This paper presents an improved theoretical damped single-axle vehicle-bridge dynamic interaction model to consider the effect of the contact patch size and motor-induced vehicle excitation. The contact patch issue is critical as it determines the minimum time step for simulation and maximum identifiable frequency, while the inclusion of the motor-induced vehicle excitation benefits the design of autonomous self-driven rather than towed vehicles. Estimations of the contact patch size for both the pneumatic tire and solid wheel scenarios are discussed. The contact patch responses, which degenerate into contact point responses when the contact patch size is assumed to be infinitely small, were derived for the first time both from the vehicle and bridge responses to confirm their equivalence. The minimum time step, which determines maximum identifiable frequency but is arbitrarily chosen in literature, is proposed to be determined by the vehicle speed and contact patch length. The procedures to extract multiple bridge triad information including natural frequencies, mode shapes, and damping ratios from the vehicle responses are also presented. Based on extensive parametric analyses, the sinusoidal vehicle excitation becomes more prominent as its amplitude and/or frequency increase and may overshadow the analysis of bridge frequencies of interest. The vehicle acceleration leads to a more accurate extraction of bridge mode shapes and damping ratios than the vehicle displacement since the displacement is dominated by the fundamental mode of bridge vibration. The damping ratio extraction shows an average error of 0.28% from the instantaneous amplitude of the vehicle acceleration signal.


Civil, Architectural and Environmental Engineering


National Science Foundation, Grant TPF-5(395

Keywords and Phrases

Contact patch; Damping ratio; Mode shape; Natural frequency; Vehicle bridge interaction; Vehicle excitation

International Standard Serial Number (ISSN)

1873-7323; 0141-0296

Document Type

Article - Journal

Document Version


File Type





© 2023 Elsevier, All rights reserved.

Publication Date

01 Jan 2024