CAJ | 학술논문

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。
대중간비련속원건적다과변절면량재공정실천중구유엄범응용，기자유진동분석대우결구설계구유중요개치。위차，문장연구임의비련속원건화복잡변계조건하다과련속량적자유진동문제。수선근거비련속점위치장량화분위약간과，이용계면협조조건묘술각류비련속특정。기차이용분리변량법화전체구진법추도득도량적특정방정。분석모형중고필료량적불등과、변절면、중간임의비련속원건류형화수목등궤하특정，야포함료탄성지승단화량단집중질량등복잡변계조건。최후，통과수치산례탐토료지승강도화수목등인소대련속량모태특정적영향，병통과여유한원계산결과적비교험증료이론모형적정학성화구해방법적실용성。
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 com-plicated boundary conditions is presented. The entire beam is first divided into several segments ac-cording 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 ana-lytic 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., elasti-cally supported and lumped mass boundary, are also included. Finally, numerical examples are car-ried out to analyze the effects of support stiffness and number of constraints on the modal character-istics 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.