Non-linear vibration of Timoshenko beams by finite element method

• Autorzy: Rakowski J. , Guminiak M.

Identyfikatory

DOI

10.15632/jtam-pl.53.3.731

• Języki publikacji: EN

Abstrakty

EN

The paper is concerned with free vibrations of geometrically non-linear elastic Timoshenko beams with immovable supports. The equations of motion are derived by applying the Hamilton principle. The approximate solutions are based on the negligence of longitudinal inertia forces but inclusion of longitudinal deformations. The Ritz method is used to determine non-linear modes and the associated non-linear natural frequencies depending on the vibration amplitude. The beam is discretized into linear elements with independent displacement fields. Consideration of the beams divided into the regular mesh enables one to express the equilibrium conditions for an arbitrary large number of elements in form of one difference equation. Owing to this, it is possible to obtain an analytical solution of the dynamic problem although it has been formulated by the finite element method. Some numerical results are given to show the effects of vibration amplitude, shear deformation, thickness ratio, rotary inertia, mass distribution and boundary conditions on the non-linear natural frequencies of discrete Timoshenko beams.

Słowa kluczowe

EN

Timoshenko beams; non-linear vibrations; eigenvalue problem; finite elements

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2015
• Tom: Vol. 53 nr 3
• Strony: 731—743
• Opis fizyczny: Bibliogr. 21 poz., rys., tab.

Twórcy

autor

Rakowski J.

• Poznań University of Technology, Institute of Structural Engineering, Poznań, Poland

autor

Guminiak M.

• Poznań University of Technology, Institute of Structural Engineering, Poznań, Poland

Bibliografia

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