Full Content is available to subscribers

Subscribe/Learn More  >

Free and Forced Vibration Analysis of Non-Local Euler-Bernoulli Beam Resting on Nonlinear Foundation

[+] Author Affiliations
Ma’en S. Sari

German Jordanian University, Amman, Jordan

Bashar R. Qawasmeh

The University of Jordan, Amman, Jordan

Paper No. SMASIS2015-8882, pp. V001T03A013; 10 pages
  • ASME 2015 Conference on Smart Materials, Adaptive Structures and Intelligent Systems
  • Volume 1: Development and Characterization of Multifunctional Materials; Mechanics and Behavior of Active Materials; Modeling, Simulation and Control of Adaptive Systems
  • Colorado Springs, Colorado, USA, September 21–23, 2015
  • Conference Sponsors: Aerospace Division
  • ISBN: 978-0-7918-5729-8
  • Copyright © 2015 by ASME


In this study, the primary response of an Euler-Bernoulli beam resting on nonlinear elastic foundation is investigated. The beam is subjected to thermal and magnetic axial loads. The nonlocal Eringen’s elasticity theory is used to derive the mathematical model to account for the scale effect of the beam. A simply supported beam is considered in the analysis, and the multi-mode approach is used to obtain the reduced nonlinear temporal equations of motion that contain quadratic and cubic nonlinear terms. The method of multiple-scales is applied to obtain approximate analytical solutions for the nonlinear natural frequencies in addition to the primary resonance response curves. Moreover, the effective nonlinearity is obtained as a function of the natural frequencies and the coefficients of the elastic foundation. The results reveal that the scale parameter has a significant effect on the frequencies and amplitudes of the beam. The obtained results are presented over a selected range of physical parameters such as the scale effect parameter, foundation parameters, thermal and magnetic loads, and the excitation level. Time responses, phase planes and Poincaré maps are generated for the beam under consideration.

Copyright © 2015 by ASME



Interactive Graphics


Country-Specific Mortality and Growth Failure in Infancy and Yound Children and Association With Material Stature

Use interactive graphics and maps to view and sort country-specific infant and early dhildhood mortality and growth failure data and their association with maternal

Citing articles are presented as examples only. In non-demo SCM6 implementation, integration with CrossRef’s "Cited By" API will populate this tab (http://www.crossref.org/citedby.html).

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In