Publication informationJournal of Sound and Vibration, 328 (3): 291-300Publisher Elsevier __________________________________________________________________________ AbstractThe determination of the natural frequencies and mode shapes of structures requires an analytical, semi-analytical or numerical method. This paper presents a new semi-analytical approach to determine natural frequencies and mode shapes of a multi-span, continuous, orthotropic bridge deck. The suggested approach is based on the modal method, which differs from other approaches in its decomposition of the admissible functions defining the mode shapes. Implementation of this technique is simple and enables avoidance of cumbersome mathematical calculations. In this paper, application of the semi-analytic approach to a threespan, orthotropic roadway bridge deck is compared in the first 16 modes of previously published fully analytical results and to a finite element method analysis. The simplified implementation matches within 2 % in all cases, with the additional benefit of including intermodal coupling. The approach can be extended to similar bridges with more than three spans.
__________________________________________________________________________The response of a multi-span, continuous orthotropic bridge deck during truck loading is investigated to better understand the dynamic interaction between moving vehicles and highway bridge decks. The present study is based on a recently published, semi-analytical approach for free vibration in which the modal superposition method incorporates intermodal coupling. Herein, the bridge deck is modeled as a jointless, multi-span, orthotropic plate, and the vehicle is modeled as a dynamic, multi-body system. The road surface roughness randomness is modeled as a normal, stationary, random process described by its PSD. The coupled equations of the motion vehicle/bridge deck are solved by Newmark's method. An iterative process in each time step is performed to find the equilibrium between the bridge deck and vehicle tires using an uncoupled algorithm previously developed by other authors.Two numerical application examples are presented: an isotropic and an orthotropic, threespan bridge deck both crossed by an AASHTO-based vehicle model. In example one, the intermodal coupling affects the dynamic deflection of bridge deck but only slightly. Example two demonstrates that the loading mode and the vehicle speed have a significant influence on the Dynamic Amplification Factor. However, the most important parameter to affect the 2 dynamic vehicle/bridge deck interaction force is the road's surface roughness, as has been shown for other bridge types under various load conditions. Key-words:
Abstract. This paper extends a single equation, semi-analytical approach for three-span bridges to multispan ones for the rapid and precise determination of natural frequencies and natural mode shapes of an orthotropic, multi-span plate. This method can be used to study the dynamic interaction between bridges and vehicles. It is based on the modal superposition method taking into account intermodal coupling to determine natural frequencies and mode shapes of a bridge deck. In this paper, a four-and a five-span orthotropic roadway bridge decks are compared in the first 10 modes with a finite element method analysis using ANSYS software. This simplified implementation matches numerical modeling within 2% in all cases. The paper verifies that applicability of single formula approach as a simpler alternative to finite element modeling.
In this paper, a new three-dimensional vehicle with tandem axels at the rear is developed to determine dynamic response of bridge deck under load applying truck. The vehicle is modeled by a three-axle dynamic system with 9 degrees of freedom to accurately simulate the disposition and the intensity of loads on the bridge deck. The bridge deck is modeled by a thin, orthotropic, multi-span plate. The road surface irregularities are modeled by a random function characterized by a spectral roughness coefficient and power spectral density. The modal method is used to solve the equation of motion of the bridge deck. Equations of motion of the vehicle are obtained using the virtual work principle. The coupled equations of motion vehicle/bridge deck are integrated numerically by Newmark's method. A computational algorithm in FORTRAN is then elaborated to solve the integrated equations of motion in a decoupled, iterative process. A numerical example of an orthotropic, three-span bridge deck, excited by a 9 degree of freedom truck is presented. The resulting distribution of the Dynamic Amplification Factor (DAF) on the bridge deck does not reflect any particular trend, because high values can be obtained at points where the vertical displacement is small. The DAF is significant only under the interaction force. Thus, the road surface roughness was shown to have a significant influence on the dynamic vehicle/bridge deck interaction forces.
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