Stephen A. Hambric

Development of a design curve for particle impact dampers

Particle impact dampers (PIDs) are enclosures partially filled with particles of various sizes and materials. When attached to a vibrating structure, they dissipate energy through inelastic collisions between the particle bed and the enclosure wall, as well as between particles. In this work, the development of a design curve that can be used to predict the damping characteristics of particle impact dampers is presented. A power measurement technique enabled the time-efficient measurement of the damping properties of the PID. This technique enjoys several advantages over traditional loss factor measurements, including the flexibility to analyze the behavior of the PID at any frequency or excitation amplitude, and the ability to estimate the damping contribution for any structure operating such that the PID experiences similar conditions. Using this power measurement technique, a large number of experiments were conducted to determine the effects of vibration amplitude, excitation frequency, gap size, particle size, and particle mass on the dissipated power and effective mass of the PID. The power data were then systematically collapsed into a pair of two-dimensional master design curves with unitless axes which are comprised of combinations of design parameters. A “damping efficiency” of the PID may be predicted from the design curves for specific applications. A physical interpretation of the design curves is given, and the performance of a PID on a structure is used to verify their predictive capabilities.

Power flow in coupled bending and longitudinal waves in beams

In complex structures, curvature and impedance discontinuities (e.g., junctions) couple bending and longitudinal waves. Propagation losses for longitudinal waves are often much less than losses for bending waves, and damping treatments often less effective on longitudinal waves. When the dissipation in longitudinal waves is less than that on bending waves, longitudinal waves can provide an efficient means of power flow between bending waves generated at one location and bending waves that are a source of acoustic radiation at another location. In order to design and locate effective treatments, knowledge of the power flow in longitudinal as well as bending waves is required. The measurement of power in both bending and longitudinal waves when both waves are present is demonstrated. Measurements conducted on a straight beam and a T-beam are compared to predictions obtained using finite element methods. The effect of coupling between waves at the junction in a T-beam is illustrated using results from measurements of power flow.

Simulating and measuring structural intensity fields in plates induced by spatially and temporally random excitation

The structure-borne power in bending waves is well understood, and has been studied by many investigators in ideal beam and plate structures. All studies to date, however, have considered only the structural intensity induced by deterministic, localized drives. Since many structures of practical interest are excited by spatially random pressure fields, such as diffuse and turbulent boundary layer pressure fluctuations, techniques for measuring and predicting the structural intensity patterns in flat plates excited by such fields are presented here. The structural intensity at various frequencies in a simply supported, baffled, flat plate driven by a diffuse pressure field is simulated using analytical techniques and measured by post-processing data from a scanning laser Doppler vibrometer and reference accelerometer using finite differencing techniques. The measured and simulated fields are similar, and show intensity patterns different from those caused by deterministic point drives. Specifically, no clear source regions are apparent in the randomly driven intensity fields, although the energy flow patterns do clearly converge toward a point damper attached to the plate.

Development of a design curve for Particle Impact Dampers

Particle impact dampers (PIDs) are enclosures partially filled with particles of various sizes and materials. When attached to a vibrating structure, they add damping by dissipating energy through inelastic particle-enclosure collisions as well as through momentum transfer. The development of a design curve that can be used to predict the damping characteristics of particle impact dampers is presented here. A power measurement technique enabled time-efficient measurement of the damping properties of the PID. This technique enjoys several advantages over traditional loss-factor measurements, including the flexibility to analyze the behavior of the PID at any frequency or amplitude of the excitation, and the ability to estimate the damping contribution for any structure operating within the bounds of the design curve. Using the power measurement technique, a large number of experiments were conducted to determine the effects of vibration amplitude, excitation frequency, gap size, nominal particle diameter, and particle mass on the dissipated power and effective mass of the PID. The power data were then systematically collapsed into a pair of two-dimensional master design curves with non-dimensional quantities for the axes. The quantities are comprised of combinations of design parameters. For specific applications, a damping efficiency of the PID may be predicted from the design curves. A physical interpretation of the design curves is given. The performance of a PID on a structure verified the predictive capabilities.

Grating lobe reduction in transducer arrays through structural filtering of supercritical plates

The effect of placing a structural acoustic filter between water and the transducer elements of an array to help reduce undesirable grating lobes is investigated. A supercritical plate is mounted to transducer elements with a thin decoupling polyurethane layer between the transducers and the plate. The plate acts as a radiation/incidence angle filter to pass energy at angles near normal incidence, but suppress energy at large incidence angles. Grating lobe reduction is achieved at the expense of limiting the available steering of the main lobe. Within this steer angle limitation, the main lobe can be steered as normal while the grating lobe level is reduced by the plates angular filtering. The insertion of a plate structural filter provides, in principal, an inexpensive and easily implemented approach to extend usable frequency bandwidth with reduced level grating lobes, without increasing the number of array elements. Even though the data match theory well, a practical material has yet to be found that possesses optimal material properties to make the proposed idea practical. This work represents the first attempt to advantageously utilize a plate above its critical frequency to provide angular dependent sound transmission filtering.

Sound and Structural Vibration, 2nd Edition

This article reviews Sound and Structural Vibration, 2nd Edition by Frank Fahy, Paolo Gardonio , New York, 2007. 633 pages,

On the steering of sound energy through a supercritical plate by a near-field transducer array

95 (paperback) ISBN 10: 0-12-373633-1.

Simulations and Measurements of the Vibroacoustic Effects of Replacing Rolling Element Bearings With Journal Bearings in a Simple Gearbox

The ability to direct sound energy through the flexural vibrations of a submerged plate at various angles of incidence using a near-field transducer array is investigated. An alumina bar is placed in front of a one-dimensional, eight-element transducer array, between the array and the water. Operating in a receive mode, data were taken as a function of angle of incidence and compared to data taken without the presence of the alumina bar. The array was also operated in transmit mode and results were compared to corresponding receive mode data, showing that reciprocity holds. Results show that in fact sound energy can be steered through a plate, and that the measurement method used provides a convenient method of measuring the angular dependence of transmission through a plate, including measurements at frequencies above the plates critical frequency. Experimental results of sound transmission versus angle of incidence of finite sized plates agree qualitatively with theoretical results from an analysis of the transmission through an unbounded flexible partition.

Comment on plate modal wavenumber transforms in Sound and Structural Vibration [Academic Press (1987, 2007)] (L)

The effects of replacing rolling element bearings with journal bearings on the noise and vibration of a simple gearbox are computationally and experimentally evaluated. A modified component mode synthesis (CMS) approach is used, where the component modes of the shafting and gearbox housing are modeled using finite element analysis (FEA). Instead of using component modes with free boundary conditions, which is typical of CMS, the shafting and gearbox are coupled using nominal impedances computed for the different bearing types, improving convergence of the solution. Methods for computing the actual bearing impedances, including the high damping coefficients in journal bearings, are summarized. The sound radiated by the gearbox is computed using a boundary element (BE) model. The modeling results are validated against measurements made at the NASA Glenn Research Center. Both simulations and measurements reveal that the journal bearings, although highly damped, do not necessarily lead to strong reductions in gearbox vibration and noise.

A Method to Simulate Structural Intensity Fields in Plates and General Structures Induced by Spatially and Temporally Random Excitation Fields

The wavenumber transform for rectangular, simply supported, isotropic thin plates has been rederived to correct a technical error found in the text Sound and Structural Vibration (Academic Press, 1985/2007) by Fahy/Fahy and Gardonio. The text states that the modal wavenumber corresponds to the peak of the wavenumber spectrum. While this is approximately true for higher-order modes, it does not hold for lower-order modes due to coupling between positive and negative wavenumber energy. The modal wavenumber is shown to be related to the zeros in the wavenumber spectrum by an integer multiple of 2π normalized by the plate length.