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Abstract:
Vehicle–road coupled system is inherently time–varying, and its responses are traditionally calculated using time–domain methods which involves significant computational effort. Aiming to improve the efficiency of response calculation for the coupled system, this paper proposes a fast calculation method in frequency domain, based on the newly developed moving frequency response function (FRF). Firstly, considering the vibration characteristics of an infinitely long road, the road response is straightforwardly expressed using the road impulse response function (IRF). Subsequently, the concept of the road moving IRF is proposed and derived with respect to the moving observation points. The moving FRF is then obtained by applying Fourier transform, which allows the responses of the road moving observation points to be established in frequency domain for fast calculation under moving loads. Furthermore, by analyzing the vehicle–road coupled vibrations, based on the vehicle FRF and road moving FRF, a formula for the vehicle–road coupling force is derived in frequency domain, along with an expression for the responses at the vehicle–road contact points. Finally, the approach is illustrated in numerical simulations of vehicle–road coupled systems, and its computational efficiency and accuracy are verified through comparison with currently popular methods.

Keywords:
vehicle-road coupled vibration, frequency domain, frequency response function, impulse response function, numerical simulations

Abstract:
The paper deals with an overview of some industrial applications leading to a formulation for advanced numerical techniques. The applications comprise squeeze casting processes, forming of tablets and petroleum reservoir modelling. All of the problems lead to solutions of highly nonlinear, coupled sets of multiphysics equations.

Keywords:
squeeze forming, powder compaction, oil fields, coupled problems, thermomechanics, porous media, fluid flow, nonlinear solid mechanics, phase transformations, microstructural solidification models, numerical methods, contact problems, discrete elements, finite elements.