Samuel Case Bradford

Propagating Waves in the Steel, Moment-Frame Factor Building Recorded during Earthquakes

Wave-propagation effects can be useful in determining the system identification of buildings such as the densely instrumented University of California, Los Angeles, Factor building. Waveform data from the 72-channel array in the 17-story moment-resisting steel frame Factor building are used in comparison with finite- element calculations for predictive behavior. The high dynamic range of the 24-bit digitizers allows both strong motions and ambient vibrations to be recorded with reasonable signal-to-noise ratios. A three-dimensional model of the Factor building has been developed based on structural drawings. Observed displacements for 20 small and moderate, local and regional earthquakes were used to compute the impulse response functions of the building by deconvolving the subbasement records as representative input motions at its base. The impulse response functions were then stacked to bring out wave-propagation effects more clearly. The stacked data are used as input into theoretical dynamic analysis simulations of the building’s response.

Design, fabrication and testing of active carbon shell mirrors for space telescope applications

A novel active mirror concept based on carbon fiber reinforced polymer (CFRP) materials is presented. A nanolaminate facesheet, active piezoelectric layer and printed electronics are implemented in order to provide the reflective surface, actuation capabilities and electrical wiring for the mirror. Mirrors of this design are extremely thin (500-850 µm), lightweight (~ 2 kg/m2) and have large actuation capabilities (~ 100 µm peak- to-valley deformation per channel). Replication techniques along with simple bonding/transferring processes are implemented eliminating the need for grinding and polishing steps. An outline of the overall design, component materials and fabrication processes is presented. A method to size the active layer for a given mirror design, along with simulation predictions on the correction capabilities of the mirror are also outlined. A custom metrology system used to capture the highly deformable nature of the mirrors is demonstrated along with preliminary prototype measurements.

Piezocomposite Actuator Arrays for Correcting and Controlling Wavefront Error in Reflectors

Three reflectors have been developed and tested to assess the performance of a distributed network of piezocomposite actuators for correcting thermal deformations and total wave-front error. The primary testbed article is an active composite reflector, composed of a spherically curved panel with a graphite face sheet and aluminum honeycomb core composite, and then augmented with a network of 90 distributed piezoelectric composite actuators. The piezoelectric actuator system may be used for correcting as-built residual shape errors, and for controlling low-order, thermally-induced quasi-static distortions of the panel. In this study, thermally-induced surface deformations of 1 to 5 microns were deliberately introduced onto the reflector, then measured using a speckle holography interferometer system. The reflector surface figure was subsequently corrected to a tolerance of 50 nm using the actuators embedded in the reflectors back face sheet. Two additional test articles were constructed: a borosilicate at window at 150 mm diameter with 18 actuators bonded to the back surface; and a direct metal laser sintered reflector with spherical curvature, 230 mm diameter, and 12 actuators bonded to the back surface. In the case of the glass reflector, absolute measurements were performed with an interferometer and the absolute surface was corrected. These test articles were evaluated to determine their absolute surface control capabilities, as well as to assess a multiphysics modeling effort developed under this program for the prediction of active reflector response. This paper will describe the design, construction, and testing of active reflector systems under thermal loads, and subsequent correction of surface shape via distributed peizeoelctric actuation.

Variations in the Natural Frequencies of Millikan Library Caused by Weather and Small Earthquakes

In 2001, the Southern California Seismic Network (a part of the California Integrated Seismic Network) installed a 3-component Episensor force-balance accelerometer on the top floor of Millikan Library (station name MIK). This accelerometer is recorded by a 24-bit Quanterra data logger, and the dynamic range of the system is about 10 to the 7th. This means that ambient vibrations of the building can be recorded with a signal to noise ratio exceeding 100. Data from this system is recorded in a similar fashion to other more conventional seismographs that are installed in the ground throughout southern California. In particular, data is stored at 80 sps for any local earthquakes large enough to record on the seismic network, and data is also stored continuously after anti-alias filtering and resampling to 20 sps. The authors analyze a near-continuous three-year-long recording of the motion of the top floor of Millikan Library, which is a 9-story concrete building (a combination of shear walls and moment-resisting frames) built in 1966. The fundamental mode natural frequencies of the building (about 1.7 Hz N-S, 1.2 Hz E-W, and 2.5 Hz torsion) can be clearly observed from even short stretches of ambient vibration data. Using this data the authors have documented that changes in natural frequency are unambiguously correlated with the following factors. 1) There are diurnal variations in all natural frequencies on the order of 1-2%. 2) Heavy rain increases the E-W and torsional frequencies by up to 3%. The frequencies typically return to the pre-rain levels within about 5 days. 3) High temperatures (40 ° C) raise all natural frequencies by 1-2%. 4) Strong winds (50 kph) decrease natural frequencies. 5) Construction of non-structural office partitions on floors 3, 4, and 5 in 2003 increased natural frequencies, with the E-W frequency increasing by 5%. In addition to studying ambient vibrations, the authors also studied the apparent natural frequencies in a number of small to moderate earthquakes in southern California. They obtained the apparent natural frequencies by deconvolving the ground motions at a site 100 meters from the building (SCSN station GSA) from the Millikan roof records. They observed that the natural frequency dropped significantly for even small motions. For example, the E-W apparent frequency dropped from 1.18 Hz (ambient) to 1.06 Hz during a M 5.4 earthquake at a distance of 119 km (peak ground acceleration of 0.018 g). It returned to pre-earthquake levels within several minutes.

Analysis of the Impedance Resonance of Piezoelectric Multi-Fiber Composite Stacks

Multi-Fiber Composites™ (MFC’s) produced by Smart Materials Corp behave essentially like thin planar stacks where each piezoelectric layer is composed of a multitude of fibers. We investigate the suitability of using previously published inversion techniques [9] for the impedance resonances of monolithic co-fired piezoelectric stacks to the MFC™ to determine the complex material constants from the impedance data. The impedance equations examined in this paper are those based on the derivation by Martin [5,6,10]. The utility of resonance techniques to invert the impedance data to determine the small signal complex material constants are presented for a series of MFC’s. The technique was applied to actuators with different geometries and the real coefficients were determined to be similar within changes of the boundary conditions due to change of geometry. The scatter in the imaginary coefficient was found to be larger. The technique was also applied to the same actuator type but manufactured in different batches with some design changes in the non active portion of the actuator and differences in the dielectric and the electromechanical coupling between the two batches were easily measureable. It is interesting to note that strain predicted by small signal impedance analysis is much lower than high field stains. Since the model is based on material properties rather than circuit constants, it could be used for the direct evaluation of specific aging or degradation mechanisms in the actuator as well as batch sorting and adjustment of manufacturing processes.

Energy-Efficient Active Reflectors with Improved Mechanical Stability and Improved Thermal Performance

Controlling surface wavefront of apertures using a distributed array of actuators to mechanically correct the surface has been widely studied. Traditional active reflector systems require a sustained voltage profile which holds each actuator at a specific strain state to control the surface of the reflector. Each actuator, typically piezoelectric, draws a small amount of power under nominal operation. This power draw is small, but can complicate mission designs that depend on a cryogenic primary reflector surface. In this study we have extended the results of our previous work to include nonlinear piezoelectric actuation for active reflector systems. By deliberately operating in the nonlinear regime, it is possible to deform the actuators in such a way that the reflector surface maintains its corrected shape without sustained power. Demonstration of unpowered primary mirror wavefront control has positioned the technology as suitable for cryogenic/infrared systems. This report describes a nonlinear piezoelectric characterization campaign, and the associated nonlinear energy-efficient active reflector demonstration.

Energy-Efficient Active Reflectors with Improved Mechanical Stability

Active reflectors use an array of distributed actuators to control static surface deformations. In addition to meeting mission requirements with lower mass and lower costs, an active reflector adds robustness to a mission design by allowing for correction of unexpected orbital deformations. To control the wavefront of an active reflector, first the surface aberration is measured (via, e.g., a Shack-Hartmann sensor, direct imaging of the reflector surface, interferometric metrology, imagebased PSF estimation, or other methods). Based on an actuator sensitivity matrix, a voltage profile is calculated that best reduces the observed aberration. In addition to controlling the static wavefront, piezoelectric actuators can easily be used to control structural vibrations in the frequency ranges of interest for active reflectors (50 to 2000Hz). Operational vibrations (e.g., microdynamics, ACS-induced vibrations, slew, thermally-induced stick-slip events) can effectively be rejected from the reflector system. Launch load vibrations are typically drivers for structural requirements, and typical mission concepts would have reflector actuators unpowered or shorted during launch. By incorporating a vibration control system into the actuator power circuitry, launch loads on the fragile reflector structure can be significantly reduced. By improving the electromechanical coupling and deliberately operating in a new nonlinear piezoelectric regime, we have optimized the surface correction and use the same actuators developed for surface control as structural control elements. This has yielded improved performance in terms of power draw and also enabled vibration suppression for launch load and operational disturbances.

Multilayer active shell mirrors for space telescopes

A novel active mirror technology based on carbon fiber reinforced polymer (CFRP) substrates and replication techniques has been developed. Multiple additional layers are implemented into the design serving various functions. Nanolaminate metal films are used to provide a high quality reflective front surface. A backing layer of thin active material is implemented to provide the surface-parallel actuation scheme. Printed electronics are used to create a custom electrode pattern and flexible routing layer. Mirrors of this design are thin (< 1.0 mm), lightweight (2.7 kg/m2), and have large actuation capabilities. These capabilities, along with the associated manufacturing processes, represent a significant change in design compared to traditional optics. Such mirrors could be used as lightweight primaries for small CubeSat-based telescopes or as meter-class segments for future large aperture observatories. Multiple mirrors can be produced under identical conditions enabling a substantial reduction in manufacturing cost and complexity. An overview of the mirror design and manufacturing processes is presented. Predictions on the actuation performance have been made through finite element simulations demonstrating correctabilities on the order of 250-300× for astigmatic modes with only 41 independent actuators. A description of the custom metrology system used to characterize the active mirrors is also presented. The system is based on a Reverse Hartmann test and can accommodate extremely large deviations in mirror figure (> 100 μm PV) down to sub-micron precision. The system has been validated against several traditional techniques including photogrammetry and interferometry. The mirror performance has been characterized using this system, as well as closed-loop figure correction experiments on 150 mm dia. prototypes. The mirrors have demonstrated post-correction figure accuracies of 200 nm RMS (two dead actuators limiting performance).

Controlling Wavefront in Lightweight Reflector Systems using Piezocomposite Actuator Arrays

As part of a three-year research task, we have investigated active reflector systems as a less costly, lightweight alternative for future missions needing high surface precision reflectors. An active reflector can correct thermally-induced deformations, which reduces the structural constraints and gives the required thermal performance with a lighter system. Active reflectors can also correct manufacturing errors that dominate large composite reflector fabrication, which in turn reduces the manufacturing cost required to meet a given surface tolerance. As an added benefit, an active reflector adds robustness to the mission performance, with the ability to correct for deployment misalignments, mechanical creep in the structure, and other unpredicted disturbances. The benefits of an active reflector are balanced against increased complexity. The original Active Composite Reflector (ACR) testbed was developed to assess the authority of flat piezoelectric patches integrated into the back facesheet of a large (meter-scale) microwave reflector. Based on the success of the initial results, a control and metrology testbed was developed to pursue open-loop and closed-loop thermal distortion compensation in the meter-scale reflector and achieved sub-micron RMS surface quality under 10 microns of thermally-induced distortion. Smaller bench-scale reflectors at the 150-250 mm scale were also tested to assess surface performance as a function of substrate mechanical properties such as thickness and modulus. Final testing pushed the limits of the distributed actuator array concept to reach optical performance. A parallel multiphysics model was developed to support orbital performance simulations. This report describes the final experimental and modeling results for lightweight, low-cost, reflector systems with piezocomposite actuators.