Active vibration control of beam structures using acceleration feedback control with piezoceramic actuators

In this study, the active vibration control of clamped–clamped beams using the acceleration feedback (AF) controller with a sensor/moment pair actuator configuration is investigated. The sensor/moment pair actuator is a non-collocated configuration, and it is the main source of instability in the direct velocity feedback control system. First, the AF controller with non-collocated sensor/moment pair actuator is numerically implemented for a clamped–clamped beam. Then, to characterize and solve the instability problem of the AF controller, a parametric study is conducted. The design parameters (gain and damping ratio) are found to have significant effects on the stability and performance of the AF controller. Next, based on the characteristics of AF controllers, a multimode controllable single-input single-output (SISO) AF controller is considered. Three AF controllers are connected in parallel with the SISO architecture. Each controller is tuned to a different mode (in this case, the second, third and fourth modes). The design parameters are determined on the basis of the parametric study. The multimode AF controller with the selected design parameters has good stability and a high gain margin. Moreover, it reduces the vibration significantly. The vibration levels at the tuned modes are reduced by about 12 dB. Finally, the performance of the AF controller is verified by conducting an experiment. The vibration level of each controlled mode can be reduced by about 12 dB and this value is almost same as the theoretical result.     

Geometrically nonlinear free vibration of shear deformable piezoelectric carbon nanotube/fiber/polymer multiscale laminated composite plates

The nonlinear free vibration of carbon nanotubes/fiber/polymer composite (CNTFPC) multi-scale plates with surface-bonded piezoelectric actuators is studied in this paper. The governing equations of the piezoelectric nanotubes/fiber/polymer multiscale laminated composite plates are derived based on first-order shear deformation plate theory (FSDT) and von Kármán geometrical nonlinearity. Halpin–Tsai equations and fiber micromechanics are used in hierarchy to predict the bulk material properties of the multiscale composite. The carbon nanotubes are assumed to be uniformly distributed and randomly oriented through the epoxy resin matrix. A perturbation scheme of multiple time scales is employed to determine the nonlinear vibration response and the nonlinear natural frequencies of the plates with immovable simply supported boundary conditions. The effects of the applied constant voltage, plate geometry, volume fraction of fibers and weight percentage of single-walled carbon nanotubes (SWCNTs) and multi-walled carbon nanotubes (MWCNTs) on the linear and nonlinear natural frequencies of the piezoelectric nanotubes/fiber/polymer multiscale composite plate are investigated through a detailed parametric study.     

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.     

Periodic geometrically nonlinear free vibrations of circular plates

The geometrically nonlinear free vibrations of thin isotropic circular plates are investigated using a multi-degree-of-freedom model, which is based on thin plate theory and on Von Kármán's nonlinear strain-displacement relations. The middle plane in-plane displacements are included in the formulation and the common axisymmetry restriction is not imposed. The equations of motion are derived by the principle of the virtual work and an approximated model is achieved by assuming that the in-plane and transverse displacement fields are given by weighted series of spatial functions. These spatial functions are based on hierarchical sets of polynomials, which have been successfully used in p-version finite elements for beams and rectangular plates, and on trigonometric functions. Employing the harmonic balance method, the differential equations of motion are converted into a nonlinear algebraic form and then solved by a continuation method. Convergence with the number of shape functions and of harmonics is analysed. The numerical results obtained are presented and compared with available published results; it is shown that the hierarchical sets of functions provide good results with a small number of degrees of freedom. Internal resonances are found and the ensuing multimodal oscillations are described.     

Active suppression of panel flutter with piezoelectric actuators using eigenvector orientation method

This paper examines the use of eigenvector orientation method to detect the onset of subsonic and supersonic flutter of panels modeled by finite elements. The accuracy of the eigenvector orientation method for prediction of the flutter boundary (indicated by a gradual loss of orthogonality between two eigenvectors) is demonstrated by using the examples of a swept-back cantilever plate model at subsonic speed and a simply supported plate model at supersonic speed. Piezoelectric layers are assumed to be bonded to the top and bottom surfaces of the simply supported plate in order to provide bending moments to control motions of each finite element. An approach of optimal control design is presented to actively suppress the possible flutter based on linear quadratic regulator theory and the nonlinear modal equations of motions. To illustrate the applicability and effectiveness of using the piezoelectric layers as controllers, several cases are studied and presented. The effects of varying locations of control moments are studied so as to fulfill the objective of adjusting the flutter speed to be within a desirable range. The results illustrate that the control moment manipulation can offset the flutter occurrence and additionally generate a lead time for possibly executing flutter control.     

Flexural vibration analyses of piezoelectric ceramic tubes with mass loads in ultrasonic actuators

Based on Timoshenko beam model, a theoretical model of radially polarized piezoelectric ceramic tubes is investigated. In the model, the piezoelectric effects are considered, and the shear correction factor is introduced which reveals effects of the size of the cross-section and Poisson’s ratio. Based on the model, the particular attentions are devoted to effects of the boundary conditions at two ends on flexural resonance frequencies of the piezoelectric ceramic tubes. Changing the sizes of the tubes and the mass loads at both free ends, the variations of the flexural resonance frequencies of free–free piezoelectric ceramic tubes are calculated theoretically. Besides, the flexural resonance frequencies of the piezoelectric ceramic tube cantilevers with mass loads at one free end are also investigated theoretically. To verify accuracy of the theoretical mode, the flexural resonance frequencies for different lengths of the piezoelectric ceramic tubes and different loaded masses are measured experimentally. The theoretical results agree well with the experimental measurement, which demonstrates that the model is accurate for analyzing the flexural resonance frequencies of the piezoelectric ceramic tubes with mass loads.     

Active vibration suppression of multilayered plates integrated with piezoelectric fiber reinforced composites using an efficient finite element model

The active vibration suppression of hybrid composite and fiber metal laminate (FML) plates integrated with piezoelectric fiber reinforced composite (PFRC) sensors and actuators is studied for the first time, using an efficient and advanced layerwise plate theory. Unlike the conventional finite elements, the equipotential condition of electroded surfaces of sensors is satisfied exactly and conveniently using a novel concept of electric node. The effective electromechanical properties of the PFRC laminas are computed using a coupled three-dimensional iso-field micromechanical model. Numerical results are presented for both classical constant gain velocity feedback (CGVF) and optimal control strategies. The instability phenomena in CGVF control with conventionally collocated actuator-sensor pairs, and its remedy with a truly collocated arrangement are illustrated. The effect of segmentation of electrodes on the control response is studied. The segmentation of electrodes leads to a multi-input-multi-output (MIMO) configuration. The effects of piezoelectric fiber orientation, volume fraction and dielectric ratio of PFRC on the control response and the actuation/sensing authority are investigated for cantilever and simply supported plates.     

线耦合平板瞬态高频振动响应预报

提出了一种用于线耦合平板瞬态高频振动分析的预报方法.基于瞬态统计能量分析,从子系统能量平衡方程的动力学相似性,推导出了时域尺度变换法则:在时间尺度上进行缩尺变换,而损耗因子相应地成反比变换。在此基础上,针对线耦合平板的能量传递特点,导出了两种不同变换方式:一种对结构的材料参数进行变换,另一种对结构的几何参数进行变换。采用两种连接方式的线耦合平板模型对时域尺度变换方法进行数值验证,结果表明该方法能以较高的计算效率准确获得结构的瞬态高频振动响应。     

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.     

Adaptive active control of periodic vibration using maglev actuators

In this paper, active control of periodic vibration is implemented using maglev actuators which exhibit inherent nonlinear behaviors. A multi-channel feedforward control algorithm is proposed to solve these nonlinear problems, in which maglev actuators are treated as single-input–single-output systems with unknown time-varying nonlinearities. A radial basis function network is used by the algorithm as its controller, whose parameters are adapted only with the model of the linear system in the secondary path. Compared with the strategies in the conventional magnetic-levitation system control as well as nonlinear active noise/vibration control, the proposed algorithm has the advantage that the nonlinear modeling procedure of maglev actuators and the usage of displacement sensors could be both avoided. Numerical simulations and real-time experiments are carried out based on a multiple-degree-of-freedom vibration isolation system. The results show that the proposed algorithm not only could efficiently compensate for the actuators’ time-varying nonlinearities, but also has the ability to greatly attenuate the energy of periodic vibration.     

Actuation of a discontinuous structure with piezoelectric actuators

An alternate approach to exciting a one-dimensional structure with discontinuities using a piezoelectric actuator is presented and examined. Instead of being bonded to the uniform side of a beam, the piezoelectric actuator is attached such that it spans two adjacent rib discontinuities. In this configuration, the actuator generates an eccentric actuation force on the structure and induces both axial and transverse motions. The goal of this work is to first model the axial and transverse response caused by the piezoelectric actuator. Then, the change in that response is examined for the case where an external disturbance force is present. The system is modeled by coupling the piezoelectric strain and structural dynamic response. The characteristics of the voltage-generated piezoelectric forces are discussed through numerical examples. The structural response found using the dynamic force–voltage model for the actuator is then compared to the response when the actuator model is approximated by its static or zero-frequency value. Furthermore, the ability of the actuator to potentially provide better control authority by using this alternate configuration is examined. The numerical study shows that when the actuator spans two discontinuities, there is potential for greater control authority than when that same actuator is placed on the uniform side of the structure.     

径向极化压电陶瓷长圆管复合超声换能器的径向振动

提出了一种圆管式径向复合压电陶瓷换能器,并对其径向振动特性进行了分析。该换能器由径向极化的压电陶瓷圆管以及金属外圆管组成。利用解析法得出了金属圆管以及具有任意壁厚的径向极化压电陶瓷圆管径向振动的机电等效电路。基于金属圆管与压电圆管的机械边界条件,得出了换能器的六端机电等效电路。在此基础上得出了换能器共振及反共振频率方程的解析表达式,给出了换能器的共振及反共振频率与其几何尺寸之间的依赖关系。利用数值方法对换能器的径向振动特性进行了模拟及仿真,并与解析结果进行了比较。最后,设计并加工了一些径向复合管式压电陶瓷换能器,利用精密阻抗分析仪对其共振及反共振频率进行了实验测试。研究结果表明,利用解析理论得出的换能器共振及反共振频率与数值模拟结果以及实验测试结果符合很好。     

Parity-time symmetric acoustic system constructed by piezoelectric composite plates with active external circuits

Researches on parity-time (PT) symmetry in acoustic field can provide an efficient platform for controlling the travelling acoustic waves with balanced loss and gain. Here, we report a feasible design of PT-symmetric system constructed by piezoelectric composite plates with two different active external circuits. By judiciously adjusting the resistances and inductances in the external circuits, we obtain the exceptional point due to the spontaneous breaking of PT symmetry at the desired frequencies and can observe the unidirectional invisibility. Moreover, the system can be at PT exact phase or broken phase at the same frequency in the same structure by merely adjusting the external circuits, which represents the active control that makes the acoustic manipulation more convenient. Our study may provide a feasible way for manipulating acoustic waves and inspire the application of piezoelectric composite materials in acoustic structures.     

复合圆环弯曲振动四极子模态分析

针对压电圆环弯曲振动机电转换性能较差的问题,提出了一种复合圆环弯曲振动换能器,它由一个径向极化的压电陶瓷内圆环和一个金属外圆环复合而成。基于能量原理推导得到了复合圆环弯曲振动的谐振频率和有效机电耦合系数,探讨了弯曲振动四极子模态特性与其结构尺寸间的关系。当压电圆环尺寸不变时,随外侧金属圆环壁厚增加,复合圆环弯曲振动四极子模态谐振频率上升,有效机电耦合系数迅速上升到极大值后缓慢下降。最后,设计制作了圆环换能器并对其谐振频率和有效机电耦合系数进行了实验测试,测试结果与解析结果和数值模拟结果吻合得较好。     

Active control effort of hybrid piezoelectric absorber for structural control

This paper aims at addressing the active control effort of the active-shunted hybrid piezoelectric absorber for structural vibration suppression. Both active control efforts of the integrated and separated hybrid piezoelectric absorbers are analyzed by using a simple cantilevered beam example. It is recognized that a new hybrid piezoelectric absorber based on a switching operation is capable of reducing the active control effort. A switching type of the hybrid piezoelectric absorber can be developed by the simple combination of integrated and separated hybrid piezoelectric absorbers. It is demonstrated that the switching type of the absorber has the capability of the trade-off between the active control effort and the damping performance.     

复合圆环弯曲振动四极子模态分析

针对压电圆环弯曲振动机电转换性能较差的问题,提出了一种复合圆环弯曲振动换能器,它由一个径向极化的压电陶瓷内圆环和一个金属外圆环复合而成。基于能量原理推导得到了复合圆环弯曲振动的谐振频率和有效机电耦合系数,探讨了弯曲振动四极子模态特性与其结构尺寸间的关系。当压电圆环尺寸不变时,随外侧金属圆环壁厚增加,复合圆环弯曲振动四极子模态谐振频率上升,有效机电耦合系数迅速上升到极大值后缓慢下降。最后,设计制作了圆环换能器并对其谐振频率和有效机电耦合系数进行了实验测试,测试结果与解析结果和数值模拟结果吻合得较好。     

Active control of wall-bounded turbulence for drag reduction with piezoelectric oscillators

An experimental investigation was performed for active control of coherent structure bursting in the near-wall region of the turbulent boundary layer. By means of synchronous and asynchronous vibrations with double piezoelectric vibrators,the influence of periodic vibration of the double piezoelectric vibrators on the mean velocity profile, drag reduction rate, and coherent structure bursting is analyzed at Re_θ= 2766. The case with 100 V/160 Hz-ASYN is superior to other conditions in the experiment and a relative drag reduction rate of 18.54% is exciting. Asynchronous vibration is more effective than synchronous vibration in drag reduction at the same voltage and frequency. In all controlled cases, coherent structures at large scales are regulated while the small-scale structures are stimulated. The fluctuating velocity increases significantly. A periodic regulating effect on the coherent structure can be seen in the ASYN control conditions at the frequency of 160 Hz.     

径向复合压电陶瓷超声换能器的径向振动特性研究

对径向复合压电陶瓷超声换能器的径向振动特性进行了分析。该换能器由一个厚度极化的压电陶瓷实心圆盘和一个金属圆环在半径方向复合而成。论文首先研究了压电陶瓷圆盘及金属圆环的径向振动,推出了其径向振动的机电等效电路。在此基础上,利用换能器的径向边界条件,得出了径向复合压电陶瓷换能器的机电等效电路及其共振频率方程。探讨了换能器的共振频率和有效机电耦合系数与其几何尺寸之间的依赖关系。设计并实际制作了一些径向复合超声换能器,对其径向共振及反共振频率进行了测试,并利用有限元法进行了数值模拟。研究表明,利用文中理论得出的换能器的共振频率与实测值及数值模拟结果基本符合。