Synonyms
Definition
The elastic waves are divided on displacement, strain, stress, and energy waves, but they are studied mainly as the displacement waves. The elastic displacement wave is defined in elastic continuum as the displacement propagating in space and time from one part of space to another one with finite velocity of propagation. Achenbach (1973), Babich and Kiselev (2014), Bedford and Drumheller (1994), Chen (1972), Dieulesaint and Royer (1974), Drumheller (1998), Fedorov (1968), Graff (1991), Graham (1993), Gurtin (1981), Guz (2016), Harris (2001), Hudson (1980), Lempriere (2002), Lur’e (1990), Maugin (2000), Miklowitz (1978), Nigul and Engelbrecht (1972), Royer and Dieulesaint (2000), Rushchitsky (2011, 2014), Sedov (1970), Slepian (1972), Tolstoy (1973), Viktorov (1967), Wasley (1973), Wesolowski (1974), Whitham (1974). A transition to the stress waves is possible if only the continuum model of elastic deformation is chosen which takes into...
References
Achenbach JD (1973) Wave propagation in elastic solids. North-Holland, Amsterdam
Babich VM, Kiselev AP (2014) Elastic waves. High-frequency theory. BHV-Peterburg, Sankt-Peterburg. (In Russian)
Batchelor GK (1967,2000) An introduction to fluid dynamics. Cambridge University Press, Cambridge
Bedford A, Drumheller DS (1994) Introduction to elastic wave propagation. Wiley, Chichester
Bland DR (1960) The theory of linear viscoelasticity. Oxford University Press, Oxford
Boley BA, Weiner HJ (1960) Theory of thermal stresses. Wiley, New York
Brown WF (1960) Magnetoelastic interaction. Springer, New York
Chen PJ (1972) Wave motion in solids. In: Flügge’s Handbuch der Physik, vol VIa/3. Springer, Berlin
Christensen RM (1971) Theory of viscoelasticity. An introduction. Academic, New York
Davies RM (1956) Stress waves in solids. Cambridge University Press, Cambridge
Dieulesaint E, Royer D (1974) Ondes elastiques dans les solides. Application au traitement du signal. Masson et C’ie, Paris
Dill EH (2006) Continuum mechanics: elasticity, plasticity, viscoelasticity. CRC Press, Berlin
Donell LH (1976) Beams, plates, and shells. McGraw-Hill, New York
Drumheller DS (1998) Introduction to wave propagation in nonlinear fluids and solids. Cambridge University Press, Cambridge
Encyclopedia of physics (1973) Chief editor S. Flűgge, Vol. VIa / I, Mechanics of solids I. Editor C. Truesdell. Springer, Berlin
Fedorov FI (1968) Theory of elastic waves in crystals. Plenum Press, New York
Gould PL (1999) Analysis of plates and shells. Prentice Hall, Upper Saddle River
Graff KF (1991) Wave motion in elastic solids. Dover, London
Graham RA (1993) Solids under high-pressure shock compression. Springer, New York
Gross B (1968) Mathematical structure of the theories of viscoelasticity. Herrmann, Paris
Gurtin ME (1981) An introduction to continuum mechanics. Academic, New York
Guz AN (2016) Elastic waves in bodies with initial (residual) stresses, 2 vols. LAP LAMBERT Academic Publishing, Saarbrücken (In Russian)
Hahn HG (1985) Elastizitätstheorie. B. G. Teubner, Stuttgart. (in German) University Press, Cambridge
Harris JG (2001) Linear elastic waves, Cambridge texts in applied mathematics. Cambridge University Press, Cambridge
Hetnarski RB, Ignaczak J (2011) The mathematical theory of elasticity. CRC Press/Taylor and Francis, Boca Raton
Hudson JA (1980) The excitation and propagation of elastic waves. Cambridge University Press, Cambridge
Kolsky H (1953) Stress waves in solids. Oxford University Press, Oxford
Lempriere BM (2002) Ultrasound and elastic waves: frequently asked questions. Academic, New York
Lubliner J (2008) Plasticity theory. Dover, New York
Lurie AI (1999,2005,2011) Theory of elasticity. Springer, Berlin
Lur’e AI (1990) Nonlinear theory of elasticity. North-Holland series in applied mathematics and mechanics. North-Holland, Amsterdam
Maugin GA (1988) Continuum mechanics of electromagnetic solids. North-Holland, Amsterdam
Maugin G (2000) Nonlinear waves in elastic crystals. Oxford University Press, Oxford
Miklowitz J (1978) The theory of elastic waves and waveguides. North-Holland, Amsterdam
Nigul UK, Engelbrecht JK (1972) Nonlinear and linear transient wave processes of deformation of thermoelastic and elastic bodies. AN Est.SSR Publishing House, Tallinn. (in Russian)
Nowacki W (1962) Thermoelasticity. Pergamon Press, Oxford
Perzyna P (1966) Fundamental problems in viscoplasticity. In: Advances in applied mechanics, vol 9. Academic, New York
Podstrigach JS, Povstenko YZ (1985) Introduction into mechanics of surface phenomena in solids. Naukova Dumka, Kiev. (in Russian)
Royer D, Dieulesaint E (2000) Elastic waves in solids (I,II), Advanced texts in physics. Springer, Berlin
Rushchitsky JJ (2011) Theory of waves in materials. Ventus Publishing ApS, Copenhagen
Rushchitsky JJ (2014) Nonlinear elastic waves in materials. Springer, Cham
Sedov LI (1970) Continuum mechanics, 2 vols. Nauka, Moscow (in Russian)
Slepian LI (1972) Non-stationary elastic waves. Sudostroenie, Leningrad. (in Russian)
Tiersten HF (1969) Linear piezoelectric plate vibrations. Plenum Press, New York
Timoshenko SP, Woinowsky-Krieger K (1959) Theory of plates and shells. McGraw-Hill, New York
Tolstoy I (1973) Wave propagation. McGraw Hill, New York
Truesdell C (1972) A first course in rational continuum mechanics. The John Hopkins University Press, Baltimore
Viktorov IA (1967) Rayleigh and lamb waves. Plenum Press, New York
Wasley RJ (1973) Stress wave propagation in solids. M. Dekker, New York
Wesolowski Z (1974) Dynamical problems of nonlinear theory of elasticity. PWN, Warszawa (In Polish). Translation into Russian (1981). Ed. Guz AN, Translator Rushchitsky JJ. Naukova Dumka, Kiev
Whitham J (1974) Linear and nonlinear waves. Wiley Interscience, New York
Wu H-C (2005) Continuum mechanics and plasticity. CRC Press, Boca Raton
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2018 Springer-Verlag GmbH Germany, part of Springer Nature
About this entry
Cite this entry
Rushchitsky, J.J. (2018). Elastic and Inelastic Stress Waves. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53605-6_220-1
Download citation
DOI: https://doi.org/10.1007/978-3-662-53605-6_220-1
Received:
Accepted:
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-53605-6
Online ISBN: 978-3-662-53605-6
eBook Packages: Springer Reference EngineeringReference Module Computer Science and Engineering