Nonlinear model for the dynamic analysis of a time-dependent vehicle-cableway bridge system

Abstract A flexible cableway bridge under moving vehicles is a typical time-dependent dynamic system with geometric nonlinearity. The particularities of this system are different from those of traditional nonlinear structures. An analytical model of time-dependent vehicle-cableway bridge systems has not been systematically established because the coupling effects of geometric nonlinearity are not involved. In this regard, a nonlinear model for the dynamic analysis of vehicle-cableway bridge systems is proposed in this work. The nonlinear equations of motion in incremental forms are established using an updated Lagrangian expression and the virtual work principle by regarding cableway bridges and vehicles as a whole dynamic system. A new iterative algorithm is developed for the response solution based on the implicit Wilson-θ method associated with the Newton-Raphson iterative technique. A general computational procedure for dynamic analyses of vehicle-cableway bridge systems is proposed. Three typical bridges, including a real cableway bridge in China, are taken used as examples to verify the validity of the proposed method. Detailed parametric studies are also conducted to demonstrate the effects of geometric nonlinearity and the efficiency of the iterative algorithm and investigate the resonance property of vehicle-cableway bridge systems. The made observations indicate that the proposed method can perform an efficient nonlinear dynamic analysis of a vehicle-cableway bridge system.