Technology & Engineering
Surface Waves
Surface waves are a type of mechanical wave that travels along the boundary between two different mediums, such as air and water or between layers of the Earth's crust. They have both longitudinal and transverse motion, and are responsible for the destructive force of earthquakes and tsunamis. In engineering, understanding surface waves is crucial for designing structures that can withstand their impact.
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6 Key excerpts on "Surface Waves"
eBook - PDFPhysical Acoustics V10
Principles and Methods
- Warren P. Mason(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
They propagate with speeds equal to the bulk velocities of the media, and hence represent simply bulk waves in the medium on either side of the interface, which may propagate along the latter due to the discontinuity which it represents. These waves are known as lateral waves (see, e.g., Brekhovskikh, 1960). Waves of all these types have been studied extensively on plane interfaces, both theoretically and experimentally. In particular, Rayleigh waves have received considerable attention in view of their usefulness for the detection of surface faults in ultrasonic nondestructive testing of materials. In addition, they have been employed in the construction of electromechanical delay lines, used for radar and communications systems. Several review papers have appeared in the recent literature emphasizing one or the other of these technological aspects of Rayleigh waves (Becker and Richardson, 1970; Dransfeld and Salzmann, 1970; Farnell, 1970; Nickerson, 1970; Kallard, 1971); furthermore, the more fundamental properties of Surface Waves have also been treated (Brekhovskikh, 1959; Viktorov, 1967). Analogous Surface Waves exist also on surfaces with simple or arbitrary curvature. In this case the situation is considerably more complex and much less well understood. Investigations are less numerous, although a certain amount of progress has been made in the last few years. In the present article we intend to survey the essential results obtained concerning acoustic Surface Waves on curved surfaces, and to establish their relationships with the corresponding plane Surface Waves. In view of the limited generality of the existing literature, the excitation mechanisms considered here for the generation of such Surface Waves have mostly been taken as those provided by a plane incident acoustic wave; more general mechanisms are briefly mentioned in Section V I .
- Arthur R. McGurn(Author)
- 2022(Publication Date)
- Springer(Publisher)
They often require a rather specific set of conditions be present on the media and the parameters char- acterizing the interface geometry for their existence. In general, the amplitudes of the Surface Waves are large at the surface and decay exponentially to zero with increasing separation from the surface. Consequently, the energy within these excitations is often highly concentrated near the surface and moves parallel to the interface. The Surface Waves have different propagation characteristics than bulk waves and exist as distinct excitations at different frequencies from the bulk excitations. Consequently, at a planar interface between two media bulk waves can pass from one bulk medium to the other indepen- dent of the presence of Surface Waves. In this regard, Surface Waves on the interface can only be excited on the interface by bulk waves that couple to the surface wave through geometric features on the interface. On planar interfaces, the Surface Waves are isolated from the bulk excitations, but the presences of roughness or surface bumps which destroy the translational symmetry of the surface creates a coupling to bulk excitations in the media. As a result of this coupling, surfaces waves can be excited by the incidence of bulk waves on the interface or they can decay into bulk waves radiating away from the interface. 154 6. SURFACES AND Surface Waves The concentration of energy at the interface in surface wave excitations provides a useful mechanism employed as a basis of a number of technological applications. An important exam- ple is in the spectroscopic technique of surface enhanced Raman scattering (SERS) [5, 11, 52]. In this technique the excitation of a surface wave on an interface supporting absorbed molecules can be used to perform Raman spectroscopy on the molecules.
eBook - PDF- Agustín Udías, Elisa Buforn(Authors)
- 2017(Publication Date)
- Cambridge University Press(Publisher)
12 Surface Waves The presence of a free surface on an elastic medium, as is the case on Earth, introduces a series of phenomena that must be considered in the study of waves produced by earthquakes, as observed in seismograms. First of all, as we have seen in Section 6.4 , on a free surface there are body-wave re fl ections. Under certain condi-tions (supercritical incidence of S waves) the generation of inhomogeneous or eva-nescent P waves occurs ( Sections 6.3 and 6.4 ). These are body waves that propagate along a direction parallel to the free surface and whose amplitudes decrease with the distance from the free surface. A different phenomenon, which we will consider now, is the generation of Surface Waves from constructive interference of body waves in connection with a free surface. Surface Waves are de fi ned as those produced in media with a free surface which propagate parallel to the surface and whose amplitudes decrease with the distance from the surface. They are generated by energy brought to the free surface by incident body waves. Their existence is related to the presence of a free surface, and other surfaces of contact between layers of different elastic properties. They are very important in seismology as they produce very large ampli-tudes of surface ground motion. There are also waves of similar characteristics, but not related to a free surface, which are associated with an interface between two media in contact. 12.1 Rayleigh waves in a half-space The fi rst problem is that of determining whether, in an elastic, homogeneous half-space limited by a plane x 3 = 0 ( x 3 being positive upward), there exist Surface Waves, that is, waves that propagate in the direction of x 1 with velocity c and whose amplitudes decrease with depth ( – x 3 ) ( Fig. 12.1 ).
- Christopher Koutitas, Panagiotis D. Scarlatos(Authors)
- 2015(Publication Date)
- CRC Press(Publisher)
135 Chapter 6 Surface gravity water waves 6.1 BASIC CONCEPTS OF WATER WAVES This chapter covers the subject of water waves, that is, the propagation and transformation of surface water waves driven by the gravitational force. Gravity water waves constitute part of the free surface, unsteady (usually periodic) class of flows. Traditionally this subject is covered under the dis-ciplines of coastal, ocean or maritime engineering (U.S. Army Corps of Engineers 2002; Kim 2009). The forms of the mathematical models to be presented and numerically solved are the simplest ones, though useful and operational. Simplifying assumptions such as linearity, periodicity and single wave frequency will be made in order to avoid mathematical and numerical complications. Those assumptions, however, do not affect the intended scope and pedagogical value of the book. One-dimensional models of wave propagation will be presented and applied within their validity limits. The wave models will be used to describe, even approximately, an array of interesting physical phenomena such as wave shoaling, wave breaking, partial wave reflection, absorption of wave energy due to friction and wave generation and propa-gation due to bed deformation (the phenomenon known as tsunami waves). The models will be subsequently extended to two spatial dimensions in order to simulate wave modulation phenomena such as wave refraction, wave diffraction, wave breaking and so on. Understanding of those phe-nomena is indispensable for the design of coastal, harbour, and maritime structures (Komen et al. 1994; Lin 2008). In the following paragraphs, some basic definitions and notions of water waves theory will be reviewed and summarized (Sorensen 2006). Wavelength, L, is the distance from crest to crest (or trough to trough), c o is the wave celerity (the speed of the propagation of the surface deformation, not of the water particles) and T is the wave period.
eBook - PDFSurface Waves
New Trends and Developments
- Farzad Ebrahimi(Author)
- 2018(Publication Date)
- IntechOpen(Publisher)
Another new significant achievement of the classical physics (although not revolutionary) was the discovery of Surface Waves. At first, elastic Surface Waves were discov -ered in solids (Rayleigh 1885 and Love 1911) and then in electromagnetism (Zenneck 1907 and Sommerfeld 1909). In fact, the existence of Surface Waves in solids was predicted mathematically by the cel-ebrated British scientist Lord Rayleigh in 1885, who showed that elastic Surface Waves can propagate along a free surface of a semi-infinite body. By contrast to bulk waves, the ampli -tude of Surface Waves is confined to a narrow area adjacent to the guiding surface. Since Surface Waves are a type of guided waves, they can propagate often longer distances than their bulk counterparts and in addition, they are inherently sensitive to material properties in the vicinity of the guiding surface. It will be shown in the following of this chapter that these two properties of Surface Waves are of crucial importance in geophysics and sensor technology. First, seismographs were constructed by British engineers in 1880, working in Japan for Meiji government. Consequently, the first long distance seismogram was registered in 1889 by German astronomer Ernst von Rebeur-Paschwitz in Potsdam (Germany), who was able to detect seismic signals generated by an earthquake occurred in Japan, some 9000 km away from Potsdam (Berlin). It was obvious soon that long distance seismograms display two different phases. First (preliminary tremor), a relatively weak signal arriving with the veloc -ity of bulk waves (P and S) and second (main shock) with a much higher amplitude arriv-ing with the velocity close to that of Rayleigh Surface Waves. However, this Rayleigh wave hypothesis was not satisfactory, since large part of the main shock energy was associated with the shear horizontal (SH) component of vibrations, absent by definition in Rayleigh Surface Waves composed of shear vertical (SV) and longitudinal (L) displacements.
eBook - ePub- Thorne Lay, Terry C. Wallace(Authors)
- 1995(Publication Date)
- Academic Press(Publisher)
International Geophysics , Vol. 58, Suppl. (C), 1995ISSN: 0074-6142doi: 10.1016/S0074-6142(05)80005-1Chapter 4 Surface Waves and Free OscillationsThe last two chapters have demonstrated the remarkably simple basic character of solutions of the equations of motion for linear-elastic, isotropic, homogeneous (or weakly inhomogeneous) unbounded media. The displacement field created by a stress imbalance is completely accounted for by propagating P and S waves, no matter what type of seismic source is involved (chapter 8 ). These wavefields become increasingly complex when discontinuous material properties and localized inhomogeneities are present. Wave phenomena such as refraction, wave type conversion, frequency-dependent scattering, and diffraction take place in an inhomogeneous medium like the Earth, leading to a very complicated body wave field. The fact that the Earth’s inhomogeneity is primarily one-dimensional (i.e., varies with depth) allows us to interpret most of the body-wave complexity. The Earth has two additional fundamental attributes, shared with all finite structures, that profoundly affect the seismic wavefield. These are the presence of the free surface and the finite (quasi-ellipsoidal) shape of the planet.The free surface of an elastic medium has the special stress environment defined by the vanishing of surface tractions. For the Earth, all seismic-wave measurements are made at or near the free surface; thus it is critical to understand free-surface effects in order to interpret seismograms. At the surface both incident and reflected waves instantaneously coexist, and the total motion involves the sum of their respective amplitudes. For example, from Table 3.1 we know that a reflected SH wave has the same amplitude as the incident wave. Thus, at the free surface the amplitude of SH motion is doubled. We call this multiplicative factor the SH receiver function. Free-surface receiver functions for P and SV waves involve comparable displacement amplifications. Even more important is the interaction of incident P and SV waves with the free-surface boundary condition, which gives rise to an interference wave that effectively travels along the surface as a Rayleigh wave. Total reflection of SH waves at the free surface combines with internal layering of the Earth to trap SH reverberations near the surface, which interfere to produce horizontally propagating Love waves. Gravitationally controlled waves in water on the Earth’s surface give rise to sea waves, or tsunamis
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