多跨的三种梁的横向自由振动模型
发布时间：2018-11-07 17:38
【摘要】：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,该方法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。
[Abstract]:The transverse free vibration model of Timoshenko,Rayleigh and Shear beams is derived by parameter variation method. The complex boundary conditions of hinged bearing, concentrated mass, rotational inertia, tension spring and torsional spring are analyzed. Furthermore, the free vibration models of three kinds of beams with complex boundary conditions are given. Under its simplified Euler beam, three models of engineering practice are deduced, which are two span beam, two span beam with any concentrated mass and one span beam with any tension and compression spring. The results of the frequency equations of the three models are in good agreement with those obtained in the literature. The difference between the first order frequency and the first order frequency obtained by finite element method is less than 5, which shows that the proposed model is reasonable and usable.
【作者单位】： 南京航空航天大学机械结构力学及控制国家重点实验室;
【基金】：国家自然科学基金(51105197;51075203) 江苏高校优势学科建设工程资助项目
【分类号】：V214
[Abstract]:The transverse free vibration model of Timoshenko,Rayleigh and Shear beams is derived by parameter variation method. The complex boundary conditions of hinged bearing, concentrated mass, rotational inertia, tension spring and torsional spring are analyzed. Furthermore, the free vibration models of three kinds of beams with complex boundary conditions are given. Under its simplified Euler beam, three models of engineering practice are deduced, which are two span beam, two span beam with any concentrated mass and one span beam with any tension and compression spring. The results of the frequency equations of the three models are in good agreement with those obtained in the literature. The difference between the first order frequency and the first order frequency obtained by finite element method is less than 5, which shows that the proposed model is reasonable and usable.
【作者单位】： 南京航空航天大学机械结构力学及控制国家重点实验室;
【基金】：国家自然科学基金(51105197;51075203) 江苏高校优势学科建设工程资助项目
【分类号】：V214
【参考文献】
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