A 3D vehicle-bridge interaction framework integrating energy-conserving Hamilton’s principle and stabilized Newmark-β method

This study proposes a novel 3D (Three-dimensional) VBI (Vehicle-bridge interaction) system modeling framework based on Hamilton's principle, coupled with an improved Newmark-β method for solving dynamic responses. By considering the kinetic and potential energies of the system, Hamilton's principle accurately describes the coupled vibrations between vehicles and bridges. The dynamic equations of the VBI system are derived by constructing a Euler-Bernoulli beam theory models and vehicle a spring-damped system models, incorporating 3D road surface irregularities and random traffic loads. The coupled dynamic equations ensure energy conservation under complex traffic loads. An improved Newmark-β method is employed to solve the nonlinear dynamic responses, ensuring numerical stability and accuracy. Theoretical validation demonstrates the model's superior accuracy in describing bridge mid-span displacement and vehicle vertical displacement. Numerical simulations and case comparisons further highlight the advantages of Hamilton's principle. For example, at a vehicle speed of 40 km/h, the maximum deviation of the simulated mid-span displacement from the measured value is only 0.42 mm, with a coefficient of determination (R²) reaching 0.92 and the mean absolute error (MAE) significantly reduced to 0.24.