Extracting multiple bridge frequencies from test vehicle – a theoretical study

Abstract

The coupled differential equation group for the vehicle bridge interaction system is reestablished to include both the vehicle and bridge damping effects. The equation group can be uncoupled and closed-form solutions for both the bridge and vehicle can be obtained under the assumption that the vehicle acceleration magnitude is much lower than the gravitational acceleration constant. Then based on a simply supported boundary condition scenario, several critical parameters including bridge damping, vehicle frequency, vehicle speed, vehicle mass, and vehicle damping are studied to investigate their effects on extracting multiple bridge frequencies from the vehicle. The results show that the bridge damping plays a significant role in the vibration behaviour of both the vehicle and the bridge compared to the vehicle damping. The vehicle is preferred to be designed with a high frequency beyond the interested bridge frequencies to be extracted since low vehicle frequency tends to attenuate bridge frequencies that are higher than the vehicle frequency. A camel hump phenomenon can be observed on the extracted bridge frequencies from the vehicle, especially for scenarios that involve high bridge vibration mode and high vehicle speed. Vehicle speed is preferred to be maintained low to meet the theoretical assumption and to reduce the camel hump phenomenon. Although vehicle mass is not necessarily limited in this study, there is a magnitude balance among vehicle mass, vehicle speed, and damping to meet the theoretical assumption. This theoretical work may give some indications for designing a special field test vehicle to monitor bridge in a more comprehensive way.