John A. Judge

Effect of viscous loss on mechanical resonators designed for mass detection

Simple models are presented for estimating viscous damping of fluid (gas or liquid) loaded mechanical resonators. The models apply to beams in flexural modes of vibration, and to thin beams and plates in longitudinal modes of vibration. Predictions of the associated quality factor are compared with measured values for several macroscale and microscale resonators. The scaling of viscous loss with oscillator size is discussed. The minimum detectable mass is estimated for several oscillator designs and it is shown that, for comparably sized devices, longitudinal resonators have the lowest threshold of detection. This minimum detectable mass is proportional to scale to the power 1.75 for all resonator architectures limited by viscous damping, and it is shown that the viscous loss is 220 times larger in water than in air.

Attachment loss of micromechanical and nanomechanical resonators in the limits of thick and thin support structures

Analytical expressions are provided for the energy loss from vibrating mechanical resonators into their support structures for two limiting cases: supports that can be treated as plates, and supports that act as semi-infinite elastic media, with effectively infinite thickness. The former case is applicable to many microscale resonators, while the latter is appropriate for nanoscale devices. General formulations are given, applicable to a wide range of resonator geometries. These formulations are then applied to two geometries commonly used in microelectromechanical systems and nanelectromechanical systems applications: cantilevered beams and doubly fixed beams. Experimental data are presented to validate the finite-thickness support theory, and the predictions of the theory are also compared to data from existing literature for a microscale rectangular paddle oscillator.

Experimental Investigation of Mode Localization and Forced Response Amplitude Magnification for a Mistuned Bladed Disk

The results of an experimental investigation on the effects of random blade mistuning on the forced dynamic response of bladed disks are reported. The primary aim of the experiment is to gain understanding of the phenomena of mode localization and forced response blade amplitude magnification in bladed disks. A stationary, nominally periodic, 12-bladed disk with simple geometry is subjected to a traveling-wave out-of-plane engine order excitation delivered via phase-shifted control signals sent to piezoelectric actuators mounted on the blades. The bladed disk is then mistuned by the addition of small. unequal weights to the blade tips, and it is again subjected to a traveling wave excitation. The experimental data is used to verify analytical predictions about the occurrence of localized mode shapes, increases in forced response amplitude, and changes in resonant frequency due to the presence of mistuning. Very good agreement between experimental measurements and finite element analysis is obtained. The out-of-plane response is compared and contrasted with the previously reported in-plane mode localization behavior of the same test specimen. This work also represents an important extension of previous experimental study by investigating a frequency regime in which modal density is lower but disk-blade interaction is significantly greater.

Dissipation from microscale and nanoscale beam resonators into a surrounding fluid

Simple models for estimating viscous damping, acoustic radiation loss, and loss due to collisions with individual molecules of rarefied gas are presented and examined to show how quality factor of microscale and nanoscale resonators varies with ambient fluid pressure p and resonator geometry. For sufficiently low length to thickness aspect ratios, acoustic radiation loss is the dominant loss mechanism at pressures great enough that the fluid acts as a continuum, and the acoustic loss transitions seamlessly at low pressure to loss due to direct transfer of momentum to individual fluid molecules (both models have loss proportional to fluid pressure). For beams with greater aspect ratio, viscous loss, with loss proportional to p, dominates over a certain range of pressures, and the width of this region depends on the acoustic radiation efficiency of the beam. The transition between rarefied gas behavior and viscous (continuum) behavior occurs when the mean free path lmfp, a function of pressure, becomes shor...

Architectural considerations of micro- and nanoresonators for mass detection in the presence of a fluid

The sensitivity of various microscale and nanoscale resonator platforms, for use as mass sensors for detection of chemical or biological agents in air or water, is examined in terms of architectural considerations, including shape, scale, vibration mode, and fluid environment. Simple models for estimating damping due to various sources are used to calculate Q for several resonator designs: cantilevers and doubly fixed beams in flexure and extensional bar and disk resonators. The scaling of various contributions to Q is discussed, and the effects of support loss and fluid loss are compared as a function of aspect ratio for beam resonators. The minimum detectable mass is estimated for each of the four resonator designs, both for the case in which additional mass adsorbs uniformly over the resonator surface and the case in which functionalization of the surface is limited in order to maximize sensitivity and minimize added dissipation. The mass sensitivity is best for resonators undergoing extensional motion...

Airgun inter-pulse noise field during a seismic survey in an Arctic ultra shallow marine environment

Offshore oil and gas exploration using seismic airguns generates intense underwater pulses that could cause marine mammal hearing impairment and/or behavioral disturbances. However, few studies have investigated the resulting multipath propagation and reverberation from airgun pulses. This research uses continuous acoustic recordings collected in the Arctic during a low-level open-water shallow marine seismic survey, to measure noise levels between airgun pulses. Two methods were used to quantify noise levels during these inter-pulse intervals. The first, based on calculating the root-mean-square sound pressure level in various sub-intervals, is referred to as the increment computation method, and the second, which employs the Hilbert transform to calculate instantaneous acoustic amplitudes, is referred to as the Hilbert transform method. Analyses using both methods yield similar results, showing that the inter-pulse sound field exceeds ambient noise levels by as much as 9 dB during relatively quiet conditions. Inter-pulse noise levels are also related to the source distance, probably due to the higher reverberant conditions of the very shallow water environment. These methods can be used to quantify acoustic environment impacts from anthropogenic transient noises (e.g., seismic pulses, impact pile driving, and sonar pings) and to address potential acoustic masking affecting marine mammals.

Dynamics of soundscape in a shallow water marine environment: a study of the habitat of the Indo-Pacific humpback dolphin.

The underwater acoustic field is an important ecological element for many aquatic animals. This research examines the soundscape of a critically endangered Indo-Pacific humpback dolphin population in the shallow water environment off the west coast of Taiwan. Underwater acoustic recordings were conducted between late spring and late fall in 2012 at Yunlin (YL), which is close to a shipping lane, and Waisanding (WS), which is relatively pristine. Site-specific analyses were performed on the dynamics of the temporal and spectral acoustic characteristics for both locations. The results highlight the dynamics of the soundscape in two major octave bands: 150-300 Hz and 1.2-2.4 kHz. The acoustic energy in the former frequency band is mainly associated with passing container vessels near YL, while the latter frequency band is from sonic fish chorus at nighttime in both recording sites. In addition, large variation of low frequency acoustic energy throughout the study period was noticed at WS, where the water depths ranged between 1.5 and 4.5 m depending on tidal cycle. This phenomenon suggests that besides certain sound sources in the environment, the coastal soundscape may also be influenced by its local bathymetry and the dynamics of the physical environment.

Shaping of a system's frequency response using an array of subordinate oscillators.

The frequency response of an oscillating structure can be tailored by attaching one or more subordinate oscillators. This paper shows how the magnitude and phase of the frequency response can be deliberately shaped by prescribing the distributions of the dynamic properties in an array of such subordinate oscillators. Exact analytic governing equations of motion are derived for the coupled system composed of the primary system and the subordinate array. For a relatively small number (<100) of attached oscillators whose total mass is small (<1%) relative to the primary structure, it is possible to engineer frequency-response functions of the primary oscillator to have, for example, nearly linear phase or constant amplitude over a frequency band of interest. The frequency range over which response shaping is achieved is determined by the band of the attached oscillators. It is shown that the common analytic methodology for designing a dynamic vibration absorber represents the limiting case of a single oscillator in the subordinate set. Moreover, increasing the number of subordinate oscillators (without increasing the total added mass) offers a number of advantages in reshaping the dominant systems frequency response.

Five-axis scanning laser vibrometry for three-dimensional measurements of non-planar surfaces

A novel system for directing the beam of a single-point laser Doppler vibrometer (LDV) to measure three-dimensional velocity components of non-planar targets has been developed. A description of this measurement system is presented, along with a discussion of relative merits as compared with conventional scanning LDV systems. Two data sets are presented. In the first, sample measurements of a bulk solid are compared with an analytic model as verification of the measurement technique. In the second, measurements of the surface of sand over a buried anti-tank landmine are presented as a demonstration of the full capability of the system.

Noise sensitivity of a mass detection method using vibration modes of coupled microcantilever arrays

Numerical simulation is used to explore the sensitivity to measurement noise of a mass detection approach that uses eigenmodes of an array of nominally identical micro- or nanomechanical resonators. The mode shapes are perturbed to simulate measurement noise, and resulting errors in identifying variations in mass are quantified as a function of array size, coupling strength, and level of mass variation. Sensitivity to measurement noise is low for lightly coupled arrays of nearly identical elements and increases when mass variation causes significant mode localization. For any mass variation level, an optimal combination of array size and coupling strength minimizes noise sensitivity.