用谱元法分析Timoshenko梁-地基相互作用的振动

Saida Hamioud, S. Khalfallah, S. Boudaa
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引用次数: 0

摘要

本文用谱元法分析了弹性支承Timoshenko梁的自由振动。阐述了控制偏微分方程,以表示谱刚度矩阵。有效地,梁的非经典端边界条件是校准Timoshenko梁-土基础相互作用现象的基本任务。通过对偏微分方程进行数值求解,得到了无量纲固有频率和振型模态。在求解特征值问题后,计算前三阶振型的无量纲频率。本研究获得的结果旨在描述多个目标,例如:(1)建立有弹性弹簧和无弹性弹簧的模态分析;(2)量化梁-土-基础相互作用的影响;(3)土-基础刚度对Timoshenko梁自由振动特性的影响。为此,计算并绘制了平移弹簧和旋转弹簧不同刚度下Timoshenko梁的前三个特征值。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Vibration of Timoshenko Beam-Soil Foundation Interaction by Using the Spectral Element Method
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.
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