进行实验。实验结果表明, 改进算法能快速有效地对静态或动态畸变波前进行校正, 为基于MMDM的自适应光学系统提供了算法支持。     

极点配置法弹性平板有源隔声系统优化

对混响声场中的弹性平板有源隔声系统进行优化。根据激励频率范围确定受控模态阶次,在模态空间中建立系统降阶方程,基于极点配置方法,采用分布式系统增加受控模态的阻尼,降低低频共振声传输。同时设计模态滤波器,为控制器提供所需的状态信息。为提高控制效能,本文对传感器和作动器布放位置进行优化,尝试不同极点配置方案,并对耦合控制与独立模态控制方法的隔声效果进行比较。仿真结果显示,极点配置法有源隔声可以有效降低共振声传输,优化布放和独立模态控制方式下,控制力明显降低。优化后的有源隔声系统效能有所提升。      

磁悬浮－气囊主被动混合隔振装置理论和实验

为了更有效地控制舰船动力机械宽频和低频线谱振动的传递,提出了一种将磁悬浮作动器与气囊隔振器集成应用的磁悬浮-气囊主被动混合隔振装置。通过对磁悬浮作动器机电耦合特性和混合隔振系统动力学特性的分析研究,确定了满足线谱振动控制要求和满足混合隔振装置性能要求的参数设计方法。针对主动控制时,FxLMS (filtered-x least mean square)算法在小阻尼系统上需用高阶FIR滤波器建模,运算量大的问题,提出了分频段控制的改进FxLMS算法,并有效地解决了作动器的非线性效应问题。样机实验结果表明:理论分析是正确的,该项技术控制力需求小,装置稳定性好,具有优良的宽频隔振和低频线谱振动控制效果。