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A quasi-static model for NiMnGa magnetic shape memory alloy (MSMA) is formulated in parallel to the Brinson and Tanaka thermal SMA constitutive models. Since the shape memory effect (SME) and pseudoelasticity exist in both NiTi and NiMnGa, constitutive models for SMAs can serve as a basis for MSMA behavioral modeling. The simplified, linear, quasi-static model for NiMnGa was characterized by nine material parameters identified by conducting a series of uniaxial compression tests in a constant field environment. These model parameters include free strain, Young's modulus, fundamental critical stresses, fundamental threshold fields, and stress-influence coefficients. The Young's moduli of the material in both its field and stress preferred configurations were determined to be 450 MPa and 820 MPa respectively, while the free strain was measured to be 5.8%. These test data were used to assemble a critical stress profile that is useful for determining model parameters and for understanding the dependence of critical stresses on magnetic fields. Once implemented, the analytical model shows good correlation with test data for all modes of NiMnGa quasi-static behavior, capturing both the magnetic shape memory effect and pseudoelasticity. Furthermore, the model is also capable of predicting partial pseudoelasticity, minor hysteretic loops and stress–strain behaviors. To correct for the effects of magnetic saturation, a series of stress influence functions were developed from the critical stress profile. Although requiring further refinement, the model's results are encouraging, indicating that the model is a useful analytical tool for predicting NiMnGa actuator behavior.

Active rotorblade tips offer an alternative approach to the challenge of main rotor active vibration control. The tips are pitched with respect to the main blade via a piezo-driven bending-torsion coupled actuator beam that runs down the length of the blade. A Vlasov based, specialized one-dimensional finite beam element is developed to model the rotating actuator beam and is validated with the free-vibration and static forced response of 4:1 and 2:1 aspect ratio, bending-torsion coupled, active and passive plates. A one-eighth scale, reduced tip-speed rotor model (tip Mach 0.26), incorporating the bending-torsion actuator beam, has been previously hover tested (open loop). In these tests, blade tip deflections of the order of 2° (half peak-to-peak) were achieved at 2, 3, 4, 5/rev with corresponding dynamic vertical blade root shear variations of the order of 10-20% of the nominal blade lift at 8° collective (CT/σ = 0.07). The test results are used to validate a coupled actuator and elastic rotorblade model. The correlation of the predicted active blade-tip pitch deflections and the experimental data is within 20%. The predicted values for the active vertical root shears are within the same margin for 4° and 6° collective.

This paper presents the wind tunnel testing of a four-bladed Mach-scaled rotor model with piezoelectric bender actuated trailing-edge flaps. Correctly phased, this flap motion can be used for the active suppression of vibratory hub loads. First, the University of Maryland Advanced Rotorcraft Code was used to conduct a parametric study to determine the optimal flap sizing and location as well as the required deflection amplitudes. Next, a simplified rotor analysis which explicitly models the actuator dynamics was used to design a multi-layer actuator configuration that is capable of achieving the required flap deflections. Based on the above design studies, a matched set of four Mach-scaled rotor blades with piezo-bender actuated trailing-edge flaps were fabricated in-house. This rotor model was operated using a one-seventh scale Bell-412 Mach-scaled rotor hub. Finally, the rotor system was tested in forward flight in the Glenn L Martin wind tunnel. These tests consisted of open-loop single-frequency tests at different rotor speeds and collective settings. Some preliminary closed-loop tests using a neural network control algorithm were also conducted. Presented at the American Helicopter Society 56th Annual Forum, Virginia Beach, VA. Copyright 2000 by the American Helicopter Society, Inc. All rights reserved.

A viscoelastic solid model, comprising of a combination of linear and non-linear springs and dashpots, is developed to represent an elastomeric damper. A non-linear constitutive differential equation is derived to characterize the damper behaviour in the time domain. A system identification method is presented to determine the spring - dashpot parameters (coefficients of the constitutive equation) from experimental data. The model is able to predict the non-linear amplitude-dependent behaviour of elastomeric dampers under single as well as dual-frequency excitations. A `two-level implicit - implicit' scheme is developed for the integration of the non-linear damper model into a structural dynamic analysis. With increase in amplitude of excitation, softening behaviour of the lead spring results in lesser motion in the Kelvin chain, lower damping levels, and slower decay of initial perturbations. The baseline model is augmented with additional series and parallel non-linear springs to represent the reduction in damping (G'') at very small amplitudes, and the occurrence of limit cycle oscillations.

This paper presents the development of electromechanical actuators based on the concept of mechanical amplification with piezo and electrostrictive stacks as drivers to achieve high force and high displacement actuation. The actuators were designed for two different applications. The first actuator, with an piezo stack, was developed to actuate a `Flaperon' which consisted of a small movable surface to trip the boundary layer, located on the top surface of a wing model with span and chord of 12 in each and of NACA 0012 airfoil. The actuator was designed to produce 8 lbs of force with peak displacement of 10 mils at a maximum frequency of 40 Hz. The second actuator, with an electrostrictive stack as a driver, was designed to move a leading edge droop flap hinged at 25% chord of a wing model with span of 8 in, chord of 4 in and a VR-12 airfoil. This actuator was designed to produce 8.5 lbs of force with peak displacement of 10 mils at a maximum frequency of 45 Hz. Experiments were performed on both stacks to evaluate their important characteristics such as block force, free displacement and stiffness, that were essential in the design of the actuators. The results showed that the block force obtainable from a piezo stack was higher and that of an electrostrictive stack was lower than that specified by the respective manufacturers, while the free displacements are about the same. The dynamic response of the actuators over a frequency range of 33 Hz was evaluated. Results showed that 7 lbs of actuator force was obtainable in both cases, with the flaperon actuator producing 15 mils of dynamic displacement at 15 Hz and the droop flap actuator producing about 6 mils of displacement at 16 Hz. The results were inconclusive beyond 16 Hz due to the setup resonance. The droop flap actuator did not achieve the desired performance because the design calculations were based on the block force listed by the manufacturer which was about 20% higher than the measured value. This led to the conclusion that before the design process begins, the performance of the stack alone should be carefully measured in order to achieve the required performance. Thus, a simple actuator based on a mechanical amplification concept could be effectively designed to produce high force and high displacements.

This paper develops one-dimensional pure bending, coupled bending and extension, and combined bending, extension and torsion models of isotropic beams with induced-strain actuation. A finite thickness adhesive layer between the crystal and beam is included to incorporate shear lag effects. Experimental tests evaluate the accuracy and limitations of the models. The bending and coupled bending and extension models show acceptable correlation with static test results whereas the combined extension, bearing, torsion model predicts the system behavior poorly and needs refinement.

Significant advances in the development of a Froude scaled helicopter rotor model featuring a trailing-edge flap driven by piezoceramic bimorph actuators for active vibration suppression are discussed. A quasisteady aerodynamic analysis used to determine flap size and actuator requirements is presented. The block force and stroke of the current actuators are evaluated using two theories and compared with experimental results. The dynamic performance of the actuator as well as the actuator - flap assembly is examined. Earlier hover tests showed severe degradation in flap deflections with increasing rotor speed, and flap deflections were too small to be effectively utilized for significant vibration control. To investigate the causes of the performance degradation, new blades are constructed and tested in vacuo to isolate the effects of centrifugal loading on the actuator - flap system. A beam model of the piezo bimorph including propeller moment effects is formulated to better illustrate the physical mechanisms affecting the system in a rotating environment. The cause of the reduced deflections is traced to frictional forces created at the junction where the flap is supported during rotation of the blades. The use of a thrust bearing was found to alleviate this problem and subsequent hover tests showed a dramatic increase in flap deflection at high excitation frequencies.

The objective of this research is to develop a dynamically-scaled (Froude scale) helicopter rotor blade with embedded piezoceramic elements as sensors and actuators to control blade vibrations. A 6 ft diameter 2-bladed bearingless rotor model was built where each blade is embedded with banks of piezoelectric actuators at degree angles with respect to the beam axis on the top and bottom surfaces. A twist distribution along the blade span is achieved through in-phase excitation of the top and bottom actuators at equal potentials, while a bending distribution is achieved through out-of-phase excitation. In order to fix design variables and to optimize blade performance, a uniform strain beam theory is formulated to analytically predict the static bending and torsional response of composite rectangular beams with embedded piezoelectric actuators. Parameters such as bond thicknesses, actuator skew angle and actuator spacing are investigated by experiments and then validated by theory. The static bending and torsional response of the rotor blades is experimentally measured and correlated with theory. Dynamic torsional and bending responses are experimentally determined for frequencies from 2 - 120 Hz to assess the viability of a vibration reduction system based on piezo-actuation of blade twist. To assess the performance of the piezo-actuators in rotation, hover tests were conducted where accelerometers embedded in the blades were used to resolve the tip twist amplitudes. Although the magnitudes of blade twist attained in this experiment were small, it is expected that future models can be built with improved performance.