Skip to main content
SpringerLink
Log in

Vibrating Strings with Obstacles: The Analytic Study

  • Conference paper
Advances in Kinetic Theory and Continuum Mechanics

  • 226 Accesses

Abstract

It is a very pleasant task for me to be here in Paris to pay honour to Professor Henri Cabannes on the occasion of his retirement. I remember with a great pleasure many opportunities of scientific contact with him in the last years, and above all the period I spent in this University three years ago. I thank him for his kindness, and I wish him to take again many satisfactions in continuing his activity.

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 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
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.

References

  1. L. Amerio and G. Prouse. — “Study of the motion of a string vibrating against an obstacle”, Rend, di Mat., Ser. 6, 8, n° 2, 1975, P· 563–585.

    MathSciNet  MATH  Google Scholar 

  2. L. Amerio. — “Su un problema di vincoli unilaterali per l’equazione non omogenea delia corda vibrante”, Pubbl. I.A.C., Ser. III, 109, 1976, p. 1–11.

    Google Scholar 

  3. L. Amerio. — “On the motion of a string vibrating through a moving ring with a Continuously variable diameter”, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Natur, Ser. VIII, 62, n° 2, 1977, P. 134–142.

    MathSciNet  MATH  Google Scholar 

  4. L. Amerio. — “Continuous solutions of the problem of a string vibrating against an obstacle”, Rend. Sem. Mat. Univ. Padova, 52, 1978, p. 67–96.

    MathSciNet  Google Scholar 

  5. L. Amerio. — “A unilateral problem for a nonlinear vibrating string equation”, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Natur., Ser. VIII, 64, n° 1, 1978, p. 8–21.

    MathSciNet  MATH  Google Scholar 

  6. L. Amerio. — “Studio del moto di una corda vibrante contro una parete di forma qualsiasi, sotto l’azione di una forza esterna arbitraria: domini di appoggio: un problema unilaterale di frontiera libera”, Rend. Accad. Naz. XL, 102, Vol. VIII, n° 10, 1984, p. 185–246.

    MathSciNet  Google Scholar 

  7. L. Amerio. — “Sulla connessione tra i fenomeni di rimbalzo elastico e di appoggio per una corda vibrante”, Rend. Accad. Naz. XL, 105, Vol. XI, n° 2, 1987, P. 43–52.

    MathSciNet  Google Scholar 

  8. L. Amerio. — “On the elastic impact of two vibrating strings with different characteristic velocities: study of a free- boundary unilateral problem”, Rend. Accad. Naz. XL, 107, Vol. XIII, n° 22, 1989, p. 341–380.

    MathSciNet  Google Scholar 

  9. A. Bamberger and M. Schatzman. — “New results on the vibrating string with a continuous obstacle”, SIAM J. Math. Anal., Vol. 14, 1983, p. 560–595.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. “Analisi di un problema di propagazione con vincolo unilaterale”, Quad. I.A.C., Ser. III, n° 136, 1981, p. 1–19.

    Google Scholar 

  11. R. Burridge, J. Kappraff and C. Morshedi. — “The sitar string, a vibrating string with a one-sided inelastic constraint”, SIAM J. Appl. Math., Vol. 42, n° 6, 1982, p. 1231–1251.

    Article  MathSciNet  MATH  Google Scholar 

  12. R. Burridge and J. B. Keller. — “Peeling, slipping and cracking. Some one-dimensional free-boundary problems in mechanics”, SIAM Review, Vol. 20, n° 1, 1978, p. 31–61.

    Article  MathSciNet  MATH  Google Scholar 

  13. H. Cabannes. — “Mouvements périodiques d’une corde vibrante en présence d’un obstacle rectiligne”, ZAMP, 31, 1980, p. 473–482.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. H. Cabannes. — “Mouvements périodiques d’une corde vibrante en présence d’un obstacle ponctuel”, J. Mécanique, 20, no 1, 1982, p. 41–58.

    MathSciNet  Google Scholar 

  15. H. Cabannes. — “Mouvements d’une corde vibrante en présence d’un obstacle rectiligne fixe. II”, C. R. Acad. Sc. Paris, A 295, 1982, p. 637–640.

    MathSciNet  Google Scholar 

  16. H. Cabannes. — “Mouvements d’une corde vibrante en présence d’un obstacle rectiligne”, C. R. Acad. Sc. Paris A 296, 1983, p. 1367–1371.

    MathSciNet  Google Scholar 

  17. H. Cabannes. — “Mouvement d’une corde vibrante en présence d’un obstacle rectiligne”, Journ. Mécanique Théor. Appl., 3, n° 3, 1984, p. 397–414.

    MathSciNet  MATH  Google Scholar 

  18. H. Cabannes. — “Periodic motions of a string vibrating against a fixed point-mass obstacle: II”, Math. Meth. in the Appl. Sc, 6, 1984, p. 55–67.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. H. Cabannes. — “Cordes vibrantes avec obstacles”, Acustica, 55, 1984, p. 14–20.

    MathSciNet  Google Scholar 

  20. H. Cabannes. — “Mouvements d’une corde vibrante en présence d’un obstacle ponctuel fixe”, C. R. Acad. Sc. Paris, A 298, 1984, p. 613–616.

    MathSciNet  Google Scholar 

  21. H. Cabannes. — “Mouvements d’une corde vibrante en présence d’un obstacle convexe: un problème à frontière libre”, C. R. Acad. Sc. Paris, A 301, 1985, p. 125–129.

    MathSciNet  Google Scholar 

  22. H. Cabannes. — “Mouvements d’une corde vibrante qui oscille en présence d’un obstacle voisin de la position d’équilibre”, C. R. Acad. Sc. Paris, A 301, 1985, p. 1273–1276.

    MathSciNet  Google Scholar 

  23. H. Cabannes and C. Citrini, Editors. — “Vibrations with unilateral constraints”, Proceedings Colloquium Euromech. 209, Como (Villa Olmo), Italy, June 5–7, 1986.

    Google Scholar 

  24. H. Cabannes and A. Haraux. — “Mouvements presque périodiques d’une corde vibrante en présence d’un obstacle rectiligne”, C. R. Acad. Paris, A 291, 1980, p. 563–565.

    MathSciNet  Google Scholar 

  25. H. Cabannes and A. Haraux. — “Mouvements presque périodiques d’une corde vibrante en présence d’un obstacle fixe, rectiligne ou ponctuel”, Int. J. Nonlinear Mechanics, 16, no 5/6, 1981, p. 449–458.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. H. Cabannes and A. Haraux. — “Almost periodic motion of a string vibrating against a straight fixed obstacle”, Nonlinear Analysis, 7, 1983, P. 129–141.

    Article  MathSciNet  MATH  Google Scholar 

  27. C. Citrini. — “Sull’urto parzialmente elastico ο anelastico di una corda vibrante contro un ostacolo”, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Natur., Ser. VIII, 59, n° 5, 1975, p. 368–376.

    MathSciNet  Google Scholar 

  28. C. Citrini. — “Sull’urto parzialmente elastico ο anelastico di una corda vibrante contro un ostacolo”, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Natur., Ser. VIII, 59, n° 6, 1975, p. 667–676.

    MathSciNet  Google Scholar 

  29. C. Citrini. — “Energia ed impulso nell’urto parzialmente elastico ο anelastico di una corda vibrante contro un ostacolo”, Ist. Lombardo Accad. Sc. Lett. Rend., A 110, 1976, p. 271–280.

    MathSciNet  Google Scholar 

  30. C. Citrini. — “The energy theorem in the impact of a string vibrating against a pointshaped obstacle”, Atti Accad. Naz. Lincei Rend. Cl. Sc. Fis. Natur., Ser. VIII, 62, n° 2, 1977, p. 143–149.

    MathSciNet  MATH  Google Scholar 

  31. C. Citrini. — “Risultati tipici sul problema delia corda vibrante con ostacolo puntiforme”, Pubbl. I.A.C., Ser. III, n° 134, 1978, p. 1–24.

    Google Scholar 

  32. C. Citrini. — “Discontinuous solutions of a nonlinear hyperbolic equation with unilateral constraints”, Manuscripta Math., 29, 1979, P. 323–352.

    Article  MathSciNet  MATH  Google Scholar 

  33. C. Citrini. — “Controesempi all’unicità del moto di una corda in presenza di una parete”, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Natur., Ser. VIII, 67, n° 3–4, 1979, p. 79–85.

    MathSciNet  Google Scholar 

  34. C. Citrini and B. D’acunto. — “Sull’urto tra due corde”, Ricerche Mat., 28, n° 2, 1978, p. 375–398.

    MathSciNet  Google Scholar 

  35. C. Citrini and B. D’acunto. — “Sur le choc de deux cordes”, C.R. Acad. Sc. Paris, A 289, 1979, p. 5–7.

    MathSciNet  Google Scholar 

  36. C. Citrini and B. D’acunto. — “A remark on the elastic impact of two vibrating strings”, Rend. Accad. Naz. XL, 108, Vol. XIV (to appear).

    Google Scholar 

  37. C. Citrini and C. Marchionna. — “Sul problema dell’ostacolo puntiforme per l’equazione iperbolica = f(x,t,y,yx,yt)”, Rend. Accad. Naz., XL, 99 Vol. V, n° 5, 1981–1982, p. 53–72.

    Google Scholar 

  38. C. Citrini and C. Marchionna. — “Support domains for a quasi-linear string vibrating against a wall: a unilateral free boundary problem”, Rend. Accad. Naz. XL, 103, Vol. IX, n° 6, 1985, p. 61–86.

    MathSciNet  Google Scholar 

  39. C. Citrini and C. Marchionna. — “Some unilateral problems for the vibrating string equation”, Europ. J. Mech. A (Solids), Vol. 8, n°1, 1989, P. 73–85.

    MathSciNet  MATH  Google Scholar 

  40. C. Citrini and C. Marchionna. — “On the motion of a string vibrating against a gluing obstacle”, Rend. Accad. Naz. XL, 107, Vol. XIII, n°8, 1989, P. 141–164.

    MathSciNet  Google Scholar 

  41. B. D’acunto. — “Sull’urto elastico di una corda in un caso non lineare”, Ricerche Mat., 27, n° 2, 1978, p. 301–317.

    MathSciNet  MATH  Google Scholar 

  42. B. D’acunto. — “Teorema dell’energia nell’urto elastico di una corda in un caso non lineare”, Rend. Accad. Sc. Fis. Mat. Napoli, Ser. IV, 46, 1979, p. 27–41.

    MathSciNet  MATH  Google Scholar 

  43. M. Frontini and L. Gotusso. — “Risultati analitici dedotti da una sperimentazione numerica per l’equazione delia corda vibrante con ostacolo puntiforme”, Quad. I.A.C., Ser. III, n° 67, 1978, p. 1–20.

    Google Scholar 

  44. C. Marchionna. — “Sul problema unilaterale delia corda vibrante con ostacolo puntiforme dotato di velocità qualsiasi”, Rend. Accad. Naz., XL, 102, Vol. VIII, n° 1, 1984, p. 1–26.

    MathSciNet  Google Scholar 

  45. C. Marchionna. — “Studio del moto di una corda vibrante contro una parete con spigoli: domini e segmenti di appoggio”, Rend. Accad. Naz., XL, 102, Vol. IX, n° 13, 1985, p. 275–312.

    MathSciNet  Google Scholar 

  46. C. Marchionna. — “On the motion of a string vibrating against an interrupted wall”, Rend. Accad. Naz. XL, 104, Vol. X, n° 19, 1986, p. 213–222.

    MathSciNet  Google Scholar 

  47. A. Bachelot-Motet. — “Sur les pénalisées de l’équation des ondes”, Thèse de 3e cycle, Univ. Bordeaux I, 1982.

    Google Scholar 

  48. A. Bachelot-Motet. — “Une estimation a priori sur les solutions de l’équation des ondes pénalisée, en dimension 1 d’espace”, C. R. Acad. Sc. Paris, A 299, 1984, p. 659–662.

    MathSciNet  Google Scholar 

  49. A. Bachelot-Motet. — “Une estimation a priori sur les solutions de l’équation des ondes pénalisée, en dimension 1 et 2 d’espace”, Proc. Euromech. 209, 1986, p. 56–68.

    Google Scholar 

  50. L. Narratone. — “Su un modello matematico delia scrica elettrica in un condensatore piano e illimitato”, Quad. I.A.C., Ser. III, n° 113, 1977, p. 1–15.

    Google Scholar 

  51. C. Reder. — “Etude qualitative d’un problème hyperbolique avec contrainte unilatérale”, Thèse de 3e cycle, Univ. Bordeaux I, 1979·

    Google Scholar 

  52. M. Schatzman. — “A hyperbolic problem of second order with unilateral constraints: the vibrating string with a concave obstacle”, Journ. Math. Anal. Appl., 22, 1980, p. 138–191.

    Article  MathSciNet  Google Scholar 

  53. M. Schatzman. — “Un problème hyperbolique du 2e ordre avec contrainte unilatérale: La corde vibrante avec obstacle ponctuel”, Journ. Diff. Eq., 36, 1980, p. 295–334.

    Article  MathSciNet  MATH  Google Scholar 

  54. M. Schatzman. — “The penalty method for the vibrating string with an obstacle”, in “Analytical and numerical approaches to asymptotic problems in analysis”, Axelsson, Frank, van der Sluis Ed., North-Holland Publ. Co., 1981, p. 345–357.

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica, Politecnico di Milano, Piazza Leonardo da Vinci 32, I-20133, Milano, Italy

    C. Citrini

Authors
  1. C. Citrini
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Laboratoire de Modélisation en Mécanique, Université Pierre et Marie Curie, associé au C.N.R.S, 4 Place Jussieu, F-75252, Paris Cedex 05, France

    Renée Gatignol

  2. SPEA, CEN-Saclay, F-91191, Gif-sur-Yvette Cedex, France

    Soubbaramayer

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Citrini, C. (1991). Vibrating Strings with Obstacles: The Analytic Study. In: Gatignol, R., Soubbaramayer (eds) Advances in Kinetic Theory and Continuum Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-50235-4_22

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-50235-4_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-50237-8

  • Online ISBN: 978-3-642-50235-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation