多跨的三种梁的横向自由振动模型

运用了参数变易法对Timoshenko、Rayleigh和shear梁的横向自由振动模型进行了推导，分析了铰支座、集中质量、转动惯性、拉压弹簧和扭转弹簧的复杂边界条件的情形，进而给出了带有多个复杂边界条件的三种梁的自由振动模型。在其简化的Euler梁下对三个有一定工程实践意义的模型进行了推导，分别是双跨梁、双跨梁带有任意个集中质量和单跨梁带有任意个拉压弹簧的自由振动模型，三个模型的频率方程的结果与已有文献的结果相比具有很好的一致性。并运用Nastran将双跨梁进行了算例分析，结果本文提出的公式计算的一阶频率与有限元方法得出的一阶频率之差小于5%，表明提出的模型是合理可用的。

The transverse free vibration model of three multi-span beams

The transverse free vibration equations of Timoshenko, Rayleigh and shear beam were given by variation parameter method. The hinge support, lumped mass, rotational inertia, compression-tension spring and torsional spring were analyzed. Based on them, the free vibration model of three beams was derived. The analogous Euler beam as its simplified model was proposed to infer three models with the engineering meanings. They are the free vibration model for a two-span beam, a two-span beam with arbitrary lumped masses and a one-span beam with arbitrary spring-mass system. Comparison between the frequency equations which were derived by the three models and previous articles, they have good accordance. A two-span-beam example was given by Nastran to compute the first-order frequency. By comparing the result by Nastran with the result by formula proposed, the error is within 5%, which illustrates that the proposed model is fair and useful.