Dynamic Modeling and Analysis of a Rotating Piezoelectric Smart Beam

Control performances of smart structures depend on the size and location of the piezoelectric actuators and sensors as well as on the applied control algorithm. This article presents optimal vibration control of a thin-walled composite beam by using the fuzzy optimization strategy based on the particle swarm optimization algorithm. The optimization of the size and location of the conventionally collocated piezoelectric actuators and sensors, and optimization of the controller parameters are performed separately. The optimization criteria for optimal size and location of piezoelectric actuators and sensors are based on eigenvalues of the controllability Grammian matrix. The optimization procedure implies constraint of the original dynamic properties change and limitation of the beam mass increase. The particle swarm optimization-based linear quadratic regulator has been implemented for optimal vibration control in order to maximize the modal closed-loop damping ratios and minimize the control voltages required for actuation while keeping them below breakdown voltage for the used piezoelectric actuator. A pseudo-goal function, derived from the fuzzy set theory, gives an expression for global objective functions eliminating the use of weighting coefficients and penalty functions. The problem is formulated using the finite element method based on the third-order shear deformation theory. Several numerical examples are presented for the cantilever beam.

Exact static solutions to piezoelectric smart beams including peel stresses: I: Theoretical formulation

In this article, active flutter and aerothermal postbuckling control of the nonlinear composite laminated panel with large deformation in supersonic airflow using the piezoelectric material are investigated. The distributed piezoelectric actuator and sensor pairs are bonded on the top and bottom surfaces of the laminated panel. The von Karman strain–displacement relation is used in the structural modeling. Unsteady aerodynamic pressure is evaluated by the supersonic piston theory. Hamilton’s principle and the assumed mode method are applied to formulate the equation of motion of the structural system. A discrete linear-quadratic-Gaussian controller is designed in this study to conduct the active flutter and postbuckling control. The proportional feedback control method is also applied in designing the controller. Time domain responses of the structural system are computed using the Runge–Kutta method. The control effects of the two control methods are compared. The influences of the placements of the piezoelectric actuator and sensor pairs on the control effects are also investigated. This study is helpful for the active aeroelastic design of the nonlinear structural system.

Piezoelectric functional materials have been extensively studied and employed in numerous devices. With the rapid development of modern industries, such as power plants, aerospace, automotive, renewable energy and material processing industries, the high temperature piezoelectric materials that can work in extreme environments are in great demand. Piezoelectric materials including piezoelectric single crystals, ceramics and films, are at the heart of electromechanical actuation and sensing devices. A variety of applications where piezoelectric actuators and sensors operate at elevated temperatures (T 200℃) would be extremely desired. The actuators need to work efficiently with high strokes, torques, and forces while operating under relatively harsh conditions. These include high-temperature fans and turbines, motors for valves or natural gas industries, kiln automation, and actuators for automotive engines such as fuel injectors and cooling system elements. Yet, the majority of industrial actuator applications are at or below the 250℃ temperature limit. In addition to the increase in operational temperatures of piezoelectric motors and actuators, a future area of interest is high-temperature MEMS research, which can be used for high-temperature valving. On the other hand, the piezoelectric sensors have been widely used for structural health monitoring applications. This is due to their wide bandwidth, versatility, simplicity, high rigidity, high stability, high reproducibility, fast response time, wide operating temperature range, insensitivity to electric and magnetic fields, the capacity for miniaturization and minimal dependence on moving parts and low power consumption, and wide piezoelectric materials and mechanisms selections, which will greatly benefit the sensing applications. In addition to the temperature usage range, the piezoelectric sensors must withstand the harsh environments encountered in space, engine, power plants, and also need to possess high sensitivity, resistivity, reliability, stability and robustness. In order to use the piezoelectric materials for a specific high temperature application, many aspects need to be considered together with piezoelectric properties, such as phase transition, thermal aging, thermal expansion, chemical stability, electrical resistivity, and the stability of properties at elevated temperature. In this paper, ferroelectric materials with high Curie point, including perovskite-type ferroelectrics, bismuth layer structured ferroelectrics, tungsten-bronze structured ferroelectrics, together with non-ferroelectric piezoelectric single crystals, are surveyed. The crystal structure characteristics, high temperature piezoelectric properties, and recent research progress are discussed. A series of high temperature piezoelectric devices and their applications are reviewed, including high temperature piezoelectric detectors, sensors, transducers, actuators, etc. Finally, recent important research topics, the future development of high temperature piezoelectric materials and the potential new applications are summarized.

Active sound transmission control using a piezoelectric sensor and actuator on a thin plate is investigated experimentally. The plate made of aluminium covers the opening of an acoustic enclosure where a sound source is located. The exterior acoustic field is measured by a microphone array, which scans a hemispherical surface. The isolation performance of the passive plate is poor at its resonance frequencies. Sound transmission through the plate is actively controlled at the resonance frequencies. A one-sensor one-actuator control system minimizes the sensor output by applying a proper electric voltage to the actuator. Global sound reduction of 15-22 dB is achieved at the first three resonance frequencies by using the same sensor and actuator. Using a sensor at a different location, a reduction of 9 dB is obtained at a higher frequency. The relation between control performance and the coincidence of the responses of the transmitted sound and the sensor is briefly discussed based on the mode decomposition theory.

The effect of the time delay between the sensor output and actuation is studied on the displacement and velocity feedback control of a cantilever beam. The system consists of a piezoelectric sensor and actuator pair bonded to an Euler-Bernoulli beam to form an actively controlled laminated structure. The effects of Kelvin-Voigt damping are also included in the problem. The piezoelectric actuators and sensors are taken as patches of partial length which leads to a differential equation formulation with discontinuities. The numerical solution is obtained by replacing the original formulation with an integral equation which is solved by expanding the state function in terms of the eigenfunctions of the freely vibrating beam. This approach leads to an infinite set of linear equations which can be solved with a high degree of accuracy by computing the characteristic equation using a small number of terms. Numerical results are given to analyze the control effectiveness in terms of changes in the natural frequencies for various gains, damping coefficients and time delays.

Flutter suppression for highly flexible wings using passive and active piezoelectric effects

Refined models for the optimal design of adaptive structures using simulated annealing

A new class of materials known as ‘functionally graded materials’ (FGMs) has emerged recently, in which the material properties are graded but continuous particularly along the thickness direction. In an effort to develop the super heat resistant materials, Koizumi [1] first proposed the concept of FGM. These materials are microscopically heterogeneous and are typically made from isotropic components, such as metals and ceramics. In the quest for developing lightweight high performing flexible structures, a concept emerged to develop structures with self-controlling and self-monitoring capabilities. Expediently, these capabilities of a structure were achieved by exploiting the converse and direct piezoelectric effects of the piezoelectric materials as distributed actuators or sensors, which are mounted or embedded in the structure [2, 3]. Such structures having built-in mechanisms are customarily known as ‘smart structures’. The concept of developing smart structures has been extensively used for active control of flexible structures during the past decade [4]. Recently considerable interest has also been focused on investigating the performance of FG plates integrated with piezoelectric actuators. For example, Ootao and Tanigawa [5] theoretically investigated the simply supported FG plate integrated with a piezoelectric plate subjected to transient thermal loading. A 3-D solution for FG plates coupled with a piezoelectric actuator layer was proposed by Reddy and Cheng [6] using transfer matrix and asymptotic expansion techniques. Wang and Noda [7] analyzed a smart FG compositestructure composed of a layer of metal, a layer of piezoelectric and a FG layer in between, while in [8] a finite element model was developed for studying the shape and vibration control of FG plates integrated with piezoelectric sensors and actuators. Yang et al. [9] investigated the nonlinear thermo-electro-mechanical bending response of FG rectangular plates covered with monolithic piezoelectric actuator layers; most recently, Huang and Shen [10] investigated the dynamics of a FG plate coupled with two monolithic piezoelectric layers undergoing nonlinear vibrations in thermal environments. All the aforementioned studies focused on the rectangular-shaped plate structures. However, to the authors’ best knowledge, no researches dealing with the free vibration characteristics of the circular FGM plate integrated with the piezoelectric layers has been reported. Therefore, the present work attempts to solve the problem of providing analytical solution for free vibration of thin circular FG plates with two full size surface-bonded piezoelectric layers on the top and the bottom of the FG plate. The formulations are based

Being small in size and weight, piezoelectric transducers hold unique positions in vibration sensing and control. Here, we explore the possibility of building a compact vibration isolation system using piezoelectric sensors and actuators. The mechanical resonances of a piezoelectric actuator around a few kHz are suppressed by an order of magnitude via electrical damping, which improves the high-frequency response. Working with a strain gauge located on the piezoelectric actuator, an auxiliary control loop eliminates the drift associated with a large servo gain at dc. Following this approach, we design, optimize, and experimentally verify the loop responses using frequency domain analysis. The vibration isolation between 1 Hz and 200 Hz is achieved and the attenuation peaks at 60 near vibration frequency of 20 Hz. Restrictions and potentials for extending the isolation to lower vibration frequencies are discussed.

A finite-element model is developed for the active buckling control of laminated composite plates using piezoelectric materials. The finite-element model is based on the first-order shear deformation plate theory in conjunction with linear piezoelectric theory. The piezoelectric sensors and actuators can be surface bonded or embedded and can be either continuous or segmented. The dynamic buckling behavior of the laminated plate subjected to a linearly increasing uniaxial compressive load is investigated. The sensor output is used to determine the input to the actuator using a proportional control algorithm. The forces induced by the piezoelectric actuators under the applied voltage fields enhance the critical buckling load. Finite-element solutions are presented for composite plates with clamped and simply supported boundary conditions and the effectiveness of piezoelectric materials in enhancing the buckling loads is demonstrated.

This paper presents to verify the energy harvesting of a nonlinear piezoelectric multilayer beam under harmonic excitation. For getting the perfect performance in energy harvesting, the effect of the energy loss factor, resistive load, and excitation frequency are studied on the results of the power and voltage generated. In this paper, a numerical program is developed with matlab software. Numerical approximation of the nonlinear equations uses a mixed finite element formulation in terms of displacement and potential electrical variables. To verify the numerical results, the experimental results for the energy harvesting of a piezoelectric multilayer beam with harmonic base excitation are used. The multilayer piezoelectric beam (MPB) used consists of two bimorphs in the case of a series connection and a substructure layer of aluminum. For the considered electrical circuit, the piezoelectric energy harvesting model is connected to the resistive load and the generated power in MPB is sent to load resistance. The influence of the type of layer connection on the output voltage value is investigated. The generated voltage and electrical power of the resistive load are verified using the piezoelectric multilayer beam in both resonance and off-resonance cases. According to the results, the maximum value of electric power occurs at the optimum resistive load for the selected frequency value and the behavior of energy harvesting depends greatly on the excitation frequency. Also, the value of the capacitance and resistive load affects the voltage and power generated, and optimum resistance is vital for producing maximum power.

While the previous chapters attempt to provide a comprehensive formulation of the theory of plates applied to isotropic and composite material structures, this chapter illustrates representative areas of recent research and development. Naturally, the list of such areas is extensive, including solutions where the response of plate materials is elastic-plastic, viscoelastic or viscoplastic, plates formed of several materials and incorporating inclusions of various shapes, textile composites, shape memory alloy structures, etc. In this chapter we concentrate on two developments, i.e. plates with piezoelectric sensors and actuators and functionally graded material plates. The former area is particularly relevant to thin-walled aerospace structures whose dynamic response can be monitored and controlled by piezoelectric sensors and actuators. It is also applicable to energy harvesting and structural health monitoring systems. Functionally graded plates possess a number of potential advantages over conventional composite plate designs, including elimination of delamination tendencies present in laminated structures, reduced thermal residual stresses and improved thermal response during lifetime, possible enhancement in fatigue and fracture characteristics, etc. Since functionally graded plates are often applied in thermal applications, the discussion is centered on relevant problems.

In this work, an impact based frequency up-conversion mechanism is studied via discontinuous dynamics analysis. The mechanism consists of a moving stopper and a piezoelectric beam. The repeated free vibration of the piezoelectric beam achieved through the impaction between the stopper and the beam, With the stopper excited by a sawtooth wave. Due to the impact, the system contains complex discontinuous dynamics, hence to better understand the energy harvesting performance of the piezoelectric beam, we seek the simple periodic motions of the system. As the system parameter varies, the output voltage and power of the piezoelectric beam with periodic motions is obtained. These results were also compared with those obtained when the piezoelectric beam is directly subjected to the same sawtooth wave. The piezoelectric beam was modeled as a mass-spring-damper system, and the linear piezoelectric constitutive equations have been used to obtain the lumped model of the piezoelectric beam. In this study, numerical solutions of the generated power and voltage were obtained via discontinuous dynamics analysis. When the excitation frequency is low, the effect of frequency-up-conversion is demonstrated by comparing the generated power of two cases: piezoelectric beam excited via impact and beam directly subject to the sawtooth wave. The stable and unstable periodic motions and bifurcation trees of the impact parameters are predicted analytically versus varying excitation frequency for period-1 and period-2.

This paper studies the aeroelastic oscillations of wing-like structures with the aim to detect at an incipient stage the presence of structural cracks. Such oscillations occur normally in certain flight evolutions of aircraft or can be excited by piezoelectric actuators bonded on the wing structure. These oscillations can be used to detect at an early stage the presence of cracks by monitoring the response of several piezoelectric sensors bonded on both sides of the structure during the aeroelastic oscillations. The proposed method of crack detection uses pairs of piezoelectric strip sensors bonded on the opposite sides of the structure and is based on the fact that the presence of a crack causes a difference between the strains measured by the two sensors of a pair. The structural analysis presented in this paper uses a nonlinear model for the cracks and a finite element formulation for the piezoelectric strips coupled with the structure. A 3D panel method developed by the authors is used to determine the unsteady aerodynamic loads acting on the oscillating wing structure. The dynamic analysis in the time domain is performed for the oscillating structures with piezoelectric strips subjected to unsteady aerodynamic loads. In the present work, the efficiency of this crack detection method is studied in realistic situations, by considering the aeroelastic oscillations in flexion and torsion of a wing-like structure which are excited in one of the following modes: (i) the aeroelastic oscillations excited by a pair of piezoelectric actuators bonded on the opposite sides of the structure; (ii) the aeroelastic oscillations excited by the harmonic oscillation of the angle of attack corresponding to the flight in atmospheric turbulence (harmonic gust); (iii) the aeroelastic oscillations generated by a sudden change in the angle of attack or in the airplane velocity due to a pilot control input. The numerical simulations for these cases have been performed by the simultaneous solution of the coupled equations of unsteady fluid flow and of the structure deformation motion, by using a finite element method for the dynamic of the structures with cracks and bonded piezoelectric strips, and a 3D panel method developed by the authors for the calculation of the unsteady aerodynamic loads. These numerical simulations have shown that the presence of a crack in the structure can be efficiently detected at an early stage by monitoring the response of the pairs of piezoelectric sensors.