摘要
为了更高效分析轨道交通中的振动、噪声起因和传播,需合理构建轨道中离散支撑连续梁结构的动力学模型。在求解这类梁结构的自由振动问题时,常规解法以各阶单跨梁振型为基底函数利用里兹法求解固有特性,然后根据模态叠加法求解不同外激励下的响应。但在轨道长度不足和非周期支撑时,该方法中振型函数不能反映其离散支座特性。通过拆分连续梁为多个含弹性约束欧拉-伯努利梁,并给出梁段连接节点处的动平衡方程,得到多段梁固有频率的解析型方程组,从而求解出更符合实际的振型函数以及固有频率。进一步对比有限元模拟结果,验证所提方法的精确性,表明其在振动优化和模态分析方面具有较好的参考价值。
In order to analyze the cause and propagation of vibration and noise in rail transit more efficiently,it is necessary to construct a reasonable dynamic model of discretely-supported beams to simulate rail structure.To solve the free vibration of such structures,the modes of one-span beam are selected as the base functions and the Ritz method is used to solve the natural characteristics,then the response under different excitation is obtained by using the mode superposition method.However,in the case of insufficient track length and non-periodic support,the discrete support characteristics of the conventional solution cannot be fully expressed by the mode function.Therefore,a new segmental dynamic modeling method is proposed in this paper.In this method,the continuous beam is separated into several Euler-Bernoulli sub-beams with elastic constraints,and the dynamic equilibrium equation at each joint node of the sub-beams is derived.Then,the dynamic equilibrium equations at the nodes are assembled to establish the analytical equation sets for the multi-segment beam.Thus,more realistic mode functions and natural frequencies are obtained.Compared with the finite element simulation results,the accuracy and effectiveness of the proposed method are verified,which has a good reference value in vibration optimization and modal analysis.
作者
鲍四元
吴佳丽
沈峰
BAO Siyuan;WU Jiali;SHEN Feng(Department of Engineering Mechanics,Suzhou University of Science and Technology,Suzhou 215011,Jiangsu,China)
出处
《噪声与振动控制》
CSCD
北大核心
2023年第3期6-11,20,共7页
Noise and Vibration Control
基金
国家自然科学青年基金资助项目(51709194)。
关键词
振动与波
欧拉-伯努利梁
自由振动
固有频率
逐段梁叠加法
vibration and wave
Euler-Bernoulli beam
free vibration
natural frequency
superposition method of beam segment
