Non-linear vibrations of beams with non-symmetrical cross sections

• Type: Article in International Scientific Journal
• Date: 2013

Authors

S. Stoykov (Author) Other; P. Ribeiro (Author) FEUP

Journal

Title: International Journal of Non-Linear Mechanics

Vol. 55

Pages: 153-169

ISSN: 0020-7462

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 9 Citations

ISI Web of Science

Scopus - 14 Citations

Scientific classification

FOS: Engineering and technology > Mechanical engineering

CORDIS: Technological sciences > Engineering > Mechanical engineering > Vibration engineering

Other information

Authenticus ID: P-006-75Z

DOI: 10.1016/j.ijnonlinmec.2013.04.015

Abstract (EN): The geometrically non-linear free and forced vibrations in space of beams with non-symmetrical cross sections are investigated in the frequency domain by the p-version finite element method. The beam model is based on Timoshenko's theory for bending and Saint-Venant's theory for torsion, i.e. due to torsion, the cross section rotates as a rigid body, but may deform in the longitudinal direction due to warping. Beams with non-symmetrical cross sections are investigated, thus the warping function is calculated numerically by the boundary element method. It is shown that the non-symmetrical properties of the cross section introduce coupling of the displacement components in linear analysis and lead to additional couplings in the non-linear regime. Green's non-linear strain tensor and Hooke's law are considered, and isotropic beams are investigated. The theory employed is valid for moderate rotations and displacements, and physical phenomena like internal resonance and change of stability status can be investigated. The differential equations of motion are converted into a non-linear algebraic form employing the harmonic balance method, and then solved by the arc-length continuation method. The variation of the amplitude of vibration with the frequency of vibration is determined and presented in the form of frequency-amplitude curves. The stability of solutions in forced vibrations is studied by Floquet's theory.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 17