Publications

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Measurements are presented from a two-beam structure with several bolted interfaces in order to characterize the nonlinear damping introduced by the joints. The measurements (all at force levels below macroslip) reveal that each underlying mode of the structure is well approximated by a single degree-of-freedom (SDOF) system with a nonlinear mechanical joint. At low enough force levels, the measurements show dissipation that scales as the second power of the applied force, agreeing with theory for a linear viscously damped system. This is attributed to linear viscous behavior of the material and/or damping provided by the support structure. At larger force levels, the damping is observed to behave nonlinearly, suggesting that damping from the mechanical joints is dominant. A model is presented that captures these effects, consisting of a spring and viscous damping element in parallel with a four-parameter Iwan model. The parameters of this model are identified for each mode of the structure and comparisons suggest that the model captures the stiffness and damping accurately over a range of forcing levels.

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This paper explores methods that can be used to characterize weakly nonlinear systems, whose natural frequencies and damping ratios change with response amplitude. The focus is on high order systems that may have several modes although each with a distinct natural frequency. Interactions between modes are not addressed. This type of analysis may be appropriate, for example, for structural dynamic systems that exhibit damping that depends on the response amplitude due to friction in bolted joints. This causes the free-response of the system to seem to have damping ratios (and to a lesser extent natural frequencies) that change slowly with time. Several techniques have been proposed to characterize such systems. This work compares a few available methods, focusing on their applicability to real measurements from multi-degree-of- freedom systems. A beam with several small links connected by simple bolted joints was used to evaluate the available methods. The system was excited by impulse and the velocity response was measured with a scanning laser Doppler vibrometer. Several state of the art procedures were then used to process the nonlinear free responses and their features were compared. First the Zeroed Early Time FFT technique was used to qualitatively evaluate the responses. Then, the Empirical Mode Decomposition method and a simple approach based on band pass filtering were both employed to obtain mono-component signals from the measured responses. Once mono-component signals had been obtained, they were processed with the Hilbert transform approach, with several enhancements made to minimize the effects of noise. © The Society for Experimental Mechanics, Inc. 2012.

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A cantilever beam is released from an initial condition. The velocity at the tip is recorded using a laser Doppler vibrometer. The ring-down time history is analyzed using Hilbert transform, which gives the natural frequency and damping. An important issue with the Hilbert transform is vulnerability to noise. The proposed method uses curve fitting to replace some time-differentiation and suppress noise. Linear curve fitting gives very good results for linear beams with low damping. For nonlinear beams with higher damping, polynomial curve fitting captures the time variations. The method was used for estimating quality factors of a few shim metals and PZT bimorphs.

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To study the rebound of a sphere colliding against a flat wall, a test setup was developed where the sphere is suspended with strings as a pendulum, elevated, and gravity-released to impact the wall. The motion of the sphere was recorded with a highspeed camera and traced with an image-processing program. From the speed of the sphere before and after each collision, the coefficient of restitution was computed, and shown to be a function of impact speed as predicted analytically.

An improved theoretical approach is presented to calculate and predict the quality factors of flexible microeantilevers affected by squeeze-film damping at low ambient pressures, and moderate to high Knudsen numbers. Veijola's model [1]. originally derived for a rigid oscillating plate near a wall, is extended to a flexible cantilever beam and both the gas inertia effect and slip boundary condition are considered in deriving resulting damping pressure. The model is used to predict the natural frequencies and quality factors of silicon microeantilevers with small gaps and their dependence on ambient pressure. In contrast to non-slip, continuum models, we find that quality factor depends strongly on ambient pressure, and that the damping of higher modes is more sensitive to ambient pressure than the fundamental. Copyright © 2008 by ASME.

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A learning control algorithm is presented that reduces the closing time of a radio-frequency microelectromechanical systems switch by minimizing bounce while maintaining robustness to fabrication variability. The switch consists of a plate supported by folded-beam springs. Electrostatic actuation of the plate causes pull-in with high impact velocities, which are difficult to control due to parameter variations from part to part. A single degree-of-freedom model was utilized to design a simple learning control algorithm that shapes the actuation voltage based on the open/closed state of the switch. Experiments on three different test switches show that after 5-10 iterations, the learning algorithm lands the switch plate with an impact velocity not exceeding 0.20 m/s, eliminating bounce. Simulations show that robustness to parameter variation is directly related to the number of required iterations for the device to learn the input for a bounce-free closure. © 2009 IEEE.

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Quantitative studies of material properties and interfaces using the atomic force microscope (AFM) have important applications in engineering, biotechnology and chemistry. Emerging studies require an estimate of the stiffness of the probe so that the forces exerted on a sample can be determined from the measured displacements. Numerous methods for determining the spring constant of AFM cantilevers have been proposed, yet none accounts for the effect of the mass of the probe tip on the calibration procedure. This work demonstrates that the probe tip does have a significant effect on the dynamic response of an AFM cantilever by experimentally measuring the first few modes of a commercial AFM probe and comparing them with those of a theoretical model for a cantilever probe that does not have a tip. The mass and inertia of an AFM probe tip are estimated from scanning electron microscope images and a simple model for the probe is derived and tuned to match the first few modes of the actual probe. Analysis suggests that both the method of Sader and the thermal tune method of Hutter and Bechhoefer give erroneous predictions of the area density or the effective mass of the probe. However, both methods do accurately predict the static stiffness of the AFM probe due to the fact that the mass terms cancel so long as the mode shape of the AFM probe does not deviate from the theoretical model. The calibration errors that would be induced due to differences between mode shapes measured in this study and the theoretical ones are estimated.

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One powerful method for measuring the motion of microelectromechanical systems (MEMS) relies on a Laser Doppler Vibrometer (LDV) focused through an optical microscope. Recent data taken under a very simple and common condition demonstrate that the velocity signal produced by the LDV with an optical microscope may be different from the velocity signal produced by the LDV without a microscope. This is especially important if one wishes to estimate acceleration by differentiating velocity. In this study, the time derivatives of LDV signals are compared against the signal from an accelerometer when the LDV is focused through an optical microscope and without the microscope system. The signal from the LDV without the microscope is almost identical to the accelerometer signal. In contrast, the signal from the LDV with the microscope exhibits a nonlinear relationship with the accelerometer signal. Both the LDV and the accelerometer were measuring a sinusoidal velocity generated by an electromechanical shaker. The Fourier transform of the acceleration from the LDV with the microscope shows a multitude of high harmonics of the excitation frequency, which have much higher amplitudes than the harmonics present in the accelerometer signal. Without the microscope, the LDV gives a much less distorted sinusoidal signal, even after time differentiation. The distortion of the signal from the LDV is periodic, with the same period as the sinusoidal drive signal. The largest distortion occurs near points of maximum negative acceleration, corresponding to the positive displacement peak of the sinusoidal oscillation. Because the measured oscillation is out of plane, pseudo-vibrations caused by speckle noise do not explain the distortion. Instead, the distortion appears to be caused by the optics of the microscope.

A model for computing the force from a gas film squeezed between parallel plates was recently developed using Direct Simulation Monte Carlo simulations in conjunction with the classical Reynolds equation. This paper compares predictions from that model with experimental data. The experimental validation used an almost rectangular MEMS oscillating plate with piezoelectric base excitation. The velocities of the suspended plate and of the substrate were measured with a laser Doppler vibrometer and a microscope. Experimental modal analysis yielded the damping ratio of twelve test structures for several different gas pressures. Small perforation holes in the plates did not alter the squeeze-film damping substantially. These experimental data suggest that the model predicts squeeze-film damping forces accurately. From this comparison, it is seen that these structures have a tangential-velocity accommodation coefficient close to unity. Copyright © 2007 by ASME.

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A soft-landing actuation waveform was designed to reduce the bounce of a single-pole single-throw (SPST) ohmic radio frequency (RF) microelectromechanical systems (MEMS) switch during actuation. The waveform consisted of an actuation voltage pulse, a coast time, and a hold voltage. The actuation voltage pulse had a short duration relative to the transition time of the switch and imparted the kinetic energy necessary to close the switch. After the actuation pulse was stopped, damping and restoring forces slowed the switch to near-zero velocity as it approached the closed position. This is referred to as the coast time. The hold voltage was applied upon reaching closure to keep the switch from opening. An ideal waveform would close the switch with near zero impact velocity. The switch dynamics resulting from an ideal waveform were modeled using finite element methods and measured using laser Doppler vibrometry. The ideal waveform closed the switch with an impact velocity of less than 3 cm/s without rebound. Variations in the soft-landing waveform closed the switch with impact velocities of 12.5 cm/s with rebound amplitudes ranging from 75 to 150 nm compared to impact velocities of 22.5 cm/s and rebound amplitudes of 150 to 200 nm for a step waveform. The ideal waveform closed the switch faster than a simple step voltage actuation because there was no rebound and it reduced the impact force imparted on the contacting surfaces upon closure. © 2006 IEEE.

When a micro cantilever beam is excited by base shaking, electrostatic force makes the tip displacement response nonlinear with respect to the base acceleration input. This paper derives a single-degree-of-freedom model for the deflection in a micro cantilever due to electrostatic voltage for this excitation. The tip deflection due to electrostatic force is derived first as part of the total tip deflection, and then in terms of an equivalent base excitation. The relationship between electrostatic deflection and equivalent base excitation is determined numerically, but can be represented accurately by a simple curve-fit function.

Forces generated by a static magnetic field interacting with eddy currents can provide a novel method of vibration damping. This paper discusses an experiment performed to validate modeling [3] for a case where a static magnetic field penetrates a thin sheet of conducting, non-magnetic material. When the thin sheet experiences motion, the penetrating magnetic field generates eddy currents within the sheet. These eddy currents then interact with the static field, creating magnetic forces that act on the sheet, providing damping to the sheet motion. In the presented experiment, the sheet was supported by cantilever springs attached to a frame, then excited with a vibratory shaker. The recorded motions of the sheet and the frame were used to characterize the effect of the eddy current damping.

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The responses of micro-cantilever beams, with lengths ranging from 100-1500 microns, have been found to exhibit nonlinear dynamic characteristics at very low vibration amplitudes and in near vacuum. This work seeks to find a functional form for the nonlinear forces acting on the beams in order to aide in identifying their cause. In this paper, the restoring force surface method is used to non-parametrically identify the nonlinear forces acting on a 200 micron long beam. The beam response to sinusoidal excitation contains as many as 19 significant harmonics within the measurement bandwidth. The nonlinear forces on the beam are found to be oscillatory and to depend on the beam velocity. A piecewise linear curve is fit to the response in order to more easily compare the restoring forces obtained at various amplitudes. The analysis illustrates the utility of the restoring force surface method on a system with complex and highly nonlinear forces. Copyright © 2006 by ASME.

This report summarizes a survey of several new methods for obtaining mechanical and rheological properties of single biological cells, in particular: (1) The use of laser Doppler vibrometry (LDV) to measure the natural vibrations of certain cells. (2) The development of a novel micro-electro-mechanical system (MEMS) for obtaining high-resolution force-displacement curves. (3) The use of the atomic force microscope (AFM) for cell imaging. (4) The adaptation of a novel squeezing-flow technique to micro-scale measurement. The LDV technique was used to investigate the recent finding reported by others that the membranes of certain biological cells vibrate naturally, and that the vibration can be detected clearly with recent instrumentation. The LDV has been reported to detect motions of certain biological cells indirectly through the motion of a probe. In this project, trials on Saccharomyces cerevisiae tested and rejected the hypothesis that the LDV could measure vibrations of the cell membranes directly. The MEMS investigated in the second technique is a polysilicon surface-micromachined force sensor that is able to measure forces to a few pN in both air and water. The simple device consists of compliant springs with force constants as low as 0.3 milliN/m and Moire patterns for nanometer-scale optical displacement measurement. Fields from an electromagnet created forces on magnetic micro beads glued to the force sensors. These forces were measured and agreed well with finite element prediction. It was demonstrated that the force sensor was fully functional when immersed in aqueous buffer. These results show the force sensors can be useful for calibrating magnetic forces on magnetic beads and also for direct measurement of biophysical forces on-chip. The use of atomic force microscopy (AFM) for profiling the geometry of red blood cells was the third technique investigated here. An important finding was that the method commonly used for attaching the cells to a substrate actually modified the mechanical properties of the cell membrane. Thus, the use of the method for measuring the mechanical properties of the cell may not be completely appropriate without significant modifications. The latest of the studies discussed in this report is intended to overcome the drawback of the AFM as a means of measuring mechanical and rheological properties. The squeezing-flow AFM technique utilizes two parallel plates, one stationary and the other attached to an AFM probe. Instead of using static force-displacement curves, the technique takes advantage of frequency response functions from force to velocity. The technique appears to be quite promising for obtaining dynamic properties. More research is required to develop this technique.

This paper outlines a model for a corner-supported, thin, rectangular bimorph actuated by a two-dimensional array of segmented, orthotropic PVDF laminates; it investigates the realization and measurement of such a bimorph. First, a model is derived to determine the deflected shape of an orthotropic laminate for a given distribution of voltages over the actuator array. Then, boundary conditions are realized in a laboratory setup to approach the theoretical corner-supported boundary condition. Finally, deflection measurements of actuated orthotropic PVDF laminates are performed with Electronic Speckle Pattern Interferometry and are compared to the model results. Copyright © 2005 by ASME.

Experimental modal analysis (EMA) was carried out on a micro-machined acceleration switch to characterize the motions of the device as fabricated and to compare this with analytical results for the nominal design. Finite element analysis (FEA) of the nominal design was used for this comparison. The acceleration switch was a single-crystal silicon disc supported by four fork-shaped springs. We shook the base of the die with step sine type excitation. A Laser Doppler Velocimeter (LDV) in conjunction with a microscope was used to measure the velocities of the die at several points. The desired first three modes of the structure were identified. The fundamental natural frequency that we measured in this experiment gives an estimate of the actuation g-level for the specified stroke. The fundamental resonance and actuation g-level results from the EMA and the FEA showed large variations. The discrepancy prompted thorough dimensional measurement of the acceleration switch, which revealed discrepancies between the nominal design and tested component.