Coupled bending and torsional beam vibrations excited by a moving load. Issue 1 (25th January 2021)

• Record Type: Journal Article
• Authors: Holl, Helmut J.; Keplinger, Lukas
• Other Names: Kuhl D. guestEditor.; Meister A. guestEditor.; Ricoeur A. guestEditor.; Wünsch O. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 20:Issue 1(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-01-25
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.202000312
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: For a simply supported Bernoulli‐Euler beam under a moving load with constant velocity the bending and torsion vibrations are analysed. An analytical solution of the decoupled partial differential equations is derived based on the eigenmode expansion considering the boundary and initial conditions. For the pure bending and the pure torsion the analysis is performed and the beam vibrations are calculated. For various longitudinal speeds the results are plotted. The coupled bending and torsion deformations are computed using a modal transformation. The modal decoupling yields two separated ordinary differential equations in time which are computed using the derived closed form solutions. The solutions of the coupled equations are plotted and discussed. A comparison with a numerical calculation of a finite element model which shows good agreement.