Subsonic Waves Research Articles

Backscattering enhancements associated with subsonic Rayleigh waves on polymer spheres in water: observation and modeling for acrylic spheres

Unlike most common solids, "plastic" polymer solids typically have shear and Rayleigh wave phase velocities less than the speed of sound in water. Subsonic Rayleigh waves on smooth objects in water are not classified as leakey waves and it is necessary to reexamine backscattering mechanisms. Also the intrinsic material dissipation of the Rayleigh wave can be significant. Backscattering by acrylic or polymethlmethacrylate (PMMA) spheres in water is analyzed and measured in the region ka = 1.5-7 and it is found that prominent low-lying resonance peaks of the form function f exist. The peaks can be modeled with quantitative ray theory as the result of coupling of subsonic Rayleigh waves with sound through acoustic tunneling. The most prominent maximum of f=5.63 occurs at ka = 1.73 and is associated with the quadrupole (or n=2) partial wave. In addition to explaining the scattering, the target strength is found to be sufficiently large that such spheres may be useful for passive low frequency targets.

Wave-number-based assessment of the doubly asymptotic approximation. I. Frequency domain wet surface impedance

The doubly asymptotic approximation (DAA) is a canonical relationship for the interaction between surface normal velocity and pressure. Its validity for a slender hemicapped cylinder is examined by formulating a frequency domain version of DAA using the global basis functions employed in the wave-number-based formulation of the surface variational principle [K. Wu and J. H. Ginsberg, ASME J. Vib. Acoust. 120, 392-400 (1998)]. The wet surface impedance matrix, which relates the spectral representation of normal velocity to a corresponding representation of pressure, is obtained according to a second-order version of DAA and according to the surface variational principle. Comparison and interpretation of the results reveals that DAA fails to account for highlights associated with transition from supersonic to subsonic surface waves as the surface wavelength decreases with frequency held constant.

Galloping and spinning modes of subsonic detonation

A reduced model for a pressure-driven subsonic combustion wave spreading through an inert porous medium (subsonic detonation) is derived. It is shown that the associated planar travelling wave solution may lose its stability assuming a galloping or spinning structure as occurs in supersonic free-space detonation. The problem of subsonic detonation is found to be dynamically akin to the problem of gasless combustion known for its rich pattern-forming dynamics.

Sound radiation from a line forced perforated elastic sandwich panel

Composite barriers, consisting of thin plates separated by light matrix structures, are widely used for fuselage construction in the aircraft industry, and in partitions in the building trade. The acoustical properties of such materials can vary considerably by altering the interior geometry, and perforations can be added to one or both sides. With perforations the interior cavities can act as Helmholtz resonators, causing a substantial modification to the overall transmission and reflection properties of such barriers. Leppington [Proc. R. Soc. London, Ser. A 427, 385–399 (1990)] devised an effective boundary condition for a perforated sandwich plate structure, valid in the limit of low frequency (acoustical waves long compared with the typical dimensions of the hole/cavity construction), and obtained transmission and reflection coefficients for infinite planar structures. This article investigates the radiation properties of perforated sandwich plates by examining a simple infinite one-dimensional model (employing Leppington’s effective boundary condition) which is loaded by a line force or moment. The radiated far field, and unattenuated subsonic plate wave coefficients, are found explicitly, and are plotted over a range of frequencies for two physical configurations, namely an aluminum plate in water and in air. It is revealed that, unlike the usual thin plate equation, the model discussed herein has two bi-directional unattenuated plate waves, and for the structure in air the two waves are of similar magnitude over most frequencies. Surprisingly, these amplitudes are shown to become very large at a frequency below that of the structure’s Helmholtz resonance frequency. Further, the field radiating into air is also significantly modified by the cavity/perforations well away from the Helmholtz frequency.

Response of irregularly ribbed elastic structures, under fluid loading, to localized excitation

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Cooper A. J. and Crighton D. G. 1999Response of irregularly ribbed elastic structures, under fluid loading, to localized excitationProc. R. Soc. Lond. A.4551083–1105http://doi.org/10.1098/rspa.1999.0350SectionRestricted accessResponse of irregularly ribbed elastic structures, under fluid loading, to localized excitation A. J. Cooper A. J. Cooper Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK Google Scholar Find this author on PubMed Search for more papers by this author and D. G. Crighton D. G. Crighton Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK Google Scholar Find this author on PubMed Search for more papers by this author A. J. Cooper A. J. Cooper Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK Google Scholar Find this author on PubMed Search for more papers by this author and D. G. Crighton D. G. Crighton Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK Google Scholar Find this author on PubMed Search for more papers by this author Published:08 March 1999https://doi.org/10.1098/rspa.1999.0350AbstractThis paper investigates the response to excitation of a fluid–loaded elastic membrane supported by a finite array of irregularly spaced ribs. Fluid loading is assumed to provide the only mechanism for the transmission of energy along the structure. This gives rise to two forms of coupling, local surface wave coupling and long–range fluid coupling, which are determined by the Green'function of the unribbed membrane. When the Green'function consists only of the dominant subsonic surface wave component, irregularity gives rise to the phenomenon of Anderson localization whereby energy becomes exponentially localized around the source at all frequencies, in contrast to the pass/stop–band structure generated when the ribs are arranged strictly periodically. This, however, neglects the effect of the second, acoustic component of the Green'function which provides long–range coupling and taken alone gives rise to algebraic decay at all frequencies along a regularly ribbed membrane. It is shown, analytically and numerically that, when the Green'function consists only of the acoustic component, this algebraic decay is essentially insensitive to any degree of disorder. Similar techniques are used to show that the stop band response, when only local coupling is accounted for, can show slight delocalization in comparison with the response for the regular array. When the full Green'function is used, consisting of both components, it is shown that the exponential decay induced by irregularity in the pass bands becomes short–circuited by the much slower algebraic decay so that the energy transmission levels become significantly higher. This, with similar behaviour in the stop bands, suggests that the effect of long–range coupling would frustrate any attempt at exploiting either the Anderson localization phenomenon or stop–band localization in fluid–loaded structures. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Liu W (2022) Effect of reducing the vibration of a frame-spacing arrangement, Journal of Vibroengineering, 10.21595/jve.2022.22547, 24:8, (1428-1444), Online publication date: 31-Dec-2022. Legault J, Mejdi A and Atalla N (2011) Vibro-acoustic response of orthogonally stiffened panels: The effects of finite dimensions, Journal of Sound and Vibration, 10.1016/j.jsv.2011.07.017, 330:24, (5928-5948), Online publication date: 1-Nov-2011. Metcalfe P (2005) Ribbed elastic structures under a mean flow, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 461:2056, (913-931), Online publication date: 8-Apr-2005. This Issue08 March 1999Volume 455Issue 1983 Article InformationDOI:https://doi.org/10.1098/rspa.1999.0350Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online08/03/1999Published in print08/03/1999 License: Citations and impact Keywordsirregular rib arraylong–range couplingensemble averagefluid–loaded structureAnderson localizationalgebraic decay

EFFICIENCY OF A MONOPOLE SOUND SOURCE IN THE VICINITY OF A WATER-LOADED PLATE

This paper presents numerical results for the power output of a sound source in the vicinity of an elastic structure. The source is a monopole characterized by a constant rate of volume injection. The structure is a thin elastic plate of infinite extent. The coupling of the plate's flexural motion and the acoustic field is taken into account. The acoustic energy emitted by the source is carried away to infinity by acoustic radiation as well as by flexural waves that travel along the plate, accompanied by a coupled, subsonic surface wave in the fluid. For the case of steel plates in water, numerical results have been obtained for the total power delivered by the source as well as for the various power flows involved. The dependence of these results upon two parameters is investigated by extensive numerical calculations. These parameters are: (i) the diffraction or Helmholtz numberk0d, wherek0is the fluid wavenumber anddis the distance from the source to the plate, and (ii) the ratio of the plate thicknesshandd. The power output of the source depends strongly upon the region of interest in this two-parameter space. Fork0d≥1 the total power output approaches the free field value, but also shows the typical modulation due to the finite distance to the plate. Forh/d≥0·1 this modulation effect is comparable to that for an infinite rigid wall, while forh/d≤0·01 it resembles the effect for a free surface. Fork0d<1 andh/d≤k0d/20 the results do not vary withh/d, but the effect of the plate is very close to that for a perfectly compliant surface. In a third regime, i.e., for 0·1≥h/d≥k0d/10 the efficiency of the source is independent ofk0h, but increases strongly with decreasingk0d2/h.

Solitary Waves in Flexible, Arbitrary Elastic Helix

The traveling solitary wave was recently discovered to be a very stable object existing in an inextensible, flexible helical fiber. In the present work, a flexible helical fiber with an arbitrary stress-strain relation is considered, and a general, analytical, steady-state solution of the 3D nonlinear vector equation is found. This solution describes a new class of spatial motion of an elastic string, which is shown to be a waveguide for subsonic solitary waves. The results confirm that the known solution for an inextensible fiber is a low-velocity or low-energy asymptote of the solution presented here. Another type of asymptotic solution derived here corresponds to a high-energy wave. In this case, when the amplitude of the wave increases, the wave speed and energy tend to infinity, and the effective wavelength tends to zero.

Shaping dynamics and structure of large-scale surface plasma formations under single-pulse laser action on various materials

It is established that, in the case of laser action on materials in large illuminated spots in atmospheric-pressure air for a laser radiation power density q≤2 MW/cm2 (λ=1.315 μm), an evaporative regime with plane scattering of the laser-produced erosion plasma is realized while, for q≈5–17 MW/cm2, the plasma front is transferred to the air, leading to plasma screening of the target and shaping of a subsonic radiation wave in the air. As the duration of the laser pulses increases (τ∼160 μsec), in spite of the large illuminated spots (S∼150 cm2) the evaporative regime of the laser action with plane plasma scattering goes over into a regime with jet outlow and formation of a quasistationary shock wave.

Quasi-bulk Rayleigh waves in semi-infinite media of arbitrary anisotropy

Specific features ot quasi-bulk elastic waves arising in the neighbourhood of the direction ot propagation of an exceptional bulk wave are discussed. A quasi-bulk surface wave is characterized by that it penetrates into the substrate a distance far larger than the sound wavelength, and an exceptional bulk wave is a homogeneous mode with group velocity parallel to the crystal boundary and satisfying the condition of a mechanically free surface. Approximate expressions for the penetration depth, partial amplitudes, and phase velocity of quasi-bulk surface waves are derived without any assumption about the crystallographic symmetry of the medium. In particular it is found that independently of the symmetry of the crystal the penetration depth is inversely proportional to the square of angles specifying deflection from the geometry of propagation corresponding to the existence of an exceptional wave. The value of the “gap” between the phase velocity of a quasi-bulk wave and the associated limiting velocity of bulk modes is proportional to the fourth power of the values of these angles. The obtained expressions clearly demonstrate an intimate connection between the occurrence of quasi-bulk solutions and the non-existence of the subsonic Rayleigh wave for the direction of propagation of the exceptional bulk wave.

All-optical investigation of the lowest-order antisymmetrical acoustic modes in liquid-loaded membranes

The antisymmetrical Scholte–Stoneley wave in liquid-loaded metal and polymer membranes were excited via the laser-induced thermoelastic effect and were detected with a laser beam deflection technique. The experimentally determined dispersion relation for this wave is in accordance with theory in a wide frequency range. However, no evidence of the propagating subsonic lowest-order anitsymmetrical pseudo-Lamb wave was found.

Interaction between wave-number pairs

When acoustic-structure interaction is analyzed according to the wave-number-based version of the surface variational principle (SVP), considerable computational effort is required to generate each coefficient in the quadratic sum forming the variational quantity. Examination of the wet-surface impedance, which represents the spectrum of pressure amplitudes generated by a specified spectrum of surface velocity amplitudes, reveals that many cross-impedance terms are very small. This suggests that some coefficients need not be computed. The paper introduces several a prioricriteria for selecting the impedance terms to be omitted, based on the supersonic cutoff wave number. Each scheme is assessed by comparing its predictions to the convergent SVP solution. For the nonsymmetric azimuthal harmonics, the field quantities and the radiated power are well predicted if subsonic waves are ignored. In contrast, for the axisymmetric component, substantial errors (6 dB or more) for radiated power arise, unless a broad spectrum of subsonic waves are included in the formulation. The power is mostly reactive, being associated with an evanescent field, even for the supersonic spectrum. The study shows that small interactions between subsonic waves in the axisymmetric case can result in substantial radiative effects that are not modeled in ray theory analyses.

Classifications of surface waves in anisotropic elastic materials

Surface waves in an anisotropic elastic material can be classified according to the number of distinct eigenvalues and the number of independent eigenvectors of the 6 × 6 real matrix N( υ). There are six groups under this classification. Surface waves can also be classified according to the number of partial waves in the solution and the form of each partial wave. There are again six groups according to this classification. The classifications encompass both subsonic and supersonic surface waves. The relationships between the two different classifications and the existence or non-existence of a surface wave in each group are discussed. We show how one can obtain a set of orthogonal and normalized eigenvectors and generalized eigenvectors for the matrix N( υ). The eigenvectors and generalized eigenvectors that appear in the surface wave solutions belong to a set of orthogonal eigenvectors with few exceptions, although orthonormalization is not required for surface wave construction.

Flexural Wave Propagation in a Fluid-Loaded Elastic Plate With Periodically Varying Rigidity

The method of multiple scales is utilized to analyze the propagation of flexural waves in a fluid-loaded elastic plate with periodically varying rigidity. Subsonic modes are coupled under a Bragg condition imposed by the parametric periodicity, leading to a strong stopband interaction. This interaction is analytically described by two coupled-mode equations. The results might be utilized to avoid the undesirable acoustic radiation occurring when subsonic waves encounter a discontinuity.

Wave-number space response of a near periodically ribbed shell

Employing near-field acoustic holography measurements, the wave-number space response of a ribbed shell to a point drive is investigated. The data show the dominance of flexural vibration in the mid-frequency range, and demonstrate the prominent role played by the eigensolutions of the periodic structure. The supersonic region of frequency–wave-number space is examined in detail and the fast membrane waves, although suppressed in level relative to the subsonic bending waves, provide a clear highlight in this domain at frequencies below the first radiating flexural passband. The results are also examined in kz−kφ space for several frequencies. This representation enables an interpretation of the results in terms of the slowness surface of the flexural waves and provides a simple explanation for the various complex beaming and focusing phenemena which occur in this system.

Suppression Of High Speed Flames And Quasi-detonations

Past research has identified three candidates as near term replacements for CF,Br in some aircraft total-flooding fire protection applications: CF,I, C2HF, and C,F,. The behavior of these compounds when added to lean, stoichiometric and rich propanelair mixtures exposed to subsonic and supersonic combustion waves is examined using a 10 m long, 50 mm diameter detonatioddeflagration tube. Pressure and visible radiation are measured as a function of the amount of agent in the mixture to determine the pressure ratio across the incident shock wave and the speed of the radiation front. The results are compared to earlier studies using ethene, in which significantly higher pressure ratios and wave speeds were generated. The presence of the three extinguishing compounds in the propanelair mixtures causes the combustion either to be enhanced or suppressed, and depending upon the dynamical situation and the concentration of the agent, any of the three can outperform the others. For example, C,F, is the most effective compound for attenuating combustion systems for all stoichiometries; C2HF, reduces the threat by 90 % when its volume fraction is 11 %, the best performance of the three, but amplifies the severity of the deflagration the most at a volume fraction of 5 %; and the best agent for attenuating the pressure increase of the shock wave is CF,I under most conditions.

Aerodynamic Characteristics of the F/A-18 at Large Roll Angles and High Incidence

ciated with the wave rotor were active. The active variables considered were the rotational speed of the wave rotor and the heat added to the wave rotor. Important active constraints included the limits on maximum speeds of the compressors, a 15% surge margin for all compressors, and a maximum wave› rotor exit temperature. The engine thrust was selected as the merit function. The wave› rotor› engine design became a sequence of 47 optimization subproblems, one for each mission point. Only by using the cascade strategy could the problem be solved successfully for the entire e ight envelop. For the mission point dee ned by Mach number = 0.1 and altitude = 5000 ft, the convergence of the two-optimizer cascade strategy is shown in Fig. 3. The e rst optimizer produced an infeasible design at 67,060.87-lb thrust in about e ve design iterations. The second optimizer, starting from the e rst solution with a small perturbation, produced a feasible optimum design with an optimum thrust of 66,901.28 lb. The optimum solutions for the 47 mission points obtained by using the combined tool were normalized with respect to the NEPP results and are shown in Fig. 4. The combined tool produced a higher thrust than the NEPP for mission points 12, 26, and 32. Both NEPP and COMETBOARDS› NEPP produced identical optimum thrust values for a few mission points. The maximum difference in thrust exceeded 5% for several mission points. These differences could be signie cant if the design points with increased thrust were used to size the engine. The combined COMETBOARDS› NEPP tool successfully solved the subsonic wave› rotor› engine design optimization problem.

Approximations to solitary waves on lattices, III: the monatomic lattice with second-neighbour interactions

We find new behaviour in a lattice with second-neighbour interactions. First we find solitary waves with oscillatory spatial decay, this is something that cannot occur in lattices with nearest-neighbour interactions alone. This is found by standard asymptotic analysis, which leads to an exact curve in parameter space where this behaviour starts. A number of highly accurate quasi-continuum approximations are derived and solved. One of these suggests a possible method for subsonic solitary waves to cease existing. An alternative method of approximation elegantly reveals the differences in shape between subsonic and supersonic solitary waves. This is based on the weak form of the differential - delay equation for the travelling wave, and is derived using the calculus of variations.

Elastic wave power equipartition in a finite-length ringed shell

Compressional and shear waves, trace matched on a submerged cylindrical shell by plane sound incidence near beam aspect, can couple to each other, as well as to subsonic flexural waves, at ring stiffeners and endcaps. This paper addresses whether the power in each elastic wave type (defined as energy per unit shell length multiplied by the wave axial group speed) is partitioned equally with the other two. Shell surface velocities of a ringed shell, calculated for midfrequency range 2&amp;lt;ka&amp;lt;12 via a SARA 2-D program implemented by Liu, are Fourier transformed into the wave-number domain to evaluate each wave type, and then into the time domain to evaluate transient wave power in several time windows. The time windows are based on an integral number of roundtrips of the trace matched wave in the shell. It is found that elastic wave power among the wave types differs by 10 dB in the first window, and therefore is not equipartitioned. However, the wave power difference is within 3 dB in the second window, which supports the conclusion of at least approximate wave power equipartition. [Research supported by ONR.]

Slow thermal waves in impurity seeded radiative plasmas.

Linear and nonlinear wave propagation in optically thin, impurity seeded radiative plasmas is studied in slab geometry. Taking into account the thermal force that acts on impurity ions leads to a new type of slightly damped or slightly unstable subsonic waves that propagate within limited ranges of temperature. The one-dimensional nonlinear equation reduces to that of a classical particle in a forced external field with nonlinear friction. It is shown that the slightly unstable wave may saturate due to the nonlinear character of the ``friction'' term, and the stability of the nonlinear solution is analyzed.

Ray acoustics and vibration of immersed thin elastic cylindrical shells excited by an on-surface source

Structural loadings, joints, and truncations of smooth shells act as equivalent forcings on such shells in the overall acoustic response and vibration. Choosing an on-surface phased line source as the acoustic source, this paper treats the ray synthesis of the pressure and displacement fields on a thin elastic cylindrical shell immersed in an acoustic fluid as well as the sound field in the far zone. The subsonic flexural waves and their strong resonances are observed at the shell surface, but not in the far field, thereby generating distinct field structures in these two regions. In the parameter region where the supersonic compressional and shear waves are cutoff, the surface fields are found to be represented completely by the shell guided flexural mode, while the far field is reduced to the modified geometrical acoustics field (essentially comprised of incident and reflected waves). The ray acoustic predictions prove to be accurate in comparison with the normal mode series data for ka ⩾ 2 or so (where a is the mean radius of the shell and k is the acoustic wavenumber of the fluid).