Subsonic Surface Waves Research Articles

The multi-physics metawedge: graded arrays on fluid-loaded elastic plates and the mechanical analogues of rainbow trapping and mode conversion

We consider the propagation and mode conversion of flexural-acoustic waves along a fluid-loaded graded array of elastic resonators, forming a metasurface. The multi-physics nature of the problem, coupling two disparate physical systems, brings both challenges and novel features not previously seen in so-called bifunctional metamaterials. In particular, by using an appropriately designed graded array of resonators, we show that it is possible to employ our metasurface to mode-convert sub-sonic surface flexural waves into bulk acoustic waves and vice-versa; transferring energy between two very different physical systems. Whilst the sub-sonic mechanical surface wave is dispersive, the bulk acoustic wave is dispersionless and radiates energy at infinity. We also show that this bifunctional metasurface is capable of exhibiting the classical effect of rainbow trapping for sub-sonic surface waves.

Surface and interfacial waves in anisotropic elastic quasicrystals

We present the Stroh formalism for two-dimensional subsonic steady-state motion of anisotropic quasicrystals. Using this new formalism and a series of identities and properties which follow, we investigate subsonic surface and interfacial waves in anisotropic quasicrystals. Our results suggest that there exist at most three subsonic surface wave speeds. This interesting observation is quite different from the unique surface wave speed known for anisotropic crystals. The degenerate case of decagonal quasicrystalline materials is discussed in detail.

Zero-curvature transonic states and one-component surface waves in anisotropic elastic media

The existence of one-component surface waves requires a degeneracy in the Stroh sextic equation. An extraordinary zero-curvature transonic state, a point on the slowness surface where both the curvature and its first derivative equal zero, will yield a triple degeneracy in the Stroh equation. Relationship between extraordinary zero-curvature transonic states and one-component surface waves is investigated showing that they are linked via a space of degeneracy associated with the Stroh equation. Moreover, some generalized subsonic surface waves containing generalized Stroh eigenvectors are also found along the space of degeneracy.

Existence of Surface Waves and Band Gaps in Periodic Heterogeneous Half-spaces

We find a sufficient condition for the existence of surface (Rayleigh) waves based on the Rayleigh-Ritz variational method. When specialized to a homogeneous half-space, the sufficient condition recovers the known criterion for the existence of subsonic surface waves. A simple existence criterion in terms of material properties is obtained for periodic half-spaces of general anisotropic materials. Further, we numerically compute the dispersion relation of the surface waves for a half-space of periodic laminates of two materials and demonstrate the existence of surface wave band gaps.

Explicit conditions for the existence of exceptional body waves and subsonic surface waves in anisotropic elastic solids

It is known that a subsonic surface (Rayleigh) wave exists in an anisotropic elastic half-space x 2 ⩾ 0 if the first transonic state is not of Type 1. If the first transonic state is of Type 1 but the limiting wave is not exceptional, a subsonic surface wave exists. If the first transonic state is of Type 1 and the limiting wave is exceptional, a subsonic surface wave exists when tr L ( υ ˆ ) ⩽ 0 . It is shown that an exceptional body wave is necessarily an exceptional transonic wave, and could be an exceptional limiting wave. Only two wave speeds are possible for an exceptional body wave. We present explicit conditions in terms of the reduced elastic compliances s α β ′ for the existence of an exceptional body wave. If an exceptional body wave exists, conditions are given for identifying whether the transonic state is of Type 1. Hence, through the existence of an exceptional body wave we provide explicit conditions for the existence of a subsonic surface wave with the exception when tr L ( υ ˆ ) needs to be computed.

Surface Waves, Limiting Waves and Exceptional Waves: David Barnett's Role in the Development of the Theory

A short review is presented of progress in the theory of localized eigenwaves in anisotropic solids. The main attention is paid to the problem of existence of surface wave solutions in semi-infinite elastic bodies. Here the contribution of David Barnett is most important. The general theorems of existence and uniqueness are formulated and their modifications for media with piezoelectric and/or piezomagnetic couplings are considered. The conditions for existence of supersonic surface waves in purely elastic half-spaces are displayed. The situations on both sides of the vicinity of exceptional transonic states are discussed. The criterion for the existence of quasi-bulk subsonic surface waves in elastic media of unrestricted anisotropy is obtained in terms of the general Barnett and Lothe theorem. The conditions for the existence of exceptional bulk waves and their main properties are considered. The interface wave theory of David Barnett et al is reviewed for rigid and slip contacts between elastic and piezoelectric sub-media.

Acoustic waves in bounded anisotropic media: theorems, estimations, and computations

This paper discusses some basic achievements in theoretical studies on acoustic wave propagation along boundaries in anisotropic solids. In particular, the following issues are reviewed: existence theorems for subsonic surface and interface waves, leaky surface acoustic waves (SAW) and their relation to "supersonic" SAWs and fast exceptional bulk waves, the resonance reflection of bulk waves in the vicinity of leaky wave branches. General conclusions are illustrated by numerical examples.

The explicit secular equation for surface acoustic waves in monoclinic elastic crystals.

The secular equation for surface acoustic waves propagating on a monoclinic elastic half-space is derived in a direct manner, using the method of first integrals. Although the motion is at first assumed to correspond to generalized plane strain, the analysis shows that only two components of the mechanical displacement and of the tractions on planes parallel to the free surface are nonzero. Using the Stroh formalism, a system of two second order differential equations is found for the remaining tractions. The secular equation is then obtained as a quartic for the squared wave speed. This explicit equation is consistent with that found in the orthorhombic case. The speed of subsonic surface waves is then computed for 12 specific monoclinic crystals.

On the theory of the elastic wave propagation in a crystal coated with a solid layer. II. Surface and leaky waves near a line of exceptional bulk waves

The existence of exceptional bulk, quasi–bulk–surface and pseudo–surface waves in a crystal of arbitrary anisotropy coated with a solid layer of arbitrary anisotropy is considered. One–component exceptional bulk waves that exist on the mechanically free surface are shown to disappear on the plated surface. They give rise to quasi–bulk–surface and pseudo–surface waves. The connection between the appearance of quasi–bulk subsonic surface waves and the existence of subsonic ordinary (Rayleigh) surface waves is investigated. In the plated crystal, instead of one–component exceptional waves, there arise three–component exceptional waves which involve the limiting bulk wave and two inhomogeneous modes. It is shown that the presence of an overlay in a general manner provides the existence of high–velocity (supersonic) pure surface waves near the intermediate transonic state and the existence of leaky waves near the highest transonic state.

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.

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.

Self-orthogonal sextic formalism for anisotropic elastic media: spaces of simple reflection and two component surface waves

There are six polarization and traction vectors involved as normalized Stroh eigenvectors components in the subsonic surface wave theory. By introducing new sets of self-orthogonal vectors related to the Stroh eigenvector components, a series of linear dependence/independence relations between those vectors can be established. Using such a self-orthogonal sextic formalism, analysis of the spaces of simple reflection, the existence of two component surface waves and supersonic surface waves become more explicit and straightforward.

Influence of mean shear on sound produced by turbulent flow over surface slots

An analytical investigation is made of the sound produced by low Mach number turbulent flow over a slot in a thin rigid plane and over an array of parallel slots in the plane. The plane separates the turbulent mean stream from nominally stagnant fluid. The turbulent wall pressures excite unstable oscillations of the mean shear layer in the slots, and linear perturbation theory is used to estimate the influence of these instabilities on sound generation. For both isolated slots and parallel slots, it is shown that the growth of shear layer disturbances across a slot can greatly increase the contribution from the slot trailing edge to the volume flux through the slot, and produce a corresponding increase in the net radiation relative to that predicted by the usual ‘‘diffraction theory,’’ which neglects the presence of the shear layer. Previous analyses of this problem have ignored the influence of mean shear, and their predictions at higher frequencies are typically 20–40 dB smaller than those given here. At very low frequencies, additional vorticity shed from the leading edge of a slot effectively blocks unsteady motion through the slot and predicted sound levels are then very much smaller than those of diffraction theory. An extended slotted surface can support subsonic surface waves that decay with distance into the fluid; these are shown to be unstable within a certain narrow range of frequencies, and may well be associated with the generation of tonal noise by the boundary layer.

Surface acoustic waves in piezocrystals: an example of surface wave existence with clamped boundary

It is shown by a model calculation that in a half-infinite piezoelectric-piezomagnetic a subsonic surface wave solution will exist even with a mechanically clamped boundary, for suitable material constants and suitable electric and magnetic boundary conditions. This settles a problem left open in a recent paper by Alshits, Darinskii and Lothe, “On the existence of surface waves in half-infinite anisotropic media with piezoelectric and piezomagnetic properties”, Wave Motion 16, 265–283 (1992).

Anderson localization effects in the transmission of energy down an irregularly ribbed fluid-loaded structure

The paper studies wave transmission along an infinite fluid-loaded elastic membrane supported by a finite array of irregularly spaced thin ribs, all having infinite mechanical impedance, except for the first, which is driven by a time-harmonic force. When the Green’s function of the unribbed structure is taken to consist only of its subsonic surface wave component, the response of the structure is exponentially localized (Anderson localization). A localization length is calculated, as a function of frequency, in both the small and the large disorder limits and in both of these limits the calculated localization length is found to agree extremely well with the results of numerical simulations. When a weak acoustic component is included in the Green’s function, it is shown that the exponential localization is short-circuited, the response now decaying algebraically with distance from the first rib, and with negligible sensitivity to disorder, even for rather large degrees of disorder.

The scattering of an acoustic wave from the absorbing-elastic coupling of two half-planes

The scattering of an acoustic wave from an absorbing half-plane coupled with an elastic half-plane is considered. The planes are subjected to heavy-fluid loading where the coupling between the fluid and the plate motions is significant. It is observed that the scattered field consists of a subsonic surface wave (Biot–Stoneley wave) traveling along the elastic plate and an edge diffracted wave. The effect of absorption on the scattered field is shown explicitly in terms of the absorbing parameter.

Fluid loading of irregular structures

An analytically and computationally tractable model for the response of complex fluid-loaded structures is that of a plane elastic plate or membrane subject to static fluid loading and single-frequency localized mechanical drive, and reinforced by a number of parallel ‘‘ribs’’ in regular, partially ordered, or random configurations. Coupling along the structure is provided by subsonic surface waves (equivalent to nearest-neighbor mechanical coupling) and by long-range acoustic/hydrodynamic fields. A variety of analytical and computational studies carried out by the Cambridge group will be presented, showing large effects of an isolated irregularity, Anderson localization in extensively irregular configurations under surface wave coupling, and delocalization (short circuiting) by weak long-range fields. [Work supported by ONR, Code 1132SM.]

Hot topics in structural acoustics and vibration

Acoustic holography has allowed the theoretical concept of identifying and separating radiating supersonic surface waves (identified by low wave numbers) from nonradiating subsonic surface waves (high wave numbers) to be verified experimentally. Frequency-wave-number filtering, which embodies the idea of spatial and temporal filtering, may hold the key for assessing advances in active noise control as well as for developing innovative concepts for damping treatments for passively controlling radiation. For implementation of active control, spatial anti-aliasing filters for sensors and shaped structural actuators (which prevent actuation of high wave numbers) may provide a path to stable active control technology for complex structures. The physical understanding that supersonic radiating waves are membrane waves of structures and fast compressional or shear waves of elastic bodies can lead to new ideas for incorporating damping mechanisms within structures. To extend the concept of spatial-temporal filtering to arbitrary bodies, further analytical, experimental, and signal processing efforts will be required.

On the existence of surface waves in half-infinite anisotropic elastic media with piezoelectric and piezomagnetic properties

An analysis based on a generalization of the many-dimensional surface wave formalism has yielded a number of general results for magneto-electroacoustic surface waves. For a mechanically champed, electrically closed and magnetically open surface a new subsonic surface wave may come into existence when piezomagnetic and piezoelectric effects are present simultaneously. The case of a mechanically free surface as function of electrical and magnetic boundary conditions has been analyzed in detail. There are never more than two subsonic solutions. A table is constructed with allow us, on the basis of knowledge of the number of solutions for a particular case of boundary conditions to make predictions and specific statements concerning the existence of surface wave solutions and their number for other boundary conditions.