Nesbitt W. Hagood

Damping of structural vibrations with piezoelectric materials and passive electrical networks

Abstract The possibility of dissipating mechanical energy with piezoelectric material shunted with passive electrical circuits is investigated. The effective mechanical impedance for the piezoelectric element shunted by an arbitrary circuit is derived. The shunted piezoelectric is shown to possess frequency dependent stiffness and loss factor which are also dependent on the shunting circuit. The generally shunted model is specialized for two shunting circuits: the case of a resistor alone and that of a resistor and inductor. For resistive shunting, the material properties exhibit frequency dependence similar to viscoelastic materials, but are much stiffer and more independent of temperature. Shunting with a resistor and inductor introduces an electrical resonance, which can be optimally tuned to structural resonances in a manner analogous to a mechanical vibration absorber. Techniques for analyzing systems which incorporate these shunting cases are presented and applied to a cantilevered beam experiment. The experimental results for both the resistive and resonant shunting circuits validate the shunted piezoelectric damping models.

Modelling of Piezoelectric Actuator Dynamics for Active Structural Control

The paper models the effects of dynamic coupling between a structure and an electrical network through the piezoelectric effect. The coupled equations of motion of an arbitrary elastic structure with piezoelectric elements and passive electronics are derived. State space models are developed for three important cases: direct voltage driven electrodes, direct charge driven electrodes, and an indirect drive case where the piezoelec tric electrodes are connected to an arbitrary electrical circuit with embedded voltage and current sources. The equations are applied to the case of a cantilevered beam with surface mounted piezoceramics and indirect voltage and current drive. The theoretical derivations are validated experimentally on an actively controlled cantilevered beam test article with indirect voltage drive.

Piezoelectric Fiber Composites with Interdigitated Electrodes

Piezoelectric Fiber Composites were previously introduced as an alternative to monolithic piezoceramic wafers for structural actuation applications. This manuscript was an investigation into the improvement of piezoelectric fiber composite performance through a nonconventional electroding scheme. Two microelectromechanical models were developed that predict the composite properties. These models were used to examine the trends of composite properties versus fiber volume fraction for various constituent materials. Several etched electrode PZT fiber composites, with fiber volume fractions ranging from 7% to 58%, were manufactured and tested. Experimental measurements showed excellent agreement with both the trends and magnitude of model predicted values. The maximum fiber volume fraction composites demonstrated a capacitance (E3 /Eo) of 550, piezoelectric free strain constants (d33 and d31) of 150 pm/V and-70 pm/V, and piezoelectric clamped stress (e33) of 5 C/m2, showing a substantial improvement over previous piezoelectric fiber composites with uniform electrodes. Maximum strain values of 1700 ppm were measured, indicating higher in-plane actuation than monolithic piezoceramics.

Anisotropic actuation with piezoelectric fiber composites

An investigation was made into the field of planar structural actuation with anisotropic active materials. The mechanisms for creating anisotropic actuators were discussed, and the impact of anisotropy was shown at the individual lamina level and at the laminated structure level. Models for laminated structures were developed using an augmented Classical Laminated Plate Theory incorporating induced stress terms to accommodate anisotropic actuator materials. A twistextension coupled laminate was used to exemplify how twist can be directly induced into isotropic host structures using anisotropic actuation. Four anisotropic actuators with different material anisotropies were compared using this example. Finally, a laminate incorporating piezoelectric fiber composite actuators was manufactured and tested. Excellent agreement was found between the predicted and experimental response.

Experimental investigation into passive damping enhancement for space structures

This work presents experiments which were conducted to verify kinetic and strain energy damping enhancement schemes for large/precision space structures. Two types of damping mechanisms were applied to a 5 meter long, 10 bay aluminum box truss with a quasi free-free three-dimensional suspension. Tuneable proof mass dampers (PMDs) were implemented with space realizable linear electromechanical drivers. Tuneable piezoelectric truss members were designed and constructed for the demonstration of resonant shunted piezoelectric damping concepts. The truss damping was measured and compared to analytical predictions obtained from a frequency domain system modeling technique. The proof mass damper implementation was found to increase first mode damping from 0.6 percent of critical to 6.4 percent of critical with a system mass increase of 2.7 percent. The resonant shunted piezoelectrics increased first mode damping to 6.0 percent with a similar mass penalty.

Self-sensing piezoelectric actuation - Analysis and application to controlled structures

Issues related to modeling and implementation of a self-sensing piezoelectric actuator are investigated. The necessary formulation for modeling the simultaneous sensing and actuation phenomenon is provided. Open and closed loop experiments performed on a cantilevered beam test specimen are described. The sensitivity of the results to representative errors introduced in the implementation of the transducer is demonstrated analytically and experimentally. The self-sensing actuator is also implemented using an active piezoelectric strut in a truss structure.

Hybrid finite element model for phase transitions in nonlinear electromechanically coupled material

A finite element approach for modeling phase transitions in electro-mechanically coupled material is presented. The approach is applicable to modeling a broad range of material behavior, including repolarizations in ferroelectrics (PZTs) as well as ferroelectric-antiferroelectric phase transitions in electroceramics such as lead lanthanum zirconate stannate titanate. A 3D 4 node hybrid element has been formulated. In addition to nodal displacement and voltage degrees of freedom used in conventional coupled elements, the hybrid element also utilizes internal electric displacement degrees of freedom, resulting in improved numerical efficiency. The elements utilize energy based nonlinear constitutive relations for more accurate representation of material response at high electric fields. The phase/polarization state of each element is represented by internal variable,s which are updated at each simulation step based on a phenomenological mode. The material model has been roughly fitted to response of PZT-5H under free strain conditions. The model reproduces strain and electric displacement hysteresis loops observed in the material. The hybrid finite element model results are demonstrated for a complex geometry with non-uniform fields.

Simultaneous sensing and actuation using piezoelectric materials

The possibility of using a single piezoelectric element simultaneously as both a structural actuator and collocated sensor is investigated. The coupled actuator and sensor equations for an arbitrary elastic structure with piezoelectric elements are developed using an assumed modes energy method. Examination of these equations suggests a simple implementation of collocated strain or strain rate sensing using a voltage driven piezoelectric element. The properties of such a collocated strain or strain rate sensor are presented. The general equations are applied to the case of a cantilevered beam with surface mounted piezoceramics. The theoretical derivations are validated experimentally on an actively controlled cantilevered beam test article with a single piezoelectric element used for collocated strain rate feedback.

Improved performance in piezoelectric fiber composites using interdigitated electrodes

Piezoelectric fiber composites were introduced as an alterative to monolithic piezoceramic wafers for structural actuation applications. This manuscript was an investigation into the improvement of piezoelectric fiber composite performance through a non-conventional electroding scheme. An interdigitated electrode pattern introduced the major component of electric field into the plane of the structure (along the fibers) and allowed the use of the primary piezoelectric effect. Two models were developed that predict the composite properties. These models examined the trends of composite properties versus fiber volume fraction for various constituent materials. Improvement was seen by comparing the modeled piezoelectric properties of the new electrodes to the conventional arrangement for fiber composites. Several etched electrode fiber composites were manufactured and tested to validate the models. Good agreement was seen for the capacitance, but the piezoelectric constants showed good agreement at only certain fiber volume fractions.

Preliminary Mach-scale hover testing of an integral twist-actuated rotor blade

An active blade designed for the control of rotor vibrations and noise has been developed. Active fiber composites have been integrated within the composite rotorblade spar to induced shear stresses. These shear stresses result in a distributed twisting moment along the blade. The design of an active blade model based on a 1/6th Mach-scale Chinook CH-47D is reviewed. The design goals included +/- 2 degree(s) of blade tip twist with a maximum of 20% added blade mass. Details of the requirements for the active fiber composites subjected to 160 kt, 3g maneuver loads and the experimentally determined actuator capabilities are reviewed. The testing of a half-span active blade test article is described. Twist actuation performance is compared with model predictions. Preliminary results from bench testing and full Mach-scale hover testing of the integral blade are presented.