复杂边界条件下的多跨梁的振动模型

对Timoshenko梁的横向自由振动方程进行推导,进而运用传递矩阵法给出了复杂边界条件下的多跨梁的自由振动模型.在不考虑梁的剪切变形和绕中性轴的转动惯量的影响的情况下,模型简化成了Bernoulli-Euler梁的格式.通过分析,给出了3个具有工程意义的简化模型,分别是双跨梁、悬臂梁带有集中质量模型及带有任意拉压弹簧和集中质量的自由振动模型.简化模型的分析结果与已有文献的分析结果相比具有很好的一致性,表明本文建立的模型是合理可用的.

Vibration model for multi-span beam with arbitrary complex boundary conditions

The transverse free vibration equations for Timoshenko beam were derived. Based on these equations, the vibration model for a multi-span beam with arbitrary complex boundary conditions was given by the transfer matrix method. Without considering the shear deformation and moment of inertia of the neutral axis, the model was simplified as the analogous model for Bernoulli-Euler beam. Three simplified models of some engineering significance were given. They are the free vibration model for a two-span beam, a cantilever with a lumped mass, and a beam with arbitrary lumped masses and translational springs. A comparison between the frequency equations derived by the three simplified models and those by the previous studies shows good consistency of the two, and it is thus concluded that the model developed in this paper is reasonable and feasible.