Martin H. Marcus

Thermoelastic loss in microscale oscillators

A simple model of thermoelastic dissipation is proposed for general, free standing microelectromechanical (MEMS) and nanoelectromechanical (NEMS) oscillators. The theory defines a flexural modal participation factor, the fraction of potential energy stored in flexure, and approximates the internal friction by assuming the energy loss to occur solely via classical thermoelastic dissipation of this component of the motion. The theory is compared to the measured internal friction of a high Q mode of a single-crystal silicon double paddle oscillator. The loss at high temperature (above 150 K) is found to be in good agreement with the theoretical prediction. The importance of this dissipation mechanism as a function of scale is briefly discussed. We find that the relative importance of this mechanism scales with the size of the structure, and that for nanoscale structures it is less important than intrinsic phonon–phonon scattering.

Two-dimensional array of coupled nanomechanical resonators

Two-dimensional arrays of coupled nanomechanical plate-type resonators were fabricated in single crystal silicon using e-beam lithography. Collective modes were studied using a double laser setup with independent positioning of the point laser drive and interferometric motion detector. The formation of a wide acoustic band has been demonstrated. Localization due to disorder (mistune) was identified as a parameter that limits the propagation of the elastic waves. We show that all 400 resonators in our 20×20 array participate in the extended modes and estimate group velocity and density of states. Applications utilizing the resonator arrays for radio frequency signal processing are discussed.

On the modes and loss mechanisms of a high Q mechanical oscillator

We have performed laser-Doppler vibrometry measurements of the vibration of a double-paddle oscillator. Seven modes with principally out-of-plane motion have been identified. Their resonance frequencies and mode shapes are in excellent agreement with three-dimensional finite element simulations. We have found that the second antisymmetric torsional mode has exceptionally good vibration isolation of its mode shape. This explains its extremely small low temperature internal friction below 10 K (2×10−8). By correlating the internal friction of each mode with features of their mode shapes, a criterion has been established to develop high Q oscillators.

Characterization of Silicon Micro-Oscillators by Scanning Laser Vibrometry

The dynamics of single-crystal silicon ∼100 μm size rectangular paddle oscillators at room temperature have been studied using a recently developed high-resolution scanning laser vibrometer. The dynamic mechanical behavior is determined by scans of the entire device, providing both amplitude and phase spatial maps of the vibratory response. These reveal more than 16 normal modes below 500 kHz. In addition to simple translation and torsional motion, flexural modes of the paddle plate are observed. Quality factors ranging from 1×103 to 2×104 are measured and are found to be significantly lower than those expected from well-known intrinsic absorption mechanisms. The measurements reveal that there exists significant modification of the expected eigenfrequencies and mode shapes. It is speculated that this is caused by excessive undercutting of the support structure, and that the resulting energy flow into the support leads to increased oscillator loss. Indeed, some correlation is found between observed loss an...

The vibro-acoustic response and analysis of a full-scale aircraft fuselage section for interior noise reduction

The surface and interior response of a Cessna Citation fuselage section under three different forcing functions (10-1000 Hz) is evaluated through spatially dense scanning measurements. Spatial Fourier analysis reveals that a point force applied to the stiffener grid provides a rich wavenumber response over a broad frequency range. The surface motion data show global structural modes (approximately < 150 Hz), superposition of global and local intrapanel responses (approximately 150-450 Hz), and intrapanel motion alone (approximately > 450 Hz). Some evidence of Bloch wave motion is observed, revealing classical stop/pass bands associated with stiffener periodicity. The interior response (approximately < 150 Hz) is dominated by global structural modes that force the interior cavity. Local intrapanel responses (approximately > 150 Hz) of the fuselage provide a broadband volume velocity source that strongly excites a high density of interior modes. Mode coupling between the structural response and the interior modes appears to be negligible due to a lack of frequency proximity and mismatches in the spatial distribution. A high degree-of-freedom finite element model of the fuselage section was developed as a predictive tool. The calculated response is in good agreement with the experimental result, yielding a general model development methodology for accurate prediction of structures with moderate to high complexity.

Active control of payload fairing interior noise using physics-based control laws

This paper presents results of an overview study that draws on active control technologies developed at the Naval Research Laboratory for submarine structural acoustics and aircraft interior noise problems and explores their use in reducing the interior acoustic levels inside rocket payload fairings. Research in controls at NRL includes wavenumber domain control, structural impedance control, and acoustic boundary control (ABC). ABC employs active blankets comprised of a collocated actuator and pressure-velocity sensor layers. A feedback controller is used to impose a spatially averaged local acoustic impedance at the structure-fluid boundary over the region that the blanket is attached. In the study reported here a high fidelity finite-elementinfinite-element model is used to conduct control simulations using active blankets. In this model, the main rocket body is modeled as a finite cylinder with an attached rib stiffened faking. The interior fluid is modeled with finite acoustic elements while the entire exterior fluid is modeled with finite and infinite acoustic elements. In order to better understand the physics of the problem and identify optimum physical control laws, we first conducted a study to uncover the relevant structural acoustics. Using this understanding, we use our numerical model and examine the performance of ABC active blankets as well as evaluate some simple anti-sound configurations.

Effects of annealing and temperature on acoustic dissipation in a micromechanical silicon oscillator

The temperature dependence (15–320K) of the acoustic dissipation was studied for some lower vibrational modes of a suspended silicon plate 1.5μm thick. Our oscillator was exposed to the laboratory environment prior to measurement, laser annealed while in a cryogenic vacuum, and remeasured. We find a dissipation peak at 160K, similar to results by others, and a second dissipation peak near 30K. Annealing reduced the dissipation at 160K by as much as a factor of 10, and gave quality factors as high as 1.4×106 at 470kHz and our lowest temperature. Our data support the idea that the 160K peak is related to adsorbates, and show this mechanism is important at room temperature. Post-anneal room-temperature dissipation appears to be limited by thermoelastic loss for certain modes.

The effect of internal point masses on the radiation of a ribbed cylindrical shell

A finite element analysis is performed on a submerged cylindrical shell with internal frames and point masses attached to the frames. A point force on the shell is shown to excite resonances of the frames. Without the point masses, most of these resonances are evanescent and do not radiate to the far field. With the point masses, the high circumferential order resonances couple with those at low circumferential order with the result of increasing radiation to the far field. In this investigation, the radiation increase is about 10 dB over a broad frequency range (1.5 to 3 times the ring resonance).

Wave localization on a submerged cylindrical shell with rib aperiodicity

The results of a numerical study of vibration localization due to stiffener variability in a framed shell are reported. An axisymmetric finite element (FE)-infinite element model is used to obtain predictions in good general agreement with previously reported experimental results. Over the frequency band of this study, up to three times the ring frequency, two structural resonances dominate the vibratory response of the shell for high circumferential orders (n > 10). Localization is shown to be linked to the sensitivity of the local resonance frequencies of the system to specific geometrical parameters. Specifically, rib thickness variations strongly affect the first pass band, while rib spacing variations strongly affect the second pass band.

The structural acoustics and active control of interior noise in a ribbed cylindrical shell

Numerical studies are carried out regarding the structural acoustics of a ribbed aluminum cylindrical shell structure intended to represent the essential structural features of a small aircraft fuselage. Calculations are made to determine both the wall normal displacements and the interior acoustic pressures for the case in which the shell wall is forced dynamically at a point. The structural responses are further decomposed into their frequency‐wave‐number components. Through a series of comparisons between those responses for an infinite shell, the ribbed vacuum‐filled shell, and the ribbed air‐filled shell, the relevant structural acoustic mechanisms are interpreted. The frequencies at which interior acoustic ‘‘resonances’’ are observed are connected to specific mechanisms, including cavity responses driven by structural modes, cavity modes forcing the structure, and mixed structure/air‐cavity modes. Numerically based active control experiments are carried out using end actuation, and the relative performance of this control ‘‘system’’ is compared when operating on the various mode types.