Vibration of Timoshenko Beam-Soil Foundation Interaction by Using the Spectral Element Method

Journal of Solid Mechanics

مقاله 9، دوره 12، شماره 3، آذر 2020، صفحه 607-619   

نوع مقاله: Research Paper

شناسه دیجیتال (DOI): 10.22034/jsm.2020.1879476.1503

نویسندگان

S Hamioud¹؛ S Khalfallah^{* 2}؛ S Boudaa³

¹Department of Civil Engineering, University of Jijel, Jijel, Algeria

²Department of Mechanical Engineering, National Polytechnic School, Constantine, Algeria

³Civil Engineering Department, University of Constantine, Constantine, Algeria

چکیده

This article presents an analysis of free vibration of elastically supported Timoshenko beams by using the spectral element method. The governing partial differential equation is elaborated to formulate the spectral stiffness matrix. Effectively, the non classical end boundary conditions of the beam are the primordial task to calibrate the phenomenon of the Timoshenko beam-soil foundation interaction. Non-dimensional natural frequencies and shape modes are obtained by solving the partial differential equations, numerically. Upon solving the eigenvalue problem, non-dimensional frequencies are computed for the first three modes of vibration. Obtained results of this study are intended to describe multiple objects, such as: (1) the establishment of the modal analysis with and without elastic springs, (2) the quantification of the influence of the beam soil foundation interaction, (3) the influence of soil foundation stiffness’ on free vibration characteristics of Timoshenko beam. For this propose, the first three eigenvalues of Timoshenko beam are calculated and plotted for various stiffness of translational and rotational springs.

کلیدواژه‌ها

Free-vibration؛ Non classical boundary conditions؛ Timoshenko beam؛ Spectral element method؛ Finite element method؛ Beam-soil foundation interaction؛ Mechanical properties of soil

مراجع

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