Directivity patterns of laser-generated sound in solids: Effects of optical and thermal parameters

In the present paper, directivity patterns of laser-generated sound in solids are investigated theoretically. Two main approaches to the calculation of directivity patterns of laser-generated sound are discussed for the most important case of thermo-optical regime of generation. The first approach, which is widely used in practice, is based on the simple modelling of the equivalent thermo-optical source as a mechanical dipole comprising two horizontal forces applied to the surface in opposite directions. The second approach is based on the rigorous theory that takes into account all acoustical, optical and thermal parameters of a solid material and all geometrical and physical parameters of a laser beam. Directivity patterns of laser-generated bulk longitudinal and shear elastic waves, as well as the amplitudes of generated Rayleigh surface waves, are calculated for different values of physical and geometrical parameters and compared with the directivity patterns calculated in case of dipole-source representation. It is demonstrated that the simple approach using a dipole-source representation of laser-generated sound is rather limited, especially for description of generated longitudinal acoustic waves. A practical criterion is established to define the conditions under which the dipole-source representation gives predictions with acceptable errors. It is shown that, for radiation in the normal direction to the surface, the amplitudes of longitudinal waves are especially sensitive to the values of thermal parameters and of the acoustic reflection coefficient from a free solid surface. A discussion is given on the possibility of using such a high sensitivity to the values of the reflection coefficient for investigation of surface properties of real solids.Comment: 14 pages, 7 figure

Basic principles of sound radiation and scattering

The book gives a brief account of the theory of radiation and scattering of sound in liquids and gases. General principles of radiation and scattering of acoustic waves are considered, including Huygens’ principle, the reciprocity theorem, the problem of the existence and uniqueness of solutions. Acoustic fields generated by some complicated radiators are analysed in detail. Basic definitions and facts relating to the scattering of sound by an infinite cylinder, sphere, gas bubbles in liquids, etc. are considered as well. Much of attention is paid to the general theory of scattering with respect to the scattering of acoustic waves. These include the method of boundary integral equations and the methods based on the approximate solutions of the equations of Lippmann - Schwinger type. Considered are also energy conservation issues at wave scattering and the problems linked to causality and Kramers - Kronig relations. The book is intended for students and researchers working in the field of acoustics. (Abstract translated from the Russian)

Generation of ground vibration boom by high-speed trains

Railway-generated ground vibrations cause significant disturbance for residents of nearby buildings even when generated by conventional passenger or heavy-freight trains [1,2]. If train speeds increase, the intensity of railway-generated vibrations generally becomes larger. For modern high-speed trains the increase in ground vibration intensity is especially high when train speeds approach certain critical velocities of waves propagating in a track-ground system. The most important are two such critical velocities: the velocity of Rayleigh surface wave in the ground and the minimal phase velocity of bending waves propagating in a track supported by ballast, the latter velocity being referred to as track critical velocity. Both these velocities can be easily exceeded by modern high-speed trains, especially in the case of very soft soil where both critical velocities become very low. As has been theoretically predicted by the present author [3,4], if a train speed v exceeds the Rayleigh wave velocity cR in supporting soil a ground vibration boom occurs. It is associated with a very large increase in generated ground vibrations, as compared to the case of conventional trains. The phenomenon of ground vibration boom is similar to a sonic boom for aircraft crossing the sound barrier, and its existence has been recently confirmed experimentally [5,6] (see also chapter 11). The measurements have been carried out on behalf of the Swedish Railway Authorities when their West-coast Main Line from Gothenburg to Malmö was opened for the X2000 high-speed train. The speeds achievable by the X2000 train (up to 200 km/h) can be larger than lowest Rayleigh wave velocities in this part of Sweden characterised by very soft ground. In particular, at the location near Ledsgärd the Rayleigh wave velocity in the ground was around 45 m/s, so the increase in train speed from 140 to 180 km/h lead to about 10 times increase in generated ground vibrations [5] (see chapter 11). The above mentioned first observations of ground vibration boom indicate that now one can speak about “supersonic” (“superseismic”) or, more precisely, “trans-Rayleigh” trains [7-9]. The increased attention of railway companies and local authorities to ground vibrations associated with high-speed trains stimulated a growing number of theoretical and experimental investigations in this area (see, e.g. [10-13]). 2 If train speeds increase further and approach the track critical velocity, then rail deflections due to applied wheel loads may become essentially larger. Possible very large rail deflections around this speed may result even in train derailment, thus representing a serious problem for train and passenger safety [6,14-16]. From the point of view of generating ground vibrations outside the track, these large rail deflections can be responsible for an additional growth of ground vibration amplitudes, as compared to the above mentioned case of ground vibration boom [7,9,17]. In the present paper we review the current status of the theory of ground vibration boom from high-speed trains. Among the problems to be discussed are the quasi-static pressure generation mechanism, effects of Rayleigh wave velocity and track wave resonances on generated ground vibrations, effects of layered geological structure of the ground, and waveguide effects of the embankments. The results of theoretical calculations for TGV and Eurostar high-speed trains travelling along typical tracks are compared with the existing experimental observations

Effects of the embankment topography and track curvature on ground vibration boom from high-speed trains

The present paper investigates the effects of the embankment topography and track curvature on ground vibrations generated by high speed trains travelling faster than Rayleigh waves in the supporting ground. It is shown that the presence of the embankment can result in waveguide propagation of generated ground vibrations at certain range of train speeds. The presence of a track curvature (to provide the possibility of changing direction of train movement) can result in focusing of generated Rayleigh waves along the caustic line which is associated with the increase in amplitudes of generated ground vibrations

Spectra of low-frequency ground vibrations generated by high-speed trains on layered ground

Increase in speeds of modern railway trains is usually accompanied by higher levels of generated ground vibrations. In the author's earlier paper [V.V Kryloy Applied Acoustics, 44, 149-164 (1995)1, it has been shown that especially large increase in vibration level may occur if train speeds v exceed the velocity of Rayleigh surface waves in the ground c*., i.e., v ) cn Such a situation might arise, for example, with French TGV trains for which speeds over 515 krnlh have been achieved. The present paper investigates the effect of geological layered structure of the ground on ground vibrations generated by high-speed trains. It is shown that, since Rayleigh wave velocities in layered ground are dispersive and normally increase at lower frequencies associated with deeper penetration of surface wqve energy into the ground, the trans- Rayleigh condition v ) cRmay not hold at very low frequencies. This will cause a noticeable reduction in low-frequency components of generated ground vibration spectra. Theoretical results are illustrated by numerically calculated frequency spectra of ground vibrations generated by single axle loads travelling at dffirent speeds and by TGV or Eurostar high-speed trains

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