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This article examines the distribution of strain energy in the various component materials of actuated plates and investigates the manner in which the strain energy distribution is influenced by the actuated span-to-thickness ratio and the thickness of the adhesive bond layer. Furthermore, the article investigates the effect of modeling choices (e.g., kinematic assumptions and mesh density) on the predicted magnitude and mode of the dominant strain energy form in each component material. These computed parameters can be used to quantify the overall efficiency of an actuated plate in addition to aiding the understanding of the local mechanics that govern the process. The focus problem consists of a square aluminum plate with a single symmetric pair of surface-mounted piezoceramic actuators that are used to produce in-plane extension or bending in the aluminum plate. The behavior of the actuated plate is examined over a range of plate thicknesses and adhesive bond layer thicknesses by using a series of finite element models that feature different levels of kinematic complexity and different levels of two-dimensional (2-D) mesh density. The results of the study emphasize the need for discrete layer kinematics in determining the magnitude and mode of the dominant strain energy form in each constituent material; however, these computed parameters are shown to be rather insensitive to changes in 2-D mesh density. Most importantly, the study confirms the existence and quantifies the magnitude of the local kinematic effect, whereby a portion of the available actuation energy is diverted to the production of localized transverse shear deformation and transverse normal deformation, thus reducing the amount of actuation energy available to produce in-plane deformation in the structural substrate.

A quasi-static model for NiMnGa magnetic shape memory alloy is formulated along the lines of the Brinson and Tanaka SMA constitutive models. Since the shape memory effect (SME) and pseudoelasticity exist in both NiTi and NiMnGa, constitutive models for SMAs offer a basis for ferromagnetic shape memory alloys (FSMA) modeling. Two types of quasi-static tests involving constant external magnetic field and constant stress are conducted to identify nine model parameters. These model parameters include free strain, Young's moduli, fundamental critical stresses, fundamental critical threshold fields, and stress-influence coefficients. The Young's moduli of the material in its field and stress preferred states are determined to be 450 and 820 MPa respectively, while the free strain is measured to be 6.5%. These test data are used to assemble a critical stress—magnetic field intensity profile that is useful for determining the model parameters and for predicting the various states of the material for a wide range of magnetic or mechanical loading conditions. Although all of the parameters can be obtained from constant magnetic field testing, useful insight into NiMnGa actuator behavior can be gained from constant axial stress tests. Once implemented, the analytical model shows good correlation with the test data, capturing both the magnetic shape memory effect and pseudoelasticity. Because the model is piecewise linear, it does not capture material behavior resulting from nonlinear effects such as magnetic saturation. Despite its inherent limitations, this model shows encouraging results, providing a solid basis for future modeling efforts.

This article discusses finite element modeling of progressive damage in the adhesive bond layers of actuated plates and investigates the reduction in actuation capacity caused by the damaged bond layers. The primary challenge posed by this class of problems stems from the vast range of geometric scales that are represented, with the thickness of the adhesive layer representing the smallest scale, the overall thickness of the actuated plate representing the intermediate scale, and the in-plane dimensions of the plate representing the largest scale. In multiscale problems, the overall efficiency of the numerical methodology is of paramount importance, thus model development is guided by the need to obtain a sufficiently accurate solution at an acceptable computational expense. In this study, this goal is achieved through the use of a hierarchical, displacement-based, 2-D finite element model that includes the first-order shear deformation (FSD) model, Type I layerwise models (LW1) and Type II layerwise models (LW2) as special cases. Both the LW1 layerwise model and the more familiar FSD model use a reduced constitutive matrix that is based on the assumption of zero transverse normal stress; however, the LW1 model includes discrete layer transverse shear effects via in-plane displacement components that are C0 continuous with respect to the thickness coordinate. The LW2 layerwise model utilizes a full 3-D constitutive matrix and includes both discrete layer transverse shear effects and discrete layer transverse normal effects by expanding all three displacement components as C0 continuous functions of the thickness coordinate. The hierarchical finite element model incorporates a 3-D continuum damage mechanics model that predicts local orthotropic damage evolution and local stiffness reduction at the geometric scale represented by the individual material ply or, in the case of layerwise models, by the individual numerical layer. The results clearly demonstrate that the resulting model can efficiently simulate progressive damage in the adhesive layers. For rectangular actuator patches, the adhesive damage is highest near the corners of the actuator and is driven primarily by local concentrations in the transverse normal and transverse shear stresses. In contrast to previous studies that have shown that the inclusion of discrete layer transverse normal stress does not significantly influence the predicted global deformations, the present study shows that the transverse normal stress has a very significant effect in the initiation and progression of localized damage in the adhesive layers.

This article presents the material modeling and experimental characterization of SMA rod and tube actuators undergoing pure torsional deformations. The investigation of the torsional characteristics of SMAs is carried out in order to gain a fundamental understanding of the behavior of SMA torsional actuators. The proposed application is to alter the twist distribution of a tiltrotor blade from hover to forward flight modes, providing improved flight efficiency in both modes of flight. To describe the behavior of the actuator, a torsional model involving the extension of the one-dimensional (uniaxial) formulation of SMA phenomenology is presented. As an example, Brinson's model is chosen as the representative uniaxial model; however, the approach used here to extend the uniaxial model into the torsional domain is applicable to nearly any uniaxial SMA model. The parameters for the uniaxial model are derived from extensional testing of an SMA rod or tube, and are then used to predict the torsional characteristics of the same material. A major advantage of this method compared to prior art in torsional modeling is that the simplicity of deriving and implementing the parameters from uniaxial testing is carried over into the torsional domain. This simplicity derives from the fact that the measured properties (forces and displacements) in tensile loading are more readily suited to determining the model parameters than the measured properties in torsional loading which have been used by previous researchers (angles and torques which are, in fact, integrated quantities from strains and stresses). This article also presents a comprehensive experimental investigation and model correlation with both tension and torsional behavior of SMA rods and tubes. The model is compared with experimental data including torsional actuation tests against torsional springs. It is shown that the theoretical model demonstrates good agreement with the experimental data over a wide range of thermomechanical conditions. In addition, experimental phenomena associated with the torsional behavior of the SMA actuator such as the effects of heat treatment, twist rate, and loading pattern are examined.

For the simple case of a homogeneous, isotropic plate with a single, symmetric pair of actuators, previous work by the authors has demonstrated the importance of including discrete layer kinematics in predicting the global response of the actuated plate. The inclusion of discrete layer kinematics permits accurate modeling of the so-called local kinematic effect, whereby a portion of the total actuation is diverted to the production of localized transverse shear deformation near the edges of the actuator, thus reducing the amount of actuation energy available to produce the desired global deformation mode. The present study expands upon this previous effort, investigating the magnitude of the local kinematic effect for more complex actuated plates involving fiber-reinforced laminated composite substrates with multiple symmetric pairs of actuators. The results obtained from finite element simulations using a wide range of kinematic assumptions conclusively demonstrate that as the actuated span-to-thickness ratio decreases, the models with discrete layer kinematics predict a smaller global response than the models that use equivalent-single-layer kinematics. Thus, the local kinematic effect is observed to influence the global response of the actuated plates regardless of the material constitution of the structural substrate and regardless of the in-plane spacing between actuator pairs.

The effects of accurately accounting for transverse shear strain, transverse normal strain, and discrete layer kinematics on the computed global response of actuated plates are investigated using a hierarchical displacement-based, two-dimensional (2-D) finite element model that is developed specifically for composite laminates. The hierarchical model is used to obtain the first-order shear deformation model, a higher-order cubic equivalent-singlelayer model, a type-I layerwise model, and a type-II layerwise model as special cases. Each of the first three models uses a reduced constitutive matrix that is based on the assumption of zero transverse normal stress; however, the models differ significantly in their assumed distribution of transverse shear strain. The type-II layerwise model utilizes a full 3-D constitutive matrix and includes both discrete layer transverse shear effects and discrete layer transverse normal effects. The scope of the study is restricted to homogeneous plates with surface-mounted actuators covering a wide range of span-to-thickness ratios. The results clearly demonstrate that as the span-to-thickness ratio of the actuated region decreases, discrete layer kinematics become very important for accurately characterizing the global response of the actuated plate. The set of laminate kinematic assumptions utilized by a particular model influence the predicted global response primarily through the so-called local kinematic effect where a portion of the available actuation energy is diverted to the production of localized transverse shear deformation and localized transverse normal deformation in the vicinity of the actuator edges, thereby reducing the amount of actuation energy that is available for producing the intended global deformation mode.

A piezohydraulic actuator is a hybrid device consisting of a hydraulic pump driven by piezo stacks, that is coupled to a conventional hydraulic cylinder via a set of fast-acting valves. Because the performance of the actuator is strongly related to the pumping frequency, a good understanding of the dynamics of the system is essential for designing a high-efficiency actuator. This article describes the development of a frequency domain model to quantify the dynamics of a piezohydraulic hybrid actuator. The analysis treats the hydraulic circuit as a series of fluid transmission lines, each represented by a transfer matrix that determines the relationship between the pressure and velocity at the inlet and at the outlet. The model includes the effects of fluid compressibility, inertia and viscosity. An experimental procedure to measure the frequency response of the device is described, and is used to validate the analysis. The effect of tubing length and fluid viscosity on the dynamic characteristics of the system is investigated. Longer tubing lengths result in lower resonant frequencies of the system, while increasing fluid viscosity results in a decrease in the magnitude of the resonant peak.

The design, analysis, and testing of an improved Shape Memory Alloy (SMA)-based tracking tab actuator is described in this paper. The goal of the actuator is to provide in-flight tracking capability for a helicopter rotor in order to minimize 1/rev vibrations due to rotor dissimilarities. Previous SMA-based actuator designs demonstrated the potential for in-flight rotor tracking but admitted drawbacks that led to inconsistent operation under air-loads. The current research builds upon the existing knowledge base and addresses the challenges encountered in previous designs. The objective is to achieve a deflection of 58 with an accuracy of 0:18 under realistic aerodynamic loading conditions. The present actuation concept is based on the bidirectional motion of a pair of antagonistic SMA wires, with a passive friction brake to lock the tab position. A theoretical model of the actuator was developed based on Brinson’s thermomechanical model. The model was used to predict the behavior of the actuator under external loading and applied as a design tool to identify optimal actuator parameters. The actuator was integrated into a NACA 0012 12 in. chord blade section and tested in an open-jet wind tunnel at speeds of up to 120 ft/s (0.107 M) and at angles of attack up to 158. Closed-loop tracking was implemented using a PID controller with gains selected by Ziegler-Nichols tuning. The improved SMA actuator meets the project goals by achieving repeatable tab deflection of up to 58with an average accuracy of 0.058. Position hold under power-off conditions and a duty cycle of 20 cycles/h were also demonstrated.

This paper describes the design and development of a piezoelectric-hydraulic hybrid actuator operating at a high pumping frequency. The actuator is envisaged as a potential actuator for a trailing edge flap on a full scale smart rotor system. While recent research efforts based on the same concept have investigated actuators with large piezoelectric stacks operating at a relatively low pumping frequency, the goal of the present work is to investigate the behavior of the actuator at a low volumetric displacement and high pumping frequency. Preliminary design of the actuator system is carried out, and the dependence of the performance of the actuator on various system parameters is identified. This enables the optimum selection of geometric parameters and piezostack characteristics for a given external load. Challenges to achieving high pumping frequencies were identified and solutions were implemented. The actuator was driven by two piezostacks, of a total length of 36 mm and cross-sectional area 100 mm 2 . The actuator was tested up to a pumping frequency of 1 kHz, developing a maximum no-load velocity of 1.2 in/s and a blocked force of 35 lb in the unidirectional output mode. Bidirectional output performance was also measured, by incorporating a 4-way valve in the hydraulic circuit. At a frequency of 5 Hz, a no-load output displacement with an amplitude 32 mils was measured.

This paper investigates the behavior of piezoelectric elements as strain sensors. Strain is measured in terms of the charge generated by the element as a result of the direct piezoelectric effect. Strain measurements from piezoceramic (PZT) and piezofilm (PVDF) sensors are compared with strains from a conventional foil strain gage and the advantages of each type of sensor are discussed, along with their limitations. The sensors are surface bonded to a beam and are calibrated over a frequency range of 5-500 Hz. Correction factors to account for transverse strain and shear lag effects due to the bond layer are analytically derived and experimentally validated. The effect of temperature on the output of PZT strain sensors is investigated. Additionally, design of signal conditioning electronics to collect the signals from the piezoelectric sensors is addressed. The superior performance of piezoelectric sensors compared to conventional strain gages in terms of sensitivity and signal to noise ratio is demonstrated.

This paper investigates the behavior of piezoceramic sheet actuators under different types of excitation and mechanical loading. The research especially focuses on the application of these actuators to the development of smart rotor systems. The free strain response of the actuators under DC excitation is experimentally investigated along with the associated drift of the strain over time. Effect of tensile stress on the free strain response is examined. The magnitude and phase of the free strain response of the actuator under different excitation voltages and frequencies is measured, and a phenomenological model to predict this behavior is developed and validated. The power consumption of the free actuator and a pair of actuators surface bonded to a host structure is calculated by the impedance method and validated by measurement. Additionally, depoling of the actuators is discussed, along with the feasibility of recovering performance by repoling in the event of accidental depoling.

Smart structure activated trailing edge flaps are capable of actively altering the aerodynamic loads on rotor blades. Coupled with a suitable feedback control law, such actuators could potentially be used to counter the vibrations induced by periodic aerodynamic loading on the blades, without the bandwidth constraints and with a potential of lower weight penalties incurred by servo actuation methods. This paper explores new, robust individual blade control (IBC) methodologies for vibration suppression using a piezoactuated trailing edge flap. The controllers employ a single hidden layer neural network, learning in real time, to adaptively cancel the effects of periodic aerodynamic loads on the blades, greatly attenuating the resulting vibrations. Both collocated and noncollocated sensor/actuator pairs are considered. Proofs of the stability and convergence of the proposed neurocontrol strategies are provided, and numerical simulation results for a one-eighth Froude scale blade model are given which demonstrate that the controller can nearly eliminate the blade vibration arising from a wide variety of unknown, periodic disturbance sources.

This paper presents the development of an active on-blade vibration-reduction system using smart active blade tips (SABT), that are driven by a piezo-induced, bending-torsion coupled actuator. The actuator beam has a graphite substructure with surface bonded piezoceramic elements. A spanwise variation in both the bending-torsion coupling and the piezo element phasing is used to generate a pure tip twist. A small scale rotor, with 10% span active tips, was tested on the hover stand, at a reduced tip speed of Mach 0.25. At a mean thrust loading (CT/σ) of 0.07, and for an activation of 100 Vrms, SABT deflection amplitudes from 1.8 deg at 2/rev to 2.25 deg at 4/rev were achieved (half peak-to-peak). The rotor normal force measurements show a distinct coupling of the activation with the first and second flap frequencies of the rotor. The corresponding dynamic thrust, generated by a single active tip, relative to the steady thrust, ranges from 4.5% at 2/rev to 8.3% at 5/rev. For a 1/rev excitation, the single active tip generates a dynamic lift amplitude of 15% of the steady rotor thrust. The same actuator beam was used to test a rotor with controllable twist blades. The active twist blades used the same main blade section as the rotor blades with the active tips, and hence were not optimized for active twist configuration. Nonetheless, in hover, at a mean thrust loading (CT/σ) of 0.07, and with an activation of 100 Vrms, dynamic tip-twist amplitudes of 0.4 deg at 4/rev and 0.5 deg (at 5/rev) were achieved (half peak-to-peak).

This paper presents a methodology to actuate trailing edge flap in a wing model using a high performance piezostack device. A composite wing model was built around this piezostack actuator with integrated mechanical amplification. The free displacement and block force of this high voltage actuator were respectively determined as 28 mil and 16 lb at 1000 volts. The linear motion of the actuator was converted to rotary motion for flap actuation using a hinge offset mechanism. This model was tested to evaluate the performance of flap actuation without and with aerodynamic forces. The flap deflection was measured using a Hall sensor, and a maximum of 8.5 deg flap deflection was achieved. The influence of free stream velocity and angle of attack on flap deflection was examined. A 30% decrease in flap deflection at free stream velocity at 95 ft/sec was noticed. Angle of attack of 10 deg did not change the flap deflection. Flap deflection was predicted from force-displacement relation of actuator and calculated hinge moment and good correlation between experiment and prediction was achieved.

This paper presents research into an adaptive nonlinear neural network control algorithm that can be used with smart structure actuators and sensors to control the shape and suppress the vibrations of flexible beams. The algorithm presented couples an explicitly model-based adaptive component, which employs time-varying estimates of the beam material properties, with an adaptive neural network, learning in real-time, which is used to estimate the additional actuator moments needed to offset the effects of periodic external disturbances. Experimental results are given for a thin beam, with bonded piezoceramic sensors and actuators, demonstrating the ability of the algorithm to track desired bending profiles and reject the vibrations caused by external disturbances, as well as to maintain this performance despite changes in the material properties of the structure or in the properties of the external disturbance.

This paper presents an analytical model and validation tests of a Froude scaled rotor featuring piezoelectric bender (bimorph) actuated trailing-edge flaps for active vibration suppression. The analytical model for the coupled bimorph actuator trailing-edge flap dynamic response in the rotating environment takes into account the aerodynamic, centrifugal, inertial and frictional loads acting on the actuator-flap system. The linkage arm length associated with the mechanical amplification mechanism is selected to maximize flap performance in the rotating environment. The bimorph clamping is improved to prevent actuator slippage under high centrifugal loads. The analytical model is validated by carrying out a series of bench tests, vacuum chamber tests and hover tests. In hover, flap deflections of ±6 degrees at 4/rev flap excitation are achieved at 900 RPM, thus demonstrating the potential of the piezoceramic bender as a lightweight and compact actuation system for individual blade control purposes. This paper also includes a feasibility study for piezo-bimorph actuation of a trailing-edge flap for a Mach scaled rotor model.

The objective of this research is to develop a smart rotor with active control of blade twist using embedded piezoceramic elements as sensors and actuators to minimize rotor vibrations. A 1/8 Froude-scale (dynamically scaled) bearingless helicopter rotor model was built with banks of torsional actuators capable of manipulating blade twist at frequencies from 5 to 100 Hz. To assess the effectiveness of the torsional actuators and vibration suppression capabilities, systematic wind tunnel testing was conducted in the Glenn L. Martin Wind Tunnel. Using accelerometers embedded in the blade tip, the oscillatory blade twist response was measured. The changes in rotor vibratory loads due to piezo-induced twist were determined using a rotating hub balance located at the rotor hub. Experimental test results show that tip twist amplitudes on the order of 0.5 degrees are attainable by the current actuator configurations in forward flight. Although these amplitudes were less than the target value (I to 2 degrees for complete vibration suppression control), test results show that partial vibration reduction is possible. Using open-loop phase shift control of blade twist at the first four rotor harmonics, changes in rotor thrust of up to 9% of the steady-state values were measured.