考虑复杂边界条件和任意非连续元件的多跨变截面梁自由振动研究(英文)

Vibrations of Multi-span Non-uniform Beams with Arbitrary Discontinuities and Complicated Boundary Conditions

带中间非连续元件的多跨变截面梁在工程实践中具有广泛应用,其自由振动分析对于结构设计具有重要价值。为此,文章研究任意非连续元件和复杂边界条件下多跨连续梁的自由振动问题。首先根据非连续点位置将梁划分为若干跨,利用界面协调条件描述各类非连续特征。其次利用分离变量法和传递矩阵法推导得到梁的特征方程。分析模型中考虑了梁的不等跨、变截面、中间任意非连续元件类型和数目等几何特征,也包含了弹性支承端和梁端集中质量等复杂边界条件。最后,通过数值算例探讨了支承刚度和数目等因素对连续梁模态特征的影响,并通过与有限元计算结果的比较验证了理论模型的正确性和求解方法的实用性。

Multi-span flexural beams with multiple discontinuities are widely used in engineering, and to analyze the free vibrations has important significance to the efficient design of such systems, In this paper, a general solution of vibrations of multi-span beams with arbitrary discontinuities and complicated boundary conditions is presented. The entire beam is first divided into several segments according to the positions of discontinuities. The compatibility conditions are considered to account for the discontinuity configurations induced by various attachments. The characteristic equation of the beam is derived using separation of variables in conjunction with the transfer matrix method. The analytic model accounts for the geometrical characteristics of the beam with unequal span, variable cross- section as well as the arbitrariness of discontinuities. Complicated boundary conditions, i.e., elastically supported and lumped mass boundary, are also included. Finally, numerical examples are carlied out to analyze the effects of support stiffness and number of constraints on the modal characteristics of beams. From the comparison of results with those obtained with the finite element method, the validity and practicability of the present procedure are validated.