Investigation On A Variable Frequency-step Method For Bridge Buffeting Analyses

There are two general methods in regard to bridge buffeting analysis, that infrequency domain and that in time domain, respectively. Based on the modaldecomposition method, the frequency-domain method for buffeting analysis can gainthe dynamic response of bridges emerged in turbulent wind fields by making use ofstochastic vibration theory. This method has been long employed extensively inengineering fields due to a series of advantages such as simple calculation, conceptualsimplicity and relative smaller computational cost. Developed in recent years, theCQC method takes into consideration of multimode and mode-coupling effects, and isa refined method for buffeting responses of the long-span bridges. During theprocedure of buffeting analysis by the CQC method, computational work involved inthe output power spectrum (PSD) and the modal integrals is very time-consuming.Stochastic analysis in frequency domain is the fundamental to many research fields,and this deterministic algorithm stands in the kernel of some parametric proceduressuch as the issues related to fatigue and reliability assessment. This deterministic,time-consuming procedure may be repeated for tens of thousands of times during thevariation of parameters. Hence, improvements in the computational efficiency are ofpractical significance in engineering applications. Setting about from the basictheories of numerical integration, an algorithm of variable frequency-steps isproposed in combination with the specific analysis process of the coupled buffetingresponse of long-span bridges. Verified by the numerical examples, this algorithm caneliminate effectively the inefficiency of the traditional method of invariable sweepingfrequency-steps. The main work of the dissertation is as follows:(1)The effects on bridges caused by natural wind and the properties of the windare introduced. A comprehensive review centered on the the main advancementsregarding the wind-induced vibrations in half a century.(2)The methods involved in the frequency-domain buffeting analysis method aresummarized. Proceeding with the random vibration theory that is characteristic of thebuffeting, the solution process of buffeting in the frequency domain is derived at first;and then a detail recommendation of the analysis of the coupled buffeting response oflong-span bridges is proposed based on whether or not taking into consideration of themode coupling effects; finally, the buffeting response spectrum theory is introducedbriefly. (3)The study of the mechanism of the variation of the frequency-step-size in themethod of the variable sweeping frequency-steps. In view of the low efficiency ofbridge buffeting calculations with traditional frequency domain method which usingthe incremental sweep pattern, an accurate and efficient buffeting response algorithmis explored based on the CQC method, and a new variable increment frequency sweepmode is proposed in this paper; Start with the basic theory of numerical integration, acurvature step size control method is proposed, and an instance around the algorithmis discussed aiming at the efficiency of it. Based on the previous exploration, andcombined with the actual buffeting analysis process, the writer put forward the changemechanism of the frequency-step-size which suitable for the solving of long-spanbridge buffeting response, and has compiled the computational program in accordancewith the algorithm.(4)Investigation of the efficiency of the variable frequency-step sweepingmethod combining with a numerical example. With the numerical example of a largesuspension bridge, this study compared the precision and speed of the two algorithmsin the buffeting response calculation which obtained by the traditional incrementalsweep pattern and the variable frequency-step sweeping method proposed in thispaper, respectively. The results indicate that the proposed algorithm has evidentadvantages in the calculation of buffeting responses.