Skip to main content
SpringerLink
Log in

Onde Nei Solidi Con Vincoli Intebni

  • Chapter
  • First Online:
Wave Propagation

Part of the book series: C.I.M.E. Summer Schools ((CIME,volume 81))

  • 1712 Accesses

Abstract

La nozione di vincolo di incomprimibilitè in un fluido ideale è ben nota fin dai primordi;la stessa nozione è stata introdot ta nella teoria dei solidi,hen più recentemente Per quanto é a mia conoscenza la si trova in Poincaré[l8] [19] e soprattutto nel fondamentale articolo di Hellinger [12]. Solo assai più re rentemente,sono state sviluppate considerazioni generali sul vin colo di incomprimibilità uggerite inizialmente dallo studio del comportamento della gomma la quale è a dilatazione cubica nulla in ogni sua trasformazione isoterma [5] [24]. Altro tipo divia: colo cinematico studiato di recente é quello della inestendibilita in una direzione introdotto da Rivlin [20] e poi ampiamen te studiato da Adkins [2] ed altri,anch'esso suggerito dal comportamento della gomma rinforzata da una fitta trama di fili di nylon·Vincoli più complessi sono stati considerati da Wozniak [26]. Una teoria generale dei vincoli cinematici non può non far riferimento all'articolo di Truesdell e Noll [25] dello Handbuch der Physik.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 49.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

BIBLIOGRAFIA

A : Vincoli

  1. J. E. Adkins : A three-dimensional problem for highly elastic materials subject to constraints, Quart. J. Mech. Appl. Math,11,88–97 ( 1958 )

    Article  MathSciNet  MATH  Google Scholar 

  2. J.B. Adkins - R.S.Rivlin : Large elastic deformation of isotropic materials : X Reinforcement by inextensible cor ds, Phil. Trans. Roy. Soc. London A, 248 201–223 ( 1955 )

    Article  MATH  Google Scholar 

  3. T.Alts - : Termodynamics of thermoelastic bodies With kinematic constraints : fiber reinforced materials. Arch. Rat.Mech An. 61 (1976) 253–289·

    Article  MathSciNet  MATH  Google Scholar 

  4. G.B.Amendola : A general theory of thermoelastic solids restrained by an internal thermomechanical constraints, Atti Sem. Mat. Fis. Univ. Mod. 27 (1978) 1–14.

    MathSciNet  MATH  Google Scholar 

  5. J. Bell : The experimental foundations of solid mecha nics.Encycl.of Phys.Vol VI a/ 1, Springer Verlag, Berlin 1973.

    Google Scholar 

  6. G.Capriz - P.Podio- Guidugli : Formal structure and classification of theories of oriented materials, Ann. mat. pura appl. (4) 115 (1977)17–39.

    Article  MathSciNet  MATH  Google Scholar 

  7. H.H. Erbe : Wärmeleiter mit thermomechanischer in neres Zwangsbedingung, ZAM, Sonderheft 76–79 (1975)

    Google Scholar 

  8. J.L. Erikson, R.S.Rivlin : Large elastic deformations of homogeneous anisotropic materials, J. Rat. Mech. Anal. 3,281– 301,(1954)

    MathSciNet  MATH  Google Scholar 

  9. A.E.Green, J.E.Adkins : Large elastic deformations. and non -linear continuum mechanics, Oxford, Clarendon Press 1960

    MATH  Google Scholar 

  10. A.E. Green, P.M.Naghdi, J.A.Trapp : Thermodynamics of a con tinuum with internal constraints, Int. J. Engng., Sei. 8 (1970) 891–908.

    Article  MATH  Google Scholar 

  11. M. F. Gurtin, P. Podio-Guidugli : The thermodynamics of constrained materials, Arch. Rat. Mech An. 51 (1973) 192–208.

    Article  MATH  Google Scholar 

  12. E. Hellinger, Die allgemeinen Ansätze der Mechanik der Kon tinua, Enz. math. Wiss. 44, 602–694 (1914).

    Google Scholar 

  13. S. Levoni: Sulla integrazione delle equazioni della termoela sticità di solidi incomprimibili, Ann. Sc. Norm. Sup. Pisa (3), 22,(1968),515–525.

    MathSciNet  MATH  Google Scholar 

  14. T.Manacorda:Una osservazione sui vincoli interni in un soli do, Riv.Mat. Univ. Parma (3),3,( 1974 ), 169–174.

    MathSciNet  MATH  Google Scholar 

  15. T.Manacorda:Introduzione alla termomeccanica dei continui, Quaderni UMI, n.14, Pitagora Ed., Bologna 1979.

    MATH  Google Scholar 

  16. S.L.Passman: Constraints in Cosserat surface theory, Ist. Lomb. Sc. Lett. Rend. A, 106, (1972), 761–815.

    Google Scholar 

  17. A. C. Pipkin: Constraints in linearly elastic materials, J. of El. 6, (1976), 179–193.

    MathSciNet  MATH  Google Scholar 

  18. H.Poincaré; Leçons sur la théorie mathématique de la lumiè re,Paris,1889.

    Google Scholar 

  19. H.Poincaré: Leçons sur la théorie de l'élastcité,Paris,1892.

    Google Scholar 

  20. S. Rivlin : Plane strain of a net formed by inextensible cords, J. Rat. Mech. Anal. 4,(1955),951–974.

    MathSciNet  MATH  Google Scholar 

  21. A.Signorini:Trasf ormazioni termoelastiche finite, Mem.III, Ann. Mat. pura appl. (4), 39, (1955), 147–201.

    Article  MathSciNet  Google Scholar 

  22. A.J.M. Spencer: Finite deformations of an almost incompres sible elastic solid, Second-order Effect in Elasticity, Haifa 1962, Oxford, Pergamon Press, 1964.

    Google Scholar 

  23. J.A. Trapp: Reinforeed materials with thermo-mechanical constraints, Int. J. Engng. Sci. 9, (1971), 757–773.

    Article  MATH  Google Scholar 

  24. L.R.G. Treloar: The physics of rubber elasticity, Clarendon Press, Oxford, 1949.

    Google Scholar 

  25. C.Truesdell, W.Noll: The non-linear field theories of Mechanics, Encycl. of Phys. Vol.III/3, Springer Verlag, Berlin, 1965.

    Google Scholar 

B : Onde.

  1. A.Agostinelli: Sulla propagazione di onde termoelastiche in un mezzo omogeneo e isotropo, Lincei Rend. (8),50 (1971) 163–171, 304–312.

    Google Scholar 

  2. G.B.Amendola : On the propagation of first order waves in incompressible thermoelastic solids, B.U.M.I. (4) 7 (1973) 267–284.

    MATH  Google Scholar 

  3. G.B. Amendola : Acceleration waves in incompressible materrials. Atti Sem. Mat. Fis. Modena 24 (1975) 381–395.

    MATH  Google Scholar 

  4. C.E. Beevers : Evolutionary dilational shock waves in a generalized theory of thermoelasticity, Acta Mech. 20(1974) 67–79.

    Article  MATH  Google Scholar 

  5. B.R. Bland : On shock waves in hyperelastic media, IUTAM, Second order effects in Elasticity, Plasticity and Fluid Dynamics, Pergamon Press, 1964.

    Google Scholar 

  6. P. Chadwick, P. Powdrill: Singular surfaces in linear thermo elasticity, Int. J. Engng Sei. 3 (1965) 561–596.

    Article  Google Scholar 

  7. P.Chadwick, P.K.Currie : The propagation and growth of acceleration waves in heat-conducting elastic materials, Arch. Rat. Mech. An 49 (1972) 137–158.

    Article  MathSciNet  MATH  Google Scholar 

  8. P.J. Ohen : Growth and decay of waves in solids, Enc.of Physics, VI a/ 3 Springer Verlag,Berlin, 1973.

    Google Scholar 

  9. P.J. Chen, M.E. Burtin : On wave propagation in inextensible elastic bodies, Int. J. Solids Struct. 10 (1974) 275–281.

    Article  MathSciNet  MATH  Google Scholar 

  10. P. Chen, J.W. Nunziato : On wave propagation in perfectly heat conducting inextensible elastic bodies, J. of El. 5(1975) 155–160.

    MathSciNet  MATH  Google Scholar 

  11. B.D. Colemant, M.E.Gurtin, I.Herrera, C.Truesdell : Wave propagation in dissipative materials, A reprint of five memoirs, Springer Verlag, New York 1965.

    Book  MATH  Google Scholar 

  12. W6D. Collins : One-dimensional non linear wave propagation in incompressible elastic materials, Q.J. Mech.appl. Math. 19 (1966) 259–328.

    Article  MathSciNet  MATH  Google Scholar 

  13. J. Dunwoody : One dimensional shock waves in heat conducting materials with memory: l- Thermodynamic s-Arch. Rat. Mech. An. 47 (1972) 117–148; 2-Shock analysis,ibidem,192–204; 3- Evolutionary behaviour,ibidem 50;278–289.

    Article  MathSciNet  MATH  Google Scholar 

  14. J. Dunwoody: On weak shock waves in thermoelastic solids, Q.J. Mech. appl. Math. 30 (1977) 203–208.

    Article  MathSciNet  MATH  Google Scholar 

  15. J.L.Eriksen:On the propagation of waves in isotropic incompressible perfectly elastic materials, J. Rat. Mech. An. 2, (1953), 329–338.

    MathSciNet  Google Scholar 

  16. A.E. Grreen, P.M. Naghdi: A derivation of jump condition for entropy in thermomechanics, J. of Elast. 8 (1978) 179–182.

    Article  MathSciNet  MATH  Google Scholar 

  17. E.Inan: Decay of weak shock waves in hyperelastic solids, Acta Mech. 23 (1975) 103–112.

    Article  MATH  Google Scholar 

  18. T. Manacorda: On the propagation of discontinuity waves in thenaoelastic incompressible solids, Arch. Mech. Stos.(2), 24 (1971) 277–285.

    MATH  Google Scholar 

  19. T. Manacorda: Zagadnienia Elastodynamiki, Ossolineum, Varsavia, 1978. Cfr. anche A - 15.

    Google Scholar 

  20. R.W.Ogden: Growth and decay of acceleration waves in ineompressible elastic solids, Q.J. Mech. appl. Math. 27 (1974) 451–464.

    Article  Google Scholar 

  21. N. Scott: Acceleration waves in constrained elastic materials Arch. Rat. Mech. An. 58 (1975) 57–75.

    Article  MathSciNet  MATH  Google Scholar 

  22. N.Scott: Acceleration waves in incompressible elastic solids, Q.J. Mech. appl. Math. 29 (1976) 295–310.

    Article  MATH  Google Scholar 

  23. N. Scott, M. Hayes : Small vibrations of a fiber-reinforced composite, Q.J. Mech. appl. Math. 29 (1976) 467–486.

    Article  MATH  Google Scholar 

  24. C. Trimarco : Onde di accelerazione in materiali termoelastici con vincolo di inestendibilità, in pubbl. su Atti Acc. Sci. Modena.

    Google Scholar 

  25. C.Truesdell: General and exact theory of waves in finite elastic strain, Arch. Rat. Mech. An. 8 (1961),263–296.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Universitè di Pisa, Pisa, Italy

    Tristano Manacorda

Authors
  1. Tristano Manacorda
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Giorgio Ferrarese

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Manacorda, T. (2010). Onde Nei Solidi Con Vincoli Intebni. In: Ferrarese, G. (eds) Wave Propagation. C.I.M.E. Summer Schools, vol 81. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11066-5_6

Download citation

Publish with us

Policies and ethics

Search

Navigation