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Horace Lamb

Bio: Horace Lamb is an academic researcher. The author has contributed to research in topics: Adiabatic process & Dissipation. The author has an hindex of 7, co-authored 7 publications receiving 1866 citations.

Papers
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TL;DR: In this article, the authors considered the problem of two-dimensional wave propagation in a solid bounded by parallel planes, and proposed a simple solution to the problem, which has no bearing on the questions referred to in this paper.
Abstract: The theory of waves in an infinitely long cylindrical rod was discussed by Pochhammer in 1876 in a well-known paper The somewhat simpler problem of two-dimensional waves in a solid bounded by parallel planes was considered by Lord Rayleigh and by the present writer‡ in 1889 The main object in these various investigations was to verify, or to ascertain small corrections to, the ordinary theory of the vibrations of thin rods or plates, and the wave-length was accordingly assumed in the end to be great in comparison with the thickness It occurred to me some time ago that a further examination of the two-dimensional problem was desirable for more than one reason In the first place, the number of cases in which the various types of vibration of a solid, none of whose dimensions is regarded as small, have been studied is so restricted that any addition to it would have some degree of interest, if merely as a contribution to elastic theory Again, modern seismology has suggested various questions relating to waves and vibrations in an elastic stratum imagined as resting on matter of a different elasticity and density These questions naturally present great mathematical difficulties, and it seemed unpromising to attempt any further discussion of them unless the comparatively simple problem which forms the subject of this paper should be found to admit of a practical solution In itself it has, of course, no bearing on the questions referred to

1,413 citations

Journal ArticleDOI
TL;DR: In this paper, the pitch of the fundamental note of a thin circular plate or diaphragm of given material and dimensions, filling an aperture in a plane wall which is in contact on one side with an otherwise unlimited mass of water, was investigated.
Abstract: In connection with the problem of submarine signalling the question arose as to the pitch of the fundamental note of a thin circular plate or diaphragm of given material and dimensions, filling an aperture in a plane wall which is in contact on one side with an otherwise unlimited mass of water. The following investigation, which includes some extensions, is now published by permission. To simplify the theoretical treatment, the wall is supposed to be rigid, and the plate to be firmly clamped to it along the circumference, although these conditions are only imperfectly fulfilled in practice. Even with these limitations an exact solution is out of the question, but a sufficient approximation can be obtained by Rayleigh’s method of an assumed type, which gives good results if the type be suitably chosen. It is known that the frequency estimated in this way will be somewhat too high.

232 citations

Journal ArticleDOI
TL;DR: In this paper, the transverse vibrations of a circular disk of uniform thickness rotating about its axis with constant angular velocity were investigated and it was shown that the phenomenon is one of resonance between the periodic forces exerted by the steam jets and the periods of free vibration of the disk.
Abstract: 1. This paper treats of the transverse vibrations of a circular disk of uniform thickness rotating about its axis with constant angular velocity. The problem has a practical bearing, as throwing light on the occasional failure of turbine disks. In an impulse turbine blades are fitted to the rim of a thin disk, and steam is admitted to them from nozzles which are usually arranged symmetrically, but not always continuously, round the periphery. The failures appear to be sometimes due to the blades coming in contact with the adjacent parts. This points to transverse vibrations, and there can be little doubt that the phenomenon is one of resonance between the periodic forces exerted by the steam jets and the periods of free vibration of the disk. For a thorough investigation it would be necessary to ascertain, to a reasonable degree of approximation, the free periods of a symmetrical disk of any given profile. This may form the theme of a subsequent investigation by one of the authors. In the meantime the study of the simpler case now discussed illustrates the physical aspects of the problem, and has suggested an important simplification in method.

214 citations

Journal ArticleDOI
TL;DR: In this article, the free oscillations of an atmosphere whose temperature varies with the altitude were studied in some detail, and the results were most easily interpreted when the temperature gradient does not fall much below that characteristic of a state of convective equilibrium.
Abstract: 1. The chief question discussed in this paper (§§ 6—12) is that of the free oscillations of an atmosphere whose temperature varies with the altitude ; and in particular the case of a uniform vertical temperature-gradient is studied in some detail. For consistency it is assumed that the expansions and contractions follow the adiabatic law. The problem is treated as a two-dimensional one, the space co-ordinates involved being horizontal and vertical; and the more definite conclusions arrived at relate to the case where the (horizontal) wave-length is somewhat large in comparison with the height of the atmosphere. The results are most easily interpreted when the temperature-gradient does not fall much below that characteristic of a state of convective equilibrium. The normal modes of oscillation then fall into well-defined types.

101 citations

Journal ArticleDOI
TL;DR: In this paper, the authors illustrate the theory of kinetic stability, so far as such a theory can be said to exist, by a few simple examples, such as the vertical fall of a particle under gravity would be unstable; according to another, the revolution of a single particle in a circular orbit about a center of force varying inversely as the cube of the distance would be reckoned as stable, although the slightest disturbance would cause the particle either to fall ultimately into the centre, or to recede to infinity, after describing in either case a spiral path with an infinite number of
Abstract: 1. The object of this paper is to illustrate the theory of kinetic stability, so far as such a theory can be said to exist, by a few simple examples. As the theory itself appears to be by no means widely known, some preliminary recapitulation seems advisable. The difficulty of framing a definition of kinetic stability which shall be comprehensive and at the same time conform to natural prepossessions has long been recognised. Thus, according to one definition which has been proposed, the vertical fall of a particle under gravity would be unstable; according to another the revolution of a particle in a circular orbit about a centre of force varying inversely as the cube of the distance would be reckoned as stable, although the slightest disturbance would cause the particle either to fall ultimately into the centre, or to recede to infinity, after describing in either case a spiral path with an infinite number of convolutions.

21 citations


Cited by
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TL;DR: In this article, the static deformation of an elastic half-space by surface pressure is reviewed and a brief mention is made of methods for solving the problem when the medium is plane-strategized, but the major emphasis is on the solution for spherical, radially stratified, gravitating earth models.
Abstract: The static deformation of an elastic half-space by surface pressure is reviewed. A brief mention is made of methods for solving the problem when the medium is plane stratified, but the major emphasis is on the solution for spherical, radially stratified, gravitating earth models. Love-number calculations are outlined, and from the Love numbers, Green's functions are formed for the surface mass-load boundary-value problem. Tables of mass-load Green's functions, computed for realistic earth models, are given, so that the displacements, tilts, accelerations, and strains at the earth's surface caused by any static load can be found by evaluating a convolution integral over the loaded region.

1,588 citations

01 Jul 1958
TL;DR: In this paper, the evanescent field structure over the wave front, as represented by equiphase planes, is identified as one of the most important and easily recognizable forms of surface wave.
Abstract: This paper calls attention to some of the most important and easily recognizable forms of surface wave, pointing out that their essential common characteristic is the evanescent field structure over the wave front, as represented by equiphase planes. The problems of launching and supporting surface waves must, in general, be distinguished from one another and it does not necessarily follow that because a particular surface is capable of supporting a surface wave that a given aperture distribution of radiation, e.g. a vertical dipole, can excite such a wave. The paper concludes with a discussion of the behavior of surface waves and their applications.

1,244 citations

Journal ArticleDOI
TL;DR: This paper presents a review of the main developments of the matrix techniques, and their use in response and modal models, with emphasis on ultrasonics applications.
Abstract: Research into ultrasonic NDE techniques for the inspection of multilayered structures relies strongly on the use of modeling tools which calculate dispersion curves and reflection and transmission spectra. These predictions are essential to enable the best inspection strategies to be identified and their sensitivities to be evaluated. General purpose multilayer modeling tools may be developed from a number of matrix formulations which have evolved in the latter half of this century and there is now a formidable number of publications on the subject. This paper presents a review of the main developments of the matrix techniques, and their use in response and modal models, with emphasis on ultrasonics applications. >

931 citations

Book
28 Sep 1998
TL;DR: In this paper, the authors propose numerical solutions to partial differential equations and finite-differencing the equations of atmospheric dynamics, including boundary-layer and surface processes, and Radiative energy transfer.
Abstract: Preface Acknowledgements 1. Introduction 2. Atmospheric structure, composition and thermodynamics 3. The continuity and thermodynamic energy equations 4. The momentum equation in Cartesian and spherical coordinates 5. Vertical-coordinate conversions 6. Numerical solutions to partial differential equations 7. Finite-differencing the equations of atmospheric dynamics 8. Boundary-layer and surface processes 9. Radiative energy transfer 10. Gas-phase species, chemical reactions and reaction rates 11. Urban, free-tropospheric and stratospheric chemistry 12. Methods of solving chemical ordinary differential equations 13. Particle components, size distributions and size structures 14. Aerosol emission and nucleation 15. Coagulation 16. Condensation, evaporation, deposition and sublimation 17. Chemical equilibrium and dissolution processes 18. Cloud thermodynamics and dynamics 19. Irreversible aqueous chemistry 20. Sedimentation, dry deposition and air-sea exchange 21. Model design, application and testing Appendix A. Conversions and constants Appendix B. Tables References Index.

863 citations

Book
11 Aug 2014
TL;DR: The semi-analytical finite element method (SAFE) has been used for guided wave modeling as discussed by the authors, which has been shown to be useful in the analysis and display of non-destructive testing.
Abstract: Preface Acknowledgments 1. Introduction 2. Dispersion principles 3. Unbounded isotropic and anisotropic media 4. Reflection and refraction 5. Oblique incidence 6. Waves in plates 7. Surface and subsurface waves 8. Finite element method for guided wave mechanics 9. The semi-analytical finite element method (SAFE) 10. Guided waves in hollow cylinders 11. Circumferential guided waves 12. Guided waves in layered structures 13. Source influence on guided wave excitation 14. Horizontal shear 15. Guided waves in anisotropic media 16. Guided wave phased arrays in piping 17. Guided waves in viscoelastic media 18. Ultrasonic vibrations 19. Guided wave array transducers 20. Introduction to guided wave nonlinear methods 21. Guided wave imaging methods Appendix A: ultrasonic nondestructive testing principles, analysis and display technology Appendix B: basic formulas and concepts in the theory of elasticity Appendix C: physically based signal processing concepts for guided waves Appendix D: guided wave mode and frequency selection tips.

823 citations