Two-dimensional thin plates are widely used in many aerospace, automotive and marine applications. Vibration attenuation can be achieved in these structures by attaching piezoelectric elements on to the structure integrated with shunt damping circuits. This enables a compact vibration damping method without adding significant mass and volumetric occupancy, unlike the bulky mechanical dampers. Practical implementation of shunt damping technique requires accurate modeling of the host structure, the piezoelectric elements and the dynamics of the shunt circuit. Unlike other studies in the literature of piezoelectric shunt damping, this work utilizes a multi-modal equivalent circuit model (ECM) of a thin plate with multiple piezo-patches, to demonstrate the performance of shunt circuits. The equivalent system parameters are obtained from the modal analysis solution based on the Rayleigh-Ritz method. The ECM is coupled to the shunt circuits in SPICE software, where the shunt configuration consists of three branches of electrical resonators, each tuned to one vibration mode of the structure. Using the harmonic analysis in SPICE for a range of excitation frequencies, current output of each ECM branch is calculated for open-circuit and optimum shunt circuit conditions. The current of ECM branches are then converted to the displacement outputs in physical coordinates and validated by the finite-element simulations in ANSYS. It is shown that the vibration attenuation of a vibration mode can be successfully achieved when there is a reduction in the corresponding current amplitude of the ECM branch. This correlation can be utilized in the design of efficient linear/nonlinear shunt circuits.
Piezoelectric patch energy harvesters can be directly integrated to plate-like structures which are widely used in automotive, marine and aerospace applications, to convert vibrational energy to electrical energy. This paper presents two different AC-DC conversion techniques for multiple patch harvesters, namely single rectifier and respective rectifiers. The first case considers all the piezo-patches are connected in parallel to a single rectifier, whereas in the second case, each harvester is respectively rectified and then connected in parallel to a smoothing capacitor and a resistive load. The latter configuration of AC-DC conversion helps to avoid the electrical charge cancellation which is a problem with the multiple harvesters attached to different locations of the host plate surface. Equivalent circuit model of the multiple piezo-patch harvesters is developed in the SPICE software to simulate the electrical response. The system parameters are obtained from the modal analysis solution of the plate. Simulations of the voltage frequency response functions (FRFs) for the standard AC input – AC output case are conducted and validated by experimental data. Finally, for the AC input – DC output case, numerical simulation and experimental results of the power outputs of multiple piezo-patch harvesters with multiple AC-DC converters are obtained for a wide range of resistive loads and compared with the same array of harvesters connected to a single AC-DC converter.
Plate-like components are widely used in numerous automotive, marine, and aerospace applications where they can be employed as host structures for vibration based energy harvesting. Piezoelectric patch harvesters can be easily attached to these structures to convert the vibrational energy to the electrical energy. Power output investigations of these harvesters require accurate models for energy harvesting performance evaluation and optimization. Equivalent circuit modeling of the cantilever-based vibration energy harvesters for estimation of electrical response has been proposed in recent years. However, equivalent circuit formulation and analytical modeling of multiple piezo-patch energy harvesters integrated to thin plates including nonlinear circuits has not been studied. In this study, equivalent circuit model of multiple parallel piezoelectric patch harvesters together with a resistive load is built in electronic circuit simulation software SPICE and voltage frequency response functions (FRFs) are validated using the analytical distributedparameter model. Analytical formulation of the piezoelectric patches in parallel configuration for the DC voltage output is derived while the patches are connected to a standard AC-DC circuit. The analytic model is based on the equivalent load impedance approach for piezoelectric capacitance and AC-DC circuit elements. The analytic results are validated numerically via SPICE simulations. Finally, DC power outputs of the harvesters are computed and compared with the peak power amplitudes in the AC output case.
This paper presents analytical modeling and case studies of broadband and band-limited random vibration energy harvesting using a piezoceramic patch attached on a thin plate. The literature of vibration-based energy harvesting has been mostly focused on resonant cantilevered structures. However, cantilevered beam-type harvesters have limited broadband vibration energy harvesting capabilities unless they are combined with a nonlinear component. Moreover, cantilever arrangements cannot always be mounted on thin structures (which are basic components of marine, aerospace, and ground transportation systems) without significantly affecting the host system’s design and overall dynamics. A patch-based piezoelectric energy harvester structurally integrated to a thin plate can be a proper alternative to using resonant cantilevers for harvesting energy from thin structures. Besides, plate-like structures have more number of vibration modes compared to beam structures, offering better broadband performance characteristics. In this paper, we present analytical modelling of patch-based piezoelectric energy harvester attached on a thin plate for random vibrations. The analytical model is based on electromechanically-coupled distributed-parameter formulation and validated by comparing the electromechanical frequency response functions (FRFs) with experimental results. Example case studies are then presented to investigate the expected power output of a piezoceramic patch attached on an aluminum plate for the case of random force excitations. The effect of bandwidth of random excitation on the mean power and shunted mean-square vibration response are explored with a focus on the number of vibration modes covered in the frequency range of input power spectral density (PSD).
Micro Electro Mechanical Systems (MEMS) are among the new and emerging technologies of the future and have
many applications in different disciplines. This study presents the dynamic characterization methods that we use to
identify the modal parameters of a MEMS device and also the techniques that can be implemented to change the modal
parameters. A micro scanner mirror was chosen as the case study to demonstrate the developed methodologies. Initially,
the micro mirror was dynamically characterized using experimental modal analysis techniques to identify the modal
parameters such as resonance frequencies and mode shapes. Then, it was introduced in a velocity feedback control loop
to alter the effective damping of the structure. This method proves to be a very efficient method to alter the modal
damping of a micro structure, especially when high quality factors are required for MEMS applications.
KEYWORDS: Data modeling, Digital filtering, Optical filters, Space operations, Interferometers, Data acquisition, Finite element methods, Fourier transforms, Interfaces, Matrices
This paper presents a modeling methodology used to predict the performance of a flexible structure, such as a space telescope, in the presence of an on-board vibrational disturbance source, such as a reaction wheel assembly (RWA). Both decoupled and coupled analysis methods are presented. The decoupled method relies on blocked RWA disturbances, measured with the RWA hardmounted to a rigid surface. The coupled method corrects the blocked RWA disturbance boundary conditions using 'force filters' which depend on estimates of the interface accelerances of the RWA and spacecraft. Both methods were validated on the Micro-Precision Interferometer testbed at the Jet Propulsion Laboratory. Experimental results are encouraging, indicating that both methods provide sufficient accuracy compared to measured values; however, the coupled method provides the best results when the gyroscopic nature of the spinning RWA is captured in the RWA accelerance model. Additionally, the RWA disturbance cross spectral density terms are found to be influential.
Like all astrometric instruments, the Space Interferometry Mission (SIM) suffers from field-dependent errors requiring calibration. Diffraction effects in the delay line, polarization rotations on corner cubes, and beam walk across imperfect optics, all contribute to field-distortion that is significantly larger than is acceptable. The bulk of the systematic error is linear across the field - that is, it results in magnification and rotation errors. We show that the linear terms are inconsequential to the performance of SIM because they are inseparable from baseline length and orientation errors. One approach to calibrating the higher-order terms is to perform 'external' calibration; that is, SIM periodically makes differential measurements of a field of bright stars whose positions are not precisely known. We describe the requirements and constraints on the external calibration process and lay the groundwork for a specific procedure detailed in accompanying papers.
This paper summarizes two different strategies envisioned for calibrating the systematic field dependent biases present in the Space Interferometry Mission (SIM) instrument. The Internal Calibration strategy is based on pre-launch measurements combined with a set of on-orbit measurements generated by a source internal to the instrument. The External Calibration strategy uses stars as an external source for generating the calibration function. Both approaches demand a significant amount of innovation given that SIM's calibration strategy requires a post-calibration error of 100 picometers over a 15 degree field of regard while the uncalibrated instrument introduces tens to hundreds of nanometers of error. The calibration strategies are discussed in the context of the wide angle astrometric mode of the instrument, although variations on both strategies have been proposed for doing narrow angle astrometry.
An external calibration technique for SIM1,2,3 involves measurement of calibration stars whose positions must already be known to an accuracy of 2 milliarcseconds. We demonstrate a procedure that effectively 'bootstraps' calibration star positions from an ab initio catalog to the required accuracy by observing them with the uncalibrated SIM instrument.
The vibratory response of a typical mirror support/positioning system used at the experimental stations of the advanced photon source (APS) project at Argonne National Laboratory is investigated. Positioning precision and stability are especially critical when the supported mirror directs a high-intensity beam aimed at a distant target. Stability may be compromised by low level, low frequency seismic and facility-originated vibrations traveling through the ground and/or vibrations caused by flow-structure interactions in the mirror cooling system. The example case system has five positioning degrees of freedom through the use of precision actuators and rotary and linear bearings. These linkage devices results in complex, multi-dimensional vibratory behavior that is a function of the range of positioning configurations. A rigorous multibody dynamical approach is used for the development of the system equations. Initial results of the study, including estimates of natural frequencies and mode shapes, as well as limited parametric design studies, are presented. While the results reported here are for a particular system, the developed vibratory analysis approach is applicable to the wide range of high-precision optical positioning systems encountered at the APS and at other comparable facilities.
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