J. Robert Fricke

Method and apparatus for damping structural vibrations

The damped structural member includes a structural member and granular material in intimate contact with the member. In one embodiment the granular material is lightweight and has a bulk specific gravity of less than 1.5. When low weight is important, the granular material has a bulk specific gravity of less than or equal to one. The particles of the granular material are also in intimate contact with one another. The granular material may be substantially non-viscoelastic. Preferred granular material is low density polyethylene and glass microspheres. The granular material fills hollow structural members or is placed into intimate contact with open structural members. The lightweight fill effectively damps vibrational modes without excessively increasing the weight of the structural member.

Acoustic scattering from elemental Arctic ice features : numerical modeling results

In this paper acoustic scattering from Arctic ice is considered. No analytic scattering theories are able to explain the observed loss at low frequency (10–100 Hz) in long‐range propagation experiments. A finite difference method is used to solve the heterogeneous elastodynamic equations in two dimensions; this technique permits arbitrary roughness, unrestricted in slope, displacement, or radius of curvature and provides direct, physical insight into the rough ice scattering mechanism. Broadband numerical scattering simulations are conducted on pressure ridges. The specular loss due to a ridge is affected by three parameters: cross‐sectional area or mass of the ridge, excitation of plate waves, and a material‐dependent power law. The first two affect the magnitude of the loss, while the last affects the frequency dependence. Multi‐year ridges are completely frozen and are best modeled as elastic structures yielding a loss frequency dependence of ≊f9/2. Observed loss in field data, with a frequency depende...

Modal‐slowness analysis of plate vibrations

A methodology for analyzing complicated plate vibrations is presented. It is based on the Radon transform and unravels the modal structure excited by transient broadband pulses. The difference in phase velocity between flexural and longitudinal plate waves is exploited to this end. Array data collected in the x–t domain is mapped into the slowness‐tau p–τ domain. In this domain, the flexural and longitudinal mode are isolated from one another and may be analyzed individually. Several analysis tools are developed and demonstrated for two plate models: a flat, finite‐width steel plate and the same plate with a small steel block in welded contact. Examples of the analysis results are estimates for modal waveform and dispersion, modal energy content, and modal transfer functions relating incident and scattered waves at an impedance discontinuity in the plate.

Acoustic scattering from elemental Arctic ice features: Experimental results

It has been conjectured that young keels should be modeled as fluid structures while old keels should be modeled as elastic structures. If this conjecture is true, it has been shown that young keels scatter in a dipolar field and old keels scatter in a quadrupolar field. The experiment described in this paper tests the conjecture. Polypropylene chips were used to build a young keel model and a polypropylene half cylinder was used to build an old keel model. Both models were insonified in a laboratory tank with a pulse centered near 60 kHz; the experiment was nominally at a scale of 1000:1 relative to full scale Arctic experiments. Measurements of the scattered field from the two models clearly shows a dipolar field for the chips, or young, keel model. This result supports the young, fluid keel conjecture, which opens the door to relatively simple analytical modeling.

Numerical modeling of the scattered acoustic field from elastic ice

A two‐dimensional elastic finite difference modeling program written for marine geophysical applications [M. E. Dougherty and R. A. Stephen, J. Acoust. Soc. Am. 82, 238–256 (1987)] has been modified to study the ice scattering problem. The modified code was checked by comparing modeled plane‐wave reflection coefficients at various angles of incidence with the analytical solutions provided by Zoeppritz equations. These tests were calibrated for a flat interface with homogeneous half‐spaces of water and ice and resulted in favorable comparisons. Subsequently, various ice models were run to observe the scattered acoustic field. These models include flat ice, flat ice with a single keel, and ice with randomly rough surfaces (top and bottom) derived from different process models (e.g., Gaussian and Poisson). With this program, controlled numerical experiments can be performed for single realizations of ice roughness including full elastic behavior of the ice which is usually neglected in scattering theory. Suc...

Low‐density granular fill for damping structural vibrations

Granular materials have been used for many years to damp structural vibrations. Often these treatments incorporate sand or lead shot. Both are heavy and provide some of their damping effect through mass loading. This paper discusses the damping properties of a low‐density granular material, 3M glass microbubbles (tradename Scothlite). A paste was made using water and Scothlite and placed in an aluminum free‐free beam. Resonant peaks of the beam were reduced by 10 dB, and in some cases more. The specific gravity of the Scothlite is about 0.1, so mass loading effects cannot account for the damping. Further, glass is not normally considered to be highly viscoelastic at room temperature. Rather, the attenuation mechanism is thought to be activated by the low bulk sound speed of the granular fill. With a low sound speed, the wavelength is short, and incipient attenuation in the fill becomes important. The mechanism is a combination of four possibilities: (1) small but finite intrinsic material attenuation, (2)...

Coregistration of received signals with bathymetry using artist

As part of the ARSRP, a software package called Acoustical Ray‐Tracing Insonification Software (artist) was developed which performs the coregistration of received signals to areas of the seafloor for direct paths. The transmitting and receiving array beampatterns are projected onto the actual seafloor by ray‐tracing to yield two insonification patterns. The (x,y) loci of ray contacts with the seafloor are then triangulated and shadow‐zone processed so that the interior of each triangle is inside the illuminated region. Using a bivariate interpolator over each triangle of the insonification patterns, an intersection pattern is generated on a rectangular grid, yielding among other parameters: two‐way travel times, TL, beampattern values, and grazing angles. Only the points which lie in the illuminated zones of both the receiver and transmitter are kept. By using another bivariate interpolator over each patch of the intersection pattern, pairs of time contours are generated and for each patch intersected by...

Discrete Backscatter Can be Dominant in Rough Bottom Reverberation

Rough bottom acoustic backscatter observed in the 200–300 Hz frequency range has a discrete character. This is predicted by a simple facet model that has the form of Lambert’s Law, but biased by the facet’s slope angle, which then imparts a finite backscatter value as grazing angle approaches zero. Backscatter in this model is dominated by planes about one wavelength in size that, for certain orientations, scatter sufficiently in the back direction. Other orientations of larger facets scatter predominantly in the forward direction, while smaller facets of any orientation scatter too weakly to be important. The data, and the model, appear consistent with observations by others on rough bottom backscatter over a wide frequency range.

Acoustic radiation from a 3‐D truss: Direct global stiffness matrix modeling results

This study was initiated to evaluate the normalized sound power level radiated by a driven truss. The coincidence frequency for the beam elements was sufficiently high that global truss modes are not a concern. Radiation from local beam modes dominate the field. Acoustic radiation was modeled using a combination of the direct global stiffness matrix (DGSM) method and models based on radiation efficiency of cylindrical beams. Use of a nominal structural loss factor of 10−4 for the beam material (aluminum) overestimates the measured field by an order of magnitude. Earlier studies suggest that a combination of structural loss in the joints and multipath wave‐type conversion in the truss leads to a loss factor of order 10−3. For this study experimental data were inverted to estimate a frequency‐dependent loss factor, which confirms the prior estimate of order 10−3. When the DGSM based model was run with the estimated frequency‐dependent loss factor, the model results match the measured data closely. A power b...

Direct global stiffness matrix method for thin cylindrical shell dynamics

This paper introduces the direct global stiffness matrix (DGSM) method for analyzing the dynamics of cylindrical shells with axial symmetry. The dynamic stiffness matrix of a straight, circular cross‐section cylindrical element is formulated in terms of ring forces and displacements at each end on a per circumferential mode basis. The stiffness matrix is based on an exact wave‐type solution of the thin shell Donnell equations. More complicated shell systems are analyzed by assembling any number of cylindrical elements. For example, a cylinder with a gradual variation in radius may be modeled by a series of shell elements welded together at their ends. Total system dynamics are found at any given frequency by inverting the global system matrix formed from the individual stiffness element matrices and summing over circumferential mode number. Results for a test case are presented to demonstrate and verify the implementation. [Research sponsored by ONR.]