Extremum Conditions of Response of Maglev Guideway Under Train Loads
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摘要:
为研究磁浮轨道梁动力响应的变化规律，将磁浮列车简化为移动的均布荷载，采用解析法得到简支轨道梁动力响应的解析解，并讨论轨道梁最大值随车速、跨度等参数的变化规律，推导磁浮轨道梁动力响应的极值条件，利用有限元方法和车-桥耦合振动方法进行验证. 结果表明：列车与轨道梁跨度比值较大时，随列车速度的增加轨道梁跨中最大响应以波动形式增加，最大响应存在极值，轨道梁响应随轨道梁跨度、质量等参数也有类似规律；当车速和跨度的乘积为特定常数，或轨道梁一阶竖弯频率与跨度的乘积为车速特定倍数时，轨道梁产生消振现象.
Abstract:To reveal the variation law of dynamic response of maglev guideways, maglev trains were simplified as moving uniform loads, and analytical methods were employed to obtain the analytical solutions for dynamic response of simply supported guideways. The variation laws of the maximum response of guideways with train speed and guideway span were discussed, and the extremum conditions of response of maglev guideways were derived, which were verified by finite element and train-bridge coupling vibration methods. The results show that under the condition of a large train-guideway span ratio, the maximum response of midspan increases with fluctuations as the train speed increases and has extremums. Guideway response also has similar change laws with the variations of guideway span, mass, and other parameters. When the product of span and speed is a specific constant, or the product of the first-order vertical frequency and span of guideway is a specific time the train speed, the guideway produces vibration isolation.
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Key words:
- maglev guideway /
- dynamic response /
- uniform loads /
- analytical method /
- vibration isolation
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图 2 阶段Ⅰ、Ⅱ轨道梁最大跨中响应比较
Figure 2. Comparison of the maximum midspan response of the guideway at stage Ⅰ and stage Ⅱ
图 8 消振车速下阶段Ⅱ振动分解
Figure 8. Vibration decomposition diagram at stage Ⅱ at a train speed producing vibration isolation
图 9 解析法与耦合振动法结果比较
Figure 9. Comparison of analytical method and coupling vibration method
表 1 φ取值表
Table 1. Value of the auxiliary angle φ
车速范围/
（km·h−1）φ 取值/rad 备注 $ \left[\dfrac{{W{L_{\text{b}}}}}{{{\text{π}} + 2k{\text{π}} }},\dfrac{{W{L_{\text{b}}}}}{{2k{\text{π}} }}\right] $ $ \dfrac{{W{L_{\text{b}}}}}{{2V}} - \dfrac{{\text{π}} }{2} - k{\text{π}} $ $k = 1,2,\cdots $ $ \left[\dfrac{{W{L_{\text{b}}}}}{{2{\text{π}} + 2k{\text{π}} }},{\dfrac{{W{L_{\text{b}}}}}{{{\text{π}}+ 2k{\text{π}} }} }\right) $ $ \dfrac{{W{L_{\text{b}}}}}{{2V}} - \dfrac{{\text{π}} }{2} - (k + 1){\text{π}} $ $k = 0,1,\cdots $ $ \left({\dfrac{{W{L_{\text{b}}}}}{{\text{π}} }}, + \infty \right) $ $ \dfrac{{W{L_{\text{b}}}}}{{2V}} - \dfrac{{\text{π}} }{2} $ 
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