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Analytical and numerical solution of an Euler–Bernoulli beam with concentrated load using finite element method
Linnaeus University, Faculty of Technology, Department of Mathematics.
2018 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

Investigation of a fourth order Euler-Bernoulli partial differential equation governinga simply supported beam with point load is done analytically by using the Diracdeltadistribution for both homogeneous and non-homogeneous (forced) vibration.A solution is derived and plotted for the first five modes. A finite element methodis implemented for numerical solution of the resulting differential equation system.The solution of the differential equation system is implemented by the Newmark-Beta method. The results from the analytical solution and the numerical methodare logically matching. Experiments with stochastic load is also performed.

Place, publisher, year, edition, pages
2018. , p. 36
Keywords [en]
Euler-Bernoulli, PDE, Delta-Dirac, Vibration, Fourier expansion, Finite Element method, steady-state, Harmonic, Stochastic load, Uniform random number.
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-71527OAI: oai:DiVA.org:lnu-71527DiVA, id: diva2:1190632
Presentation
2018-02-21, Linnaeus University, Växjö, 09:46 (English)
Supervisors
Examiners
Available from: 2018-03-15 Created: 2018-03-15 Last updated: 2018-03-15Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
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  • Other locale
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Output format
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