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.

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.

Mechanically coupling microscale or nanoscale resonators in more than one dimension requires a departure from classic beam resonator designs. A square paddle resonator is a simple geometry that allows easy coupling into two-dimensional arrays. These resonators can have high quality factors in the fundamental vibration mode if operated in vacuum. In this paper we summarize the behavior of such a resonator and describe several design considerations. We develop an expression for the inter-resonator coupling in terms of coupling beam geometry, estimate energy dissipation due to a variety of physical mechanisms, and empirically determine the vibration amplitude at which geometric nonlinearity becomes significant. Future experimental studies can exploit the expressions presented here, which facilitate design of two-dimensional arrays of square-paddle resonators that will be useful for a variety of potential applications.

This study investigates the characteristics of the sound field during the 2013 and 2014 Southern California Behavioral Response Study. Acoustic data were collected before, during, and after simulated mid-frequency active sonar (MFAS) playbacks. A numerical approach, incremental computation method, is developed to quantify the inter-ping sound field during the simulated MFAS playback. Comparisons are made between inter-ping sound field and natural background in three distinctive frequency bands: low-frequency (4.5 kHz) bands. The results show significantly elevated sound pressure levels (SPLs) in the inter-ping interval of the MFAS-frequency band when compared to natural background levels before and after playbacks. No difference is observed between inter-ping SPLs and natural background levels in the low- and high-frequency bands. In addition, the duration of elevated inter-ping sound field depends on the MFAS source distance. The prolonged elevation of sound field beyond the brief sonar ping is likely due to volume reverberation, although multipath propagation can also be a contributor. This phenomenon underscores the need for further studies on potential acoustic masking to marine mammals by MFAS at distances.

A conformal scanning laser vibrometer was used to determine the vibrational modes of a 17-note portion of a C-lead tenor steelpan. The data represents the surface-normal motion of the instrument in response to an impulsive excitation intended to mimic the strike of a mallet. A description of this novel measurement system is presented, followed by the surface velocity data and a summary of response shapes and the frequencies at which those responses occur. The data indicate that individual note areas respond when adjacent or non-adjacent notes are struck, and clearly illustrate the complex vibration of the steelpan and the coupling between notes that produce the rich distinctive nature of the steelpan sound.