Estimating material elasticity by spherical indentation load-relaxation tests on viscoelastic samples of finite thickness

A two-step viscoelastic spherical indentation method is proposed to compensate for 1) material relaxation and 2) sample thickness. In the first step, the indenter is moved at a constant speed and the reaction force is measured. In the second step, the indenter is held at a constant position and the relaxation response of the material is measured. Then the relaxation response is fit with a multi-exponential function which corresponds to a three-branch general Maxwell model. The relaxation modulus is derived by correcting the finite ramp time introduced in the first step. The proposed model takes into account the sample thickness, which is important for applications in which the sample thickness is less than ten times the indenter radius. The model is validated numerically by finite element simulations. Experiments are carried out on a 10% gelatin phantom and a chicken breast sample with the proposed method. The results for both the gelatin phantom and the chicken breast sample agree with the results obtained from a surface wave method. Both the finite element simulations and experimental results show improved elasticity estimations by incorporating the sample thickness into the model. The measured shear elasticities of the 10% gelatin sample are 6.79 and 6.93 kPa by the proposed finite indentation method at sample thickness of 40 and 20 mm, respectively. The elasticity of the same sample is estimated to be 6.53 kPa by the surface wave method. For the chicken breast sample, the shear elasticity is measured to be 4.51 and 5.17 kPa by the proposed indentation method at sample thickness of 40 and 20 mm, respectively. Its elasticity is measured by the surface wave method to be 4.14 kPa. © 2011 IEEE.

Electrically coupled MEMS oscillators

In this paper, we demonstrate synchronization of two electrically coupled MEMS oscillators incorporating nearly identical silicon tuning fork microresonators. It is seen that as the output of the oscillators are coupled, they exhibit a synchronized response wherein the output amplitudes and signal-to-noise ratios of the two oscillators are improved relative to the case where the two oscillators are uncoupled. The observed output frequency of each oscillator before coupling is 219402.4 Hz and 219403.6 Hz respectively. In contrast, when the oscillators are driven simultaneously, they lock at a common output frequency of 219401.3 Hz and their outputs are found to be out-of-phase with respect to each other. A 6 dBm gain in output power and a reduction in the phase fluctuations of the output signal are observed for the coupled oscillators compared to the case when the oscillators are uncoupled. © 2011 IEEE.

ZnO-Based FBAR resonators with carbon nanotube electrodes

Film bulk acoustic resonator (FBAR) devices with carbon nanotube (CNT) electrodes directly grown on a ZnO film by thermal chemical vapor deposition have been fabricated. CNT electrodes possess a very low density and high acoustic impedance, which reduces the intrinsic mass loading effect resulting from the electrodes' weight and better confines the longitudinal acoustic standing waves inside the resonator, in turn providing a resonator with a higher quality factor. The influence of the CNTs on the frequency response of the FBAR devices was studied by comparing two identical sets of devices; one set comprised FBARs fabricated with chromium/ gold bilayer electrodes, and the second set comprised FBARs fabricated with CNT electrodes. It was found that the CNTs had a significant effect on attenuating traveling waves at the surface of the FBARs' membranes because of their high elastic stiffness. Three-dimensional finite element analysis of the devices fabricated was carried out, and the numerical simulations were consistent with the experimental results obtained. © 2011 IEEE.

Efficient Implementation of Spatially-Varying 3-D Ultrasound Deconvolution

Abstract—There are sometimes occasions when ultrasound beamforming is performed with only a subset of the total data that will eventually be available. The most obvious example is a mechanically-swept (wobbler) probe in which the three-dimensional data block is formed from a set of individual B-scans. In these circumstances, non-blind deconvolution can be used to improve the resolution of the data. Unfortunately, most of these situations involve large blocks of three-dimensional data. Furthermore, the ultrasound blur function varies spatially with distance from the transducer. These two facts make the deconvolution process time-consuming to implement. This paper is about ways to address this problem and produce spatially-varying deconvolution of large blocks of three-dimensional data in a matter of seconds. We present two approaches, one based on hardware and the other based on software. We compare the time they each take to achieve similar results and discuss the computational resources and form of blur model that each requires.

Micro-electro-mechanical resonant tilt sensor

This paper reports a micro-electro-mechanical tilt sensor based on resonant sensing principles. The tilt sensor measures orientation by sensing the component of gravitational acceleration along a specified input axis. Design aspects of the tilt sensor are first introduced and a design trade-off between sensitivity, resolution and robustness is addressed. A prototype sensor is microfabricated in a foundry process. The sensor is characterized to validate predictive analytical and FEA models of performance. The prototype is tested over tilt angles ranging over ±90 degrees and the linearity of the sensor is found to be better than 1.4% over the tilt angle range of ±20°. The noise-limited resolution of the sensor is found to be approximately 0.00026 degrees for an integration time of 0.6 seconds. © 2012 IEEE.

Impact of mode localization on the motional resistance of coupled MEMS resonators

This paper investigates the effect of mode-localization that arises from structural asymmetry induced by manufacturing tolerances in mechanically coupled, electrically transduced Si MEMS resonators. We demonstrate that in the case of such mechanically coupled resonators, the achievable series motional resistance (R x) is dependent not only on the quality factor (Q) but also on the variations in the eigenvector of the chosen mode of vibration induced by mode localization due to manufacturing tolerances during the fabrication process. We study this effect of mode-localization both theoretically and experimentally in two pairs of coupled double-ended tuning fork resonators with different levels of initial structural asymmetry. The measured series R x is minimal when the system is close to perfect symmetry and any deviation from structural symmetry induced by fabrication tolerances leads to a degradation in the effective R x. Mechanical tuning experiments of the stiffness of one of the coupled resonators was also conducted to study variations in R x as a function of structural asymmetry within the system, the results of which demonstrated consistent variations in motional resistance with predictions. © 2012 IEEE.

Modelling non-linearities in a MEMS square wave oscillator

The modelling of the non-linear behaviour of MEMS oscillators is of interest to understand the effects of non-linearities on start-up, limit cycle behaviour and performance metrics such as output frequency and phase noise. This paper proposes an approach to integrate the non-linear modelling of the resonator, transducer and sustaining amplifier in a single numerical modelling environment so that their combined effects may be investigated simultaneously. The paper validates the proposed electrical model of the resonator through open-loop frequency response measurements on an electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. A square wave oscillator is constructed by embedding the same resonator as the primary frequency determining element. Measurements of output power and output frequency of the square wave oscillator as a function of resonator bias and driving voltage are consistent with model predictions ensuring that the model captures the essential non-linear behaviour of the resonator and the sustaining amplifier in a single mathematical equation. © 2012 IEEE.

Modeling nonlinearities in MEMS oscillators

We present a mathematical model of a microelectromechanical system (MEMS) oscillator that integrates the nonlinearities of the MEMS resonator and the oscillator circuitry in a single numerical modeling environment. This is achieved by transforming the conventional nonlinear mechanical model into the electrical domain while simultaneously considering the prominent nonlinearities of the resonator. The proposed nonlinear electrical model is validated by comparing the simulated amplitude¿frequency response with measurements on an open-loop electrically addressed flexural silicon MEMS resonator driven to large motional amplitudes. Next, the essential nonlinearities in the oscillator circuit are investigated and a mathematical model of a MEMS oscillator is proposed that integrates the nonlinearities of the resonator. The concept is illustrated for MEMS transimpedance-amplifier-based square-wave and sine-wave oscillators. Closed-form expressions of steady-state output power and output frequency are derived for both oscillator models and compared with experimental and simulation results, with a good match in the predicted trends in all three cases. © 1986-2012 IEEE.

Acoustic properties of carbon nanotube electrodes in BAW resonators

In this paper the acoustic characterization of a layer of carbon nanotubes (CNT) deposited on AlN solidly mounted resonators is described. The structure of the CNT layer is analyzed by scanning electron microscopy and Raman spectroscopy. The electrical sheet resistance is derived from 4 point probe measurements and from the fitting of the electrical response of the resonators. Values of sheet resistance around 100 Ω/□ are measured. The longitudinal acoustic velocity is derived from the fitting of the electrical response of the resonators using Mason's model, by adjusting the overtones produced in the CNT layer. A mean value of 62000 m·s-1 is obtained, although some devices show values around 90000 m·s -1, close to the theoretical value of 100000 m·s-1. Some results on the deposition of CNT layers on metallic top electrodes and their influence on the performance of the resonator are also presented. © 2013 IEEE.

Numerical study of the impact of process variations on the motional resistance of weakly coupled MEMS resonators

This paper presents a numerical study of the impact of process-induced variations on the achievable motional resistance Rx of one-dimensional, cyclic and cross-coupled architectures of electrostatically transduced MEMS resonators operating in the 250 kHz range. Monte Carlo numerical simulations which accounted for up to 0.75% variation in critical resonator feature sizes were initiated on 1, 2, 3, 4, 5 and 9 coupled MEMS resonators for three distinct coupling architectures. Improvements of 100X in the spread of Rx and 2.7X in mean achievable Rx are reported for the case of 9 resonators when implemented in the cross-coupled topology, as opposed to the traditional one-dimensional chain. © 2013 IEEE.