双参数地基模型的变截面Timoshenko梁横向振动分析

为了考虑截面剪切变形和转动惯量对弹性地基梁横向振动的影响,研究并完善了基于Pasternak弹性地基模型上变截面Timoshenko梁的有限元分析方法,建立了任意截面的Timoshenko梁的模态分析方法。具体来讲,基于Timoshenko梁理论和牛顿第二定律建立了地基梁结构的运动微分方程,并对变截面的分析运用分段等效的思想,将梁离散成一个个均匀的梁段,每个有限单元都有4个自由度,使得每个有限元的单元和梁段一一对应。以完全支撑在弹性地基上的简支梁为例,分析了结构的自由振动的特性。通过与可信赖的半解析方法的结果进行比较,结果表明了该方法的准确性和有效性,并为变截面地基梁模型的分析拓展了一种思路。

Transverse Vibrations of Variable Cross-sectional Timoshenko Beam on Dual-parameter Elastic Foundation

To study the influence of cross sectional shear deformation and moment of inertia on transverse vibration of elastic foundation beam,the finite element analysis method for variable cross-sectional Timoshenko beam on Pas-ternak elastic foundation model was developed and improved,and the modal analysis method for arbitrary cross-sec-tion of Timoshenko beam was established. In specific,the motion differential equations of foundation beam were de-rived based on Timoshenko beam theory and Newton's second law; in the light of piecewise equivalent idea, the variable cross-sections were discretized into many simple uniform beam sections, which corresponded respectively with each finite element with four degrees of freedom. Furthermore,with beam of simply supported boundary which is fully supported on elastic foundation as an example,the characteristics of free vibration were analyzed and com-pared with those obtained from reliable semi-analytical approach. The results showed that the present method is ef-fective and accuracy and therefore a new insight is provided to the analysis of variable cross-sectional foundation-beam.