Nonlinear vibration analysis of vehicle–bridge interaction for condition monitoring

Abstract

In this paper, we investigate vehicle–bridge interactions and propose a new method for assessing bridge conditions based on nonlinear vibration analysis. A vehicle model is presented, and the dynamic load on the bridge is quantified based on bridge road roughness. The vibration of a river bridge under a moving vehicle is recorded and analyzed. The Fourier spectrum of the bridge response due to vehicle loading exhibits complicated cluster bands in addition to multiple peaks, some of which are correlated with the bridge natural modes characterized by finite element method analysis and free decay testing, and some of which are correlated with the vehicle dynamic load spectrum. To characterize the unidentified narrow band in the bridge response spectrum, the Lyapunov exponent of the response is estimated, which is found to be a positive value indicating the nonlinear properties of the bridge’s large response under vehicle loading. This finding correlates with the bridge inspection, which shows that some supporting roller bearings do not properly contact the superstructure of the bridge. To elaborate this phenomenon, a model of beam with nonideal supporting condition is analyzed, and a narrow band spectrum is characterized using He’s variational-iteration method. This research offers insight to using the vehicle–bridge interaction to monitor the health status of a bridge by using nonlinear properties, as well as linear properties.

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“…The unique phenomenon that can be modeled only through nonlinear systems, such as jump phenomenon, chaos, multiple steady-state solutions, etc., are the main significance of using the nonlinear oscillators in the vast majority of fields, especially in engineering structures. Nonlinear stiffness and friction in dynamical systems [1], complex beam and piezoelectric plate-based self-sustainable electromechanical models [2,3], nonlinear reinforced nanofibers [4], vibration caused by the interaction between vehicle and bridge [5], large amplitude vibration of beams [6][7][8][9][10][11][12] and dynamics of micro/nanoelectromechanical systems [13][14][15][16][17][18] are a few examples of nonlinear systems in the field of mechanical engineering. From the mathematical point of view, the Duffing oscillator, Van der Pol and Mathieu are well-known nonlinear equations.…”

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