Gregory S. Agnes

Modeling Discontinuous Axisymmetric Active Optical Membranes

An active optical membrane is modeled as a laminate of ine atable structural material and piezopolymer sheets. Etching theelectrodesurfacesofeach layerallowsforselectiveactuationareas,whichcanbeusedto controlsurface regions independently. The analytical solution to a simplie ed axisymmetric system is discussed. The method of integralmultiplescalesisapplied totheaxisymmetricactivemembranemodeland isstudied.Resultsforboth static and dynamic formulations are presented and indicate such a laminate can effectively dee ect an optical membrane.

Active Axisymmetric Optical Membranes

An active optical membrane is modeled as a laminate of in∞atable structural material and piezo-polymer sheets. Etching the electrode surfaces of each layer allows for selective actuation areas which can be used to independently control surface regions. Using the Method of Integral Multiple Scales, a nonlinear one-dimensional model is initially presented. Expanding on this model, an axisymmetric active membrane is then studied. Results for both static and dynamic formulations are presented and indicate such a laminate can be efiective.

Toward Modeling of Cable-Harnessed Structures: Cable Damping Experiments

In order to develop models for space flight cables, the factors that affect the dynamic response of the cables must be determined. Toward this goal, this work presents the results from a set of experimental tests on 1x18 helically twisted cables made of 26 AWG insulated wire. The excitation method, tension in the cable, zip tie attachment method, and length and tension of the excitation string were varied for a single section of cable. In addition, five sections of cable were tested to investigate the variability within a single type of cable. The variability between the cable sections was as great as the variation due to any single test set up alteration, which indicates that a statistical approach may be necessary for cable characterization. Neither the excitation method nor length or tension in the excitation string afected the cable response significantly. Frequency response did change with changes in cable tension, as well as zip tie tightness. Thus, for best repeatability, cable tension and zip tie tightness should be controlled.

Bakeout Effects on Dynamic Response of Spaceflight Cables

Spaceflight cables are investigated to determine the effect of bakeout on their dynamic response, including resonant frequencies and damping ratios. The addition of cable harnesses to spacecraft structures can affect the dynamic response of the entire structure, especially for lightweight structures with high cable mass ratios. Bakeout, a heat and vacuum treatment that spaceflight components must undergo, may change the dynamic stiffness of flight cables and thus the dynamics of the cabled host structure. Bakeout effects are examined by experimentally identifying natural frequencies and damping values for spaceflight cables before and after the bakeout process. After bakeout, the first natural frequency decreases by an average of 14% for all single-strand cables and by 24% for multistrand cables. The second natural frequency decreases by 8 to 17% for all cables. Bakeout also increases the damping percentage for single and multistrand cables. These results show that bakeout affects the dynamic response of ...

Cable Parameters for Homogenous Cable-Beam Models for Space Structures

In this paper, a method to determine the effective homogenous beam parameters for a stranded cable is presented. There is not yet a predictive model for quantifying the structural impact of cable harnesses on space flight structures, and towards this goal, the authors aim to predict cable damping and resonance behavior. Cables can be modeled as shear beams, but the shear beam model assumes a homogenous, isotropic material, which a stranded cable is not. Thus, the cable-beam model requires calculation of effectively homogenous properties, including density, area, bending stiffness, and modulus of rigidity to predict the natural frequencies of the cable. Through a combination of measurement and correction factors, upper and lower bounds for effective cable properties are calculated and shown to be effective in a cable-beam model for natural frequency prediction.

An Active Composite Reflector System for Correcting Thermal Deformations

A meter-scale piezoelectrically active composite re ector has been developed and tested. The active re ector consists of a spherically curved, graphite face sheet, aluminum honeycomb core composite panel augmented with a network of distributed piezoelectric composite actuators. The piezoelectric actuator system may be used for controlling the structural dynamic response of the re ector, or for correcting low-order, thermally-induced quasistatic distortions of the panel. In this study, thermally-induced surface deformations of 1 to 5 microns were deliberately introduced onto the re ector, then measured using a speckle holography system. The re ector surface gure was subsequently corrected to a tolerance of 100 nm using a lattice of 90 piezoelectric composite actuators distributed across the re ector’s back face sheet. Initial experimental investigations consisted of open-loop gure control to determine in uence functions and control authority for each individuallyaddressable actuator, followed by a closed-loop gure control implementation. This paper will describe the design, construction, and testing of the active composite re ector system under thermal loads, and subsequent correction of thermal deformations via distributed piezoelectric actuation.

Inclusion of shear effects, tension, and damping in a DTF beam model for cable modeling

The distributed transfer function method is applied to equations of motion for a space flight cable in an ongoing effort to characterize the effects of adding cabling to space structures. A cable model is presented in which the cable is modeled as a shear beam with multiple boundary constraints. Tension in the cable is included and a variety of damping mechanisms are incorporated. Comparison of the model results to experimental data is included, showing that the distributed transfer function cable model with equivalent cable property inputs can bound the range of cable responses and that hysteretic and connection stiffness damping improve the comparison between the model and experimental data.

Comparison of damping models for space flight cables

A model to predict the dynamic response of space flight cables is developed. Despite the influence of cable harnesses on space structures’ dynamics, a predictive model for quantifying the damping effects is not available. To further this research, hysteretic and proportional viscous damping were incorporated in Euler-Bernoulli and Timoshenko beam models to predict the dynamic response of a typical space flight cable, using hysteretic dissipation functions to characterize the damping mechanism. The Euler-Bernoulli beam model was used to investigate the hysteresis functions specifically, and it was determined that including hysteretic dissipation functions in the equations of motion was not sufficient to model the additional modes arising in damped cables; additional damping coordinates in the method of Golla, Hughes and McTavish will be necessary to predict damping behavior when using dissipation functions for this case. A Timoshenko model that included viscous and time hysteresis damping was developed as well, and will ultimately be more appropriate for cable modeling due to the inclusion of shear and rotary inertia terms and damping coefficients.

Modeling a Piezothermoelastic Beam String

An analysis of laminated piezopolymer-actuated flexible beams is presented. Complete development of the nonlinear equations of motion governing a continuous, slender, laminate of arbitrary thermal, mechanical, and electrical properties is presented. A closed-form asymptotic solution is developed using a combination or perturbation techniques. These governing equations are applied to a pressurized simple piezoelectrically actuated Kapton® material model. Both static and dynamic results indicate shape control at optical wavelengths is possible.

Asymptotic finite elements introducing the method of integral multiple scales

The method of integral multiple scales (MIMS) is introduced and applied to linear and nonlinear beam models. Based on the method of multiple scales, MIMS is applied to the system Lagrangian and directly results in a system solution. An analytical solution approach is applied to a linear beam-string model to produce a system of linear differential equations that can be solved to produce an asymptotic solution. The true power of MIMS is then demonstrated through a finite element approach by using a set of parametric shape functions based on beam strings. Where the analytic methodology is limited to continuous systems, the finite element approach is easily applied to discontinuous systems providing an analysis method useful with distributed piezoelectric laminates. Both static and dynamic results are discussed. The use of the asymptotic shape functions in the MIMS asymptotic finite element method results in extremely high precision and provides a methodology that could provide a more efficient analytical tool for the development of highly compliant discontinuous systems.