Advanced search
Publication Cover
Applicable Analysis
An International Journal
Volume 97, 2018 - Issue 8: Mathematical Contact Mechanics
Submit an article Journal homepage
59
Views
1
CrossRef citations to date
0
Altmetric
Articles

Vibrations of a beam between two rigid stops: strong solutions in the framework of vector-valued measures

Laetitia PaoliInstitut Camille Jordan, CNRS UMR 5208, University of Lyon, UJM-Saint-Etienne, Saint-Etienne, France.
&
Meir ShillorDepartment of Mathematics and Statistics, Oakland University, Rochester, MI, USA.Correspondence[email protected]
Pages 1299-1314 | Received 29 Mar 2017, Accepted 15 Jun 2017, Published online: 05 Jul 2017

References

  • Dumont Y, Paoli L. Vibrations of a beam between stops: convergence of a fully discretized approximation. ESAIM: Math Modell Num Anal (M2AN). 2006;40(4):705–734.
  • Kuttler K, Shillor M. Vibrations of abeam between two stops. Dyn Continuous Discrete Impulsive Syst Ser B. 2001;8:93–110.
  • Paoli L, Schatzman M. Mouvement à un nombre fini de degrés de liberté avec contraintes unilatérales: cas avec perte d’énergie. ESAIM: Math Model Numer Anal (M2AN). 1993;27(6):673–717.
  • Paoli L, Schatzman M. A numerical scheme for impact problems I and II. SIAM J Numer Anal. 2002;40(2):702–733 and 734-768.
  • Paoli L. An existence result for non-smooth vibro-impact problems. J Differ Equ. 2005;211(2):247–281.
  • Rockafellar RT. Convex analysis. Princeton (NJ): Princeton University Press; 1970.
  • Temam R. Navier--Stokes equations. Amsterdam: North-Holland; 1984.
  • Diestel J, Uhl Jr. JJ. Vector measures. Providence (RI): AMS; 1977.
  • Brezis H. Opérateurs maximaux monotones et semi-groupes de contraction dans les espaces de Hilbert. Amsterdam: North Holland; 1973.
  • Bock I, Jarusek J, Silhavy M. On the solutions of a dynamic contact problem for a thermoelastic von Karman plate. Nonlinear Anal RWA. 2016;32:111–135.
  • Kikuchi N, Oden JT. Contact problems in elasticity: a study of variational inequalities and finite element methods. Philadelphia (PA): SIAM; 1988.
  • Shillor M, Sofonea M, Telega JJ. Models and analysis of quasistatic contact. Berlin: Springer; 2004. (Lecture notes in physics; vol. 655).
  • Eck C, Jarusek J, Krbec M. Unilateral contact problems in mechanics. Variational methods and existence theorems. Boca Raton (FL): Chapman \ & Hall; 2005. (Monographs and textbooks in pure and applied mathematics; vol. 270).
  • Dieudonné J. Eléments d’analyse. Paris: Gauthier-Villars; 1969.
  • Rudin W. Real and complex analysis. New York (NY): McGraw-Hill; 1970.
  • Rockafellar RT. Integrals which are convex functionals. Pacific J Math. 1968;24:525–539.
  • Rockafellar RT. Integrals which are convex functionals II. Pacific J Math. 1971;39:439–469.
  • Dinculeanu N. Vector measures. Oxford: Pergamon Press; 1967.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.