Non-stationary random vibration of bridges under vehicles with variable speed

Most researchers assumed the road surface inputs as stationary random process in time domain when studying vehicles with variable speed. This assumption was made to avoid the complexity of the non-stationary random processes. This paper presented a new method of analyzing the non-stationary random response of bridges. Using the covariance equivalence technique, the non-stationary random responses of wheels in time domain were obtained, and thus a new method of analyzing the non-stationary random response of bridges was developed. A two-axle vehicle model and three bridge models were analyzed, namely, a single-span uniform Bernoulli–Euler beam, a three-span stepped beam, and a three-span continuous non-uniform bridge deck. The bridge–vehicle coupling equations were established by combining the equations of motion of both the bridge and the vehicle using the displacement relationship and the interaction force relationship at the contact points. The numerical results indicated that the responses of the tires induced by the road roughness are the non-stationary process, and the amplitudes of responses change as the vehicle velocity varies. Using the responses of the tires as the inputs to study the non-stationary vibration of bridge–vehicle system with variable speed one can obtain more accurate solutions.