Hartono Sumali

Highly sensitive mass detection and identification using vibration localization in coupled microcantilever arrays

We study the use of vibration localization in large arrays of mechanically coupled, nearly identical microcantilevers for ultrasensitive mass detection and identification. We demonstrate that eigenmode changes in such an array can be two to three orders of magnitude greater than relative changes in resonance frequencies when an analyte mass is added. Moreover, the changes in eigenmodes are unique to the cantilever to which mass is added, thereby providing a characteristic “fingerprint” that identifies the particular cantilever where mass has been added. This opens the door to ultrasensitive detection and identification of multiple analytes with a single coupled array.

A Soft-Landing Waveform for Actuation of a Single-Pole Single-Throw Ohmic RF MEMS Switch

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

Squeeze-film damping in the free molecular regime: model validation and measurement on a MEMS

Squeeze-film damping (SFD) is important in MEMS oscillators because it determines the quality factor of the oscillators. Published models for predicting SFD gave widely different results in the free-molecule regime, where the distance traveled by gas molecules between collisions in free space is much larger than the thickness of the squeezed gas film. The work presented here provides new experimental data for validating SFD models in that regime. The case studied here is where a rigid plate oscillates vertically while staying parallel to the substrate. The test device was an almost rectangular microplate supported by beam springs. The structure was excited by shaking the base. The velocities of numerous points on the plate and of the substrate were measured with a laser Doppler vibrometer and a microscope. An experimental modal analysis curve-fit the multiple frequency response functions to give the damping ratios. The test structure was contained in a vacuum chamber with air pressures controlled to provide a five-order-of-magnitude range of Knudsen numbers. The damping ratios from the measurements are compared with predictions from various published models. The measured damping ratios are close to predictions from models that are based on the Reynolds equation and take into account the inertia of the gas.

A piezoelectric array for sensing vibration modal coordinates

Abstract The ability to sense vibration modal coordinates in real time brings much advantage in sensing and controlling structural vibration and acoustic radiation. This paper discusses results from an experiment with a modal coordinate sensor. A modal coordinate sensor for a beam is created from an array of rectangular segments of piezoelectric film. The output voltages of the segments are multiplied by appropriate gains so that the weighted combinations of the outputs approximate the modal coordinates of the beam. The gains are components of a matrix which is obtained from the relationship between the slopes of the beam deflection and the output voltages of the film segments. After numerical simulation, the method is experimentally verified for a beam with simple boundary conditions. The beam is covered with segments of piezoelectric film. The electric current outputs from the segments are linearly combined with weights calculated by the theory. It is shown that this linear combination of segment outputs with correct weights results in a sensor that is sensitive to only a selected vibration mode and filters out other modes. A few problems in laboratory implementation of the sensor are addressed. This discretized version of modal sensor shows promising application in structural monitoring and vibration control.

A Simple Learning Control to Eliminate RF-MEMS Switch Bounce

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.

Application of viscous and Iwan modal damping models to experimental measurements from bolted structures

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. As a result, 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.

Squeeze-film damping of flexible microcantilevers at low ambient pressures: theory and experiment

An improved theoretical approach is proposed to predict the dynamic behavior of long, slender and flexible microcantilevers affected by squeeze-film damping at low ambient pressures. Our approach extends recent continuum gas damping models (Veijola 2004 J. Micromech. Microeng. 14 1109‐18, Gallis and Torczynski 2004 J. Microelectromech. Syst. 13 653‐9), which were originally derived for a rigid oscillating plate near a wall, to flexible microcantilevers for calculating and predicting squeeze-film damping ratios of higher order bending modes at reduced ambient pressures. Theoretical frequency response functions are derived for a flexible microcantilever beam excited both inertially and via external forcing. Experiments performed carefully at controlled gas pressures are used to validate our theoretical approach over five orders of the Knudsen number. In addition, we investigate the relative importance of theoretical assumptions made in the Reynolds-equation-based approach for flexible microelectromechanical systems. (Some figures in this article are in colour only in the electronic version)

Modeling, simulation, and testing of the mechanical dynamics of an RF MEMS switch

Mechanical dynamics can be a determining factor for the switching speed of radio-frequency microelectromechanical systems (RF MEMS) switches. This paper presents the simulation of the mechanical motion of a microswitch under actuation. The switch has a plate suspended by springs. When an electrostatic actuation is applied, the plate moves toward the substrate and closes the switch. Simulations are calculated via a high-fidelity finite element model that couples solid dynamics with electrostatic actuation. It incorporates non-linear coupled dynamics and accommodates fabrication variations. Experimental modal analysis gives results in the frequency domain that verifies the natural frequencies and mode shapes predicted by the model. An effective 1D model is created and used to calculate an actuation voltage waveform that minimizes switch velocity at closure. In the experiment, the switch is actuated with this actuation voltage, and the displacements of the switch at various points are measured using a laser Doppler velocimeter through a microscope. The experiments are repeated on several switches from different batches. The experimental results verify the model.

Identifying the Modal Properties of Nonlinear Structures Using Measured Free Response Time Histories from a Scanning Laser Doppler Vibrometer

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.

Unified theory of gas damping of flexible microcantilevers at low ambient pressures

Predicting the gas damping of microcantilevers oscillating in different vibration modes in unbounded gas at low pressures is relevant for increasing the sensitivity of microcantilever-based sensors. While existing free-molecular theories are valid only at very high Knudsen numbers, continuum models are valid only at very low Knudsen numbers. We solve the quasisteady Boltzmann equation and compute a closed-form fit for gas damping of rectangular microcantilevers that is valid over four orders of magnitude of Knudsen numbers spanning the free-molecular, the transition, and the low pressure slip flow regimes. Experiments are performed using silicon microcantilevers under controlled pressures to validate the theory.