IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v170y2020icp115-142.html
   My bibliography  Save this article

A generalization of the method of lines for the numerical solution of coupled, forced vibration of beams

Author

Listed:
  • Sarker, Pratik
  • Chakravarty, Uttam K

Abstract

Beam vibrations are encountered in real life and are important to investigate for proper monitoring of the structural health. Closed-form solutions to one-dimensional beam vibration problems are not always available, especially, if the governing equations are nonlinear or have strongly coupled multiple degrees-of-freedom for which, the numerical method is the only solution technique. The method of lines is a numerical technique for solving the initial boundary value problems; however, in the literature, the application is mostly based on simple or lower order linear governing equations with only one degree-of-freedom. Therefore, in this paper, the generalized solution of one-dimensional, axially loaded, coupled, forced beam vibration having multiple degrees-of-freedom is developed by the method of lines which is applicable to any other similar initial boundary value problems. Four different case studies featuring coupled/uncoupled, linear/nonlinear governing equations having single/multiple degree(s)-of-freedom with different types of boundary conditions are presented to demonstrate the applicability of the generalized theory. The models are validated either by theoretical solutions, simulated results, or by published results.

Suggested Citation

  • Sarker, Pratik & Chakravarty, Uttam K, 2020. "A generalization of the method of lines for the numerical solution of coupled, forced vibration of beams," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 170(C), pages 115-142.
    • Handle: RePEc:eee:matcom:v:170:y:2020:i:c:p:115-142
    DOI: 10.1016/j.matcom.2019.10.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475419303143
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2019.10.011?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Berardi, Marco & Vurro, Michele, 2016. "The numerical solution of Richards’ equation by means of method of lines and ensemble Kalman filter," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 125(C), pages 38-47.
    2. A. Bouhamidi & K. Jbilou, 2013. "A Fast Block Krylov Implicit Runge–Kutta Method for Solving Large-Scale Ordinary Differential Equations," Springer Optimization and Its Applications, in: Altannar Chinchuluun & Panos M. Pardalos & Rentsen Enkhbat & E. N. Pistikopoulos (ed.), Optimization, Simulation, and Control, edition 127, pages 319-330, Springer.
    3. Younes, A. & Konz, M. & Fahs, M. & Zidane, A. & Huggenberger, P., 2011. "Modelling variable density flow problems in heterogeneous porous media using the method of lines and advanced spatial discretization methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(10), pages 2346-2355.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      Corrections

      All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:170:y:2020:i:c:p:115-142. See general information about how to correct material in RePEc.

      If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

      If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

      For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

      Please note that corrections may take a couple of weeks to filter through the various RePEc services.

      IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.