On the existence of a symmetric acoustic mode in a quadratic solid wedge

It is shown that in a solid truncated wedge whose local thickness depends quadratically on its height, along with the earlier predicted countable set of antisymmetric acoustic modes localized near the apex, there can also exist a single symmetric acoustic mode. This mode is localizsd in the vicinity of the wedge apex: and its characteristics are close to those of Rayleigh's surface acoustic mode. The phase velocity and the field structure of tbe mode are calculated. The lowest-frequency boundary for the region of its existence is determined

Focusing of Rayleigh waves generated by high-speed trains under the condition of ground vibration boom

In the present paper, the effects of focusing of Rayleigh waves generated by high speed trains in the supporting ground under the condition of ground vibration boom are considered theoretically. These effects are similar to the effects of focusing of sound waves radiated by aircraft under the condition of sonic boom. In particular, if a railway track has a bend to provide the possibility of changing direction of train movement, the Rayleigh surface waves generated by high-speed trains under the condition of ground vibration boom may become focused. This results in concentration of their energy along a simple caustic line at one side of the track and in the corresponding increase in ground vibration amplitudes. The effect of focusing of Rayleigh waves may occur also if a train moves along a straight line with acceleration and its current speed is higher than Rayleigh wave velocity in the ground. The obtained results are illustrated by numerical calculations

Acoustic 'black holes' for flexural waves and their potential applications

Acoustic 'black holes' for flexural waves and their potential application

Transmission of a Rayleigh wave across smooth large-scale surface irregularities

The ray paths of Rayleigh waves in transmission across smooth large-scale surface irregularities are analyzed. Surface ray equations are derived, and calculations are carried out for several typical irregularities in the form of axisymmetrical recesses or protuberances and cylinders of variable curvature

On Kramers-Kronig relations for guided and surface waves

It is well known that in unbounded media the acoustic attenuation as function of frequency is linked to the frequency-dependent sound velocity (dispersion) via Kramers-Kronig dispersion relations. These relations are fundamentally important for better understanding of the nature of attenuation and dispersion and as a tool in physical acoustics measurements, where they can be used for verification purposes. However, physical acoustic measurements are frequently carried out not in unbounded media, but in acoustic waveguides, e.g. inside liquid-filled pipes. Surface acoustic waves are also often used for measurements. In the present work, the applicability of Kramers-Kronig relations to guided and surface waves is discussed using the approach based on the theory of functions of complex variables. It is demonstrated that Kramers-Kronig relations have limited applicability to guided and surface waves. In particular, they are not applicable to waves propagating in waveguides characterised by the possibility of wave energy leakage from the waveguides into the surrounding medium. For waveguides without leakages, Kramers-Kronig relations may remain valid for both ideal and viscous liquids. In the former case, Kramers-Kronig relations express the exponential decay of non-propagating (evanescent) higher-order acoustic modes below the cut-off frequencies via the dispersion of the same modes above the cut-off frequencies. Examples of numerical calculations of wave dispersion and attenuation using Kramers-Kronig relations, where applicable, are presented for different types of guided and surface waves

Generation of ground vibrations by high-speed trains travelling on soft soil

Generation of ground vibrations by high-speed trains travelling on soft soi

Generation of low-frequency rayleigh waves by heavy lorries

Generation of low-frequency ground vibrations by heavy lorries is considered theoretically for both vehicles accelerating (decelerating) with a constant accelerotion and vehicles travelling at constant speed on damaged or bumpy .surfaces. In the case of damaged or bumpy surfaces, excitation of axle-hop reson(tnces is taken into account, whereas an accelerating or braking vehicle is modelled as a point horizontal tractionforce applied to the ground and moving along with the vehicle. Frequency spectra of the vertical component of the groundvibrationvelociQ are investigatedfor dffirentfunctions of road surface roughness, acceleration,final (initial) speed ofthe vehicle, ground attenuation, Poisson's ratio, and radiation angle relative to the direction of the vehicle moveruent. It is shown that damaged or bumpy road surfaces normally generate vibrcttions of higher amplitudes, in comparison with accelerating and braking lorries. In contrast to vehicles travelling along bumpy or uneven roads and generating vibrations propagating at all directions, the ground vibrations generated by accelerating and braking vehicles are characterised by the directivity function showing that there is no radiation in the direction perpendicular to the vehicle movement

Ground vibration boom

Ground vibration boo

Acoustic emission spectra associated with the formation of brittle cracks

In the present paper, the acoustic emission accompanying the formation of brittle cracks is investigated theoretically, using the approach earlier developed by the present author and his co-workers. This approach is based on the application of Huygens' principle for elastic solids and on the use of suitable elastic Green's functions. In the framework of this approach, the main input information required for calculations of acoustic emission spectra is the normal displacements of the crack edges as a function of frequency and wavenumber. A precise description of this function for different situations of crack formation requires the solution of a complex problem of fracture mechanics, which is not always practical. For that reason, different approximations of this function can be used for practical calculations. A simple approximation of this kind is used in this paper for calculations of the acoustic emission spectra and directivity functions of a crack of finite length. A more refined approximation based on the model of a crack of finite size as a resonator for Rayleigh waves propagating along the crack edges and partly reflecting from the crack tips is briefly discussed. The obtained theoretical results are compared with the existing experimental measurements, where available

Propagation of plate bending waves in the vicinity of one- and two-dimensional acoustic ‘black holes’

One of the ways of damping resonant vibrations of engineering structures or their components is to reduce reflections of bending waves from their free edges. A new efficient method of reducing edge reflections proposed by the present author is based on using specially designed plates or bars of variable thickness in combination with strips of thin absorbing layers placed at the edges. Such plates or bars utilise gradual change in their thickness from the value corresponding to the thickness of the basic plate or bar to almost zero. If to use some specific power-law profiles for these plates or bars then they would ideally provide zero reflection of bending waves from their sharp edges even in the absence of the absorbing layers at the edges, thus materialising the so-called ‘acoustic black holes’ for bending waves. In the present paper, this effect is considered for one-dimensional and two-dimensional acoustic black holes. In the latter case black holes are materialised by cylindrically symmetrical pits (cavities) of powerlaw profile nearly protruding through the bottom of the plate. Geometrical acoustics (ray tracing) theory for plate bending wave propagation in the vicinity of one- and two-dimensional acoustic black holes is considered, including definition of ray trajectories and calculation of the reflection coefficients. Finally, we discuss possible practical applications of the abovementioned one- and two-dimensional black holes for damping structural vibrations