考慮路面粗糙度與車輛非線性勁度於橋頻間接量測法之模擬分析

Indirect Approach for Measuring the Bridge Frequencies in Consideration of the Road Surface Roughness and Nonlinear Vehicle Stiffness

吳峰賓(Fong-Bin Wu)

指導教授 ： 楊永斌

國立臺灣大學/工學院/土木工程學研究所/碩士(2010年)

https://doi.org/10.6342/NTU.2010.01705

摘要

本研究之主要目的為，探討在考慮路面粗糙度以及車輛非線性勁度情況下，當車輛通過橋梁時，由車輛的加速度反應中擷取橋梁振動頻率之可行性，並以群集經驗模態分離法(Ensemble Empirical Mode Decomposition -EEMD)來分離車輛加速度反應，觀察是否能將其中對應橋梁各模態之反應分離出來。上述由車輛動力反應中擷取橋梁振動頻率之方法，簡稱為橋頻間接量測法。
本研究以Yang and Lin (2005)所推導的車輛加速度之解析解做為理論基礎，驗證車輛加速度反應中確實存在橋梁頻率之訊號，但解析解受限於較理想的情況，因此本文以數值模擬的方式對後續更複雜的問題進行分析。模擬時所採用的橋梁為Bernoulli-Euler梁，而車輛為移動懸浮質量。作者以自行建立的有限元素動力分析程式來求解含橋梁路面粗糙度以及車輛非線性勁度情況下之車輛與橋梁振動反應，程式中利用傳統橋梁元素搭配車橋互制元素來建立車橋互制系統之控制方程式，並搭配Newmark-β直接積分法求解之。接著以快速富利葉轉換(Fast Fourier Transform -FFT)將車輛加速度反應轉至富利葉頻譜圖上，藉由此圖來擷取橋梁振動頻率。
由分析的結果可得知，路面粗糙度會對橋頻間接量測法造成負面影響，但可藉由引入同行車及提高同行車車速之方法來降低此負面影響；而車輛勁度為非線性時，只要非線性勁度所造成之車頻變異範圍未與橋頻耦合，仍可由車輛之動力反應擷取出橋梁頻率；另外，群集經驗模態分離法確實有機會將車輛加速度反應中對應橋頻之模態訊號分離出來。

關鍵字

車橋互制(VBI) ； 橋頻 ； 加速度 ； 粗糙度 ； 非線性 ； 群集經驗模態分離法(EEMD)

並列摘要

The objective of this study is to investigate the feasibility of extracting the bridge frequencies from the dynamic responses recorded for a vehicle during its passage over the bridge, in consideration of the road surface roughness and nonlinear vehicle stiffness, and to examine if the response components corresponding to the bridge frequencies can be decomposed from vehicle acceleration responses by Ensemble Empirical Mode Decomposition (EEMD). The approach for extracting the bridge frequencies from the dynamic responses of a vehicle is referred to as indirect approach for measuring the bridge frequencies.
This study is theoretically based on the analytical solutions to the vehicle-bridge interactive problem derived by Yang and Lin (2005), which verifies that the bridge frequencies dominate the dynamic responses of the vehicle. But the analytical solutions are solved under ideal assumptions, not necessarily being applicable to more complicated cases. For more complicated cases such as those with the considerations mentioned above, they are solved by numerical simulations herein, in which the bridge is modeled as a Bernoulli-Euler beam and the vehicle as a moving sprung mass. The dynamic responses of both the bridge and vehicle, in consideration of the road surface roughness and nonlinear vehicle stiffness, are solved by a finite element procedure programmed by the author, in which the governing equations of the vehicle-bridge interactive system are assembled by those of the conventional bridge elements and vehicle-bridge interaction element and are solved by Newmark-β method. Then, performing Fast Fourier Transform (FFT) to the dynamic responses of the vehicle, the bridge frequencies are extracted from the corresponding Fourier spectra.
It is observed from the simulation results that the road surface roughness may cause negative consequences on the indirect approach for measuring the bridge frequencies, but such negative consequences could be decreased by introducing multiple vehicles other than the test vehicle and by raising the speed of the accompanying vehicles, and that the bridge frequencies are still extractable from the dynamic responses of the vehicle once the range of the varying vehicle frequency caused by the nonlinear vehicle stiffness does not cover the bridge frequency, and that the response components corresponding to the bridge frequencies can be decomposed from vehicle acceleration responses by EEMD.

並列關鍵字

Vehicle-Bridge Interaction(VBI) ； the bridge frequencies ； acceleration ； roughness ； nonlinear ； Ensemble Empirical Mode Decomposition(EEMD)

參考文獻

Wu, Z., and Huang N.E. (2009), “Ensemble empirical mode decomposition: A

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