Active flutter and aerothermal postbuckling control for nonlinear composite laminated panels in supersonic airflow

A new method of smart and optimal flutter control for composite laminated panels in supersonic airflow under thermal effects

Aerothermoelastic flutter properties of nonlinear composite laminated panels in supersonic airflow are studied, and investigations on active flutter and aerothermal postbuckling suppression for the panels with time-dependent boundary conditions are also carried out using macro fiber composite actuator and sensor. The von Karman strain–displacement relation in conjunction with the supersonic piston theory is applied in structural modeling. Nonlinear dynamic equations of motion for the structural system are established using Hamilton’s principle and the assumed mode method. Frequency- and time-domain methods are used to investigate the aerothermoelastic characteristics and active flutter and aerothermal postbuckling suppression of the panels. Effects of aspect ratio and ply angle on the nonlinear aerothermoelastic behaviors are studied. The displacement feedback control is used to conduct the active flutter and postbuckling suppression. The nonlinear output controller consisting of a linear quadratic regulator and a nonlinear state estimator of extended Kalman filter is also used in designing the controller. Controlled vibration responses of the structural system under the two different controllers are compared. The results show that the developed linear quadratic regulator/extended Kalman filter controller is more effective than the displacement feedback control controller in flutter and postbuckling control of the panels with time-dependent boundary conditions in supersonic airflow.

In active vibration control study, piezoelectric actuators and sensors are bonded on the surface of a beam. They can change the frequency and modal characteristics of the system. This paper presents an analysis of the frequency response to a rotating piezoelectric smart beam. Hamilton’s principle along with the assumed mode method are employed to derive the governing equations of the first-order approximate coupling model for the piezoelectric smart beam. The coupling is taken into account as the second-order coupling effect of the axial elongation caused by the transverse displacement of the beam. Then, the equations are transformed into a dimensionless form after identifying the necessary parameters. The dimensionless natural frequencies of the piezoelectric smart beam corresponding to the bending and stretching vibrations are obtained through a numerical simulation, with comparison made of those of the beam with no actuator or sensor. Furthermore, the implication is investigated of the structural parameters and bond location on the piezoelectric actuators and sensors. Besides, the common case of a smart beam bonded with multiple pairs of piezoelectric actuators and sensors is studied, and the effects of the first natural frequency and tip deformation are analyzed. The research provides a theoretical reference for the optimization of structural parameters and location of piezoelectric actuators and sensors, thereby preventing the resonance when the excitation frequency is approximately equal to the natural frequency of the beam.

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.

Variable Angle Tows (VAT) composite materials can effectively transfer major stresses from the interior region to the edges through in-plane load redistribution, thereby significantly enhancing their structural performance. Therefore, correct handling of boundary conditions is crucial in analyzing VAT structures. Considering that most practical engineering cases involve non-ideal or non-classical boundary support, this paper proposes an efficient method to address the nonlinear thermal flutter problem of elastic supported VAT curved panels in supersonic airflow. Assuming the fiber orientation angle varies in four different ways along the x-direction, the basic equations are established based on the von Kármán large deformation plate theory and the first-order piston theory. The generalized Galerkin method, capable of handling arbitrary elastic boundary constraints, is used to solve the problem in the space domain, while the Runge-Kutta method is applied in the time domain. Numerical examples illustrate how elastically restrained conditions, fiber orientation angles, height-rise ratio, and thermal loads, along with aerodynamic pressure, influence flutter responses of VAT panels. The presented method can be used for the aeroelastic stability design of VAT curved panels under arbitrary boundary conditions.

This work is aimed at the active vibration control of a flexible structures using piezoelectric material. A simple supported plate structure, which is supported at two opposite ends, is taken as the flexible structure with piezoelectric materials as sensors and actuators. Sensors and actuators, which are square in shapes, are embedded to the parent structure. The active controller was designed to control first three modes of vibration of plate. First, the analysis for the transient vibrations in a simple supported plate structure was performed which was followed by the analysis of the same simple supported plate structure when embedded upon with a pair of sensor and actuator. The plate was discretised into several small rectangular elements (6X6, 7X7… 11X11) of identical size in order to assign the different locations to sensors and actuators, which were assumed to be of the exact shape of the discretized plate elements. Further a LQR controller is applied for attenuating the global structural vibration. Settling time for each different location of piezoelectric patch location was observed which was then followed by an interpretation for the optimal location for piezoelectric patch for maximizing the vibration control. The model designed for study was duly verified with the results from past literature and an agreement between the both was observed.

Aerothermoelastic analysis of composite laminated trapezoidal panels in supersonic airflow

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.

A flow-structure coupled numerical method was developed to study the possibility of active control of cascade flutter. With the intention of applying piezo electric device, numerical analyses were performed under transonic flow conditions. In the cascade model adopted for this study, the unsteady aerodynamic force induced by passage shock wave was dominant for blade vibration stability. To control the passage shock movement, the method in which the trailing edge of blade was actively vibrated was sought. The method was revealed to change the unsteady aerodynamic force acted on the blade from exciting force to damping force if the phase of trailing edge oscillation was properly selected. To confirm the possibility of active control of cascade flutter, on/off control method with trailing edge oscillation was numerically simulated by flow-structure coupled method. From the results, it was revealed that increase in blade amplitude was suppressed by this control.

This article investigates the active control of panel flutter with piezoelectric transducers and including linearized potential flow aerodynamics. The aerodynamic modeling is accomplished by approximating the aerodynamic generalized forces with infinite impulse response filters. These filters are coupled to the in vacuo panel dynamic system in feedback, thus, creating a coupled, aeroelastic system. The panel model is developed from a Rayleigh-Ritz approach and includes the mass and stiffness effects of a piezoelectric transducer. Acting as a self-sensing actuator, the piezoelectric transducer is used to implement direct rate feedback control. Results of an analytical implementation of this control system demonstrate a significant increase in the flutter boundaries.

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.

This paper presents the design of a sliding-mode controller for a piezoelectric-driven nanometer resolution stage. The nanometer resolution stage is developed using the features of a flexible structure, and is driven by piezoelectric actuators and also uses capacitance sensors for position feedback. The hysteresis characteristic of the piezoelectric actuators is one of the major deficiencies in a wide variety of precise tracking positioning controls. In order to design the control system, the open-loop characteristics of this nanometer resolution stage are investigated. According to the open-loop characteristics, each pair of piezoelectric actuator and capacitance sensor is treated as an independent system and modeled as a first order linear model coupled with hysteresis. When the model is identified, the hysteresis nonlinearity is linearized then the linear system model with uncertainty is used to design the controller. When designing the controller, the sliding-mode disturbance estimation and compensation scheme is used. The structure of the proposed controller is similar to the PID controller. Thus, it can be easily implemented.

Smart actuators, made of smart materials, are becoming more attractive in many applications because smart materials are not subjected to wear and does not require lubrication during services. Piezoelectric materials are a group of the many attractive smart materials that are being investigated for many applications today. Piezoelectric materials show fast responses, high efficiency/accuracy and operate on a large bandwidth. Composite materials are of interest because of their design flexibility and because they are lighter than other materials commonly used in aircraft and other applications. For the research reported here, a piezoelectric material was embedded in a composite material to form a piezoelectric composite actuator. This research was conducted to expand our knowledge of piezoelectric composite material actuators, and originated from the need to control air flow separation over an airfoil. There is a need to build a profound knowledge about such actuators before they can be implemented in an airfoil, and to understand which parameters influence the behaviour of piezoelectric composite material actuators under static and dynamic operating conditions. The actuators were manufactured and tested under static and dynamic conditions and the experimental results were compared to the finite element models. The models were incorporated with piezoelectric material properties that were determined experimentally. The results showed that a piezoelectric material’s response to an input stimulant, e.g. electric voltage and frequency, influences the actuator’s behaviour.

A complex adaptive structure for the purposes of this paper is treated as a structure with embedded piezoelectric sensors and actuators that are connected through a control loop so that the structure can adaptively or optimally respond to an external disturbance [1–4]. Such structures, also called smart structures, present special challenges in analytical and numerical modeling. The piezoelectric devices involve coupled electric and elastodynamic fields, the devices are multiple in number, the size of the structure is typically much larger in size relative to the sensors and actuators, and in real applications the geometry of the structure is complex. The response of such a structure to an external excitation and the response of the embedded sensors can only be simulated numerically. The finite element method has been successfully used to solve such problems, but the size of the resulting matrices becomes very large even for simple geometries [5–9]. To give an example, to obtain the transient response of a simple clamped plate with five pairs of sensors and actuators it is necessary to retain the first 50 structural modes and this results in an 800 × 800 matrix. In order to then interface such a numerical model with a control algorithm such as an H∞ robust controller including modeling and device uncertainties, may challenge even the fastest computers to provide the required actuator excitations for real time controlled response of the adaptive structure. The objective of this paper is to address this issue and present a technique to condense or reduce the system model while still retaining the essential dynamical features of the smart structure [7].KeywordsModel ReductionSmart StructureState Space RepresentationPiezoelectric DeviceAdaptive StructureThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The active vibration control of all kinds of structures by using the piezoelectric materialhas been extensively investigated. In this paper, the active aeroelastic flutter characteristicsand vibration control of supersonic beams applying the piezoelectric material are studiedfurther. The piezoelectric materials are bonded on the top and bottom surfaces of thebeams to act as the actuator and sensor so that the active aeroelastic flutter suppressionfor the supersonic beams can be conducted. The supersonic piston theory is adopted toevaluate the aerodynamic pressure. Hamilton’s principle with the assumed modemethod is used to develop the dynamical model of the structural systems. By usingthe standard eigenvalue methodology, the solutions for the complex eigenvalueproblem are obtained. A negative velocity feedback control strategy is used toobtain active damping. The aeroelastic flutter bounds are calculated and the activeaeroelastic flutter characteristics are analyzed. The impulse responses of the structuralsystem are obtained by using the Houbolt numerical algorithm to study the activeaeroelastic vibration control. The influences of the non-dimensional aerodynamicpressure on the active flutter control are analyzed. From the numerical results it isobserved that the aeroelastic flutter characteristics of the supersonic beams canbe significantly improved and that the aeroelastic vibration amplitudes can beremarkably reduced, especially at the flutter points, by using the piezoelectricactuator/sensor pairs which can provide an active damping. Within a certain value of thefeedback control gain, with the increase of it, the flutter aerodynamic pressure(or flutter velocity) can be increased and the control results are also improved.