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This paper presents an analytical approach to investigate the free vibration of simply supported bridge with cracks under arbitrary number of vehicles. Calculation methods for natural frequencies and mode shapes are proposed based on Euler-Bernoulli beam theory, transfer matrix method and numerical assembly method. The vehicle is modeled as a half-car planar model. Equations of motion and displacement functions for bridge and vehicle are derived, respectively. The undermined coefficient matrices for wheels, vehicles and boundary conditions are obtained based on equilibrium and continuity conditions. Numerical assembly technique is adopted to construct the overall matrix of coefficients for bridge-vehicle vibration system. And natural frequencies and corresponding mode shapes are determined based on iterative method and overall matrix solution. Numerical simulation is presented to verify the effectiveness of the proposed method. The results reveal that solutions of the proposed method have favorable reliability. Natural frequencies and associate modal shapes of simply supported multi-girder bridge under the effects of crack and vehicle are investigated. The influences of crack and vehicle parameters on dynamic characteristics are also demonstrated. Meanwhile, a practical simply supported box-girder bridge model is analyzed by the proposed method and an effective crack identification algorithm is proposed.

Free vibration analysis of a cracked simply supported bridge considering bridge-vehicle interaction