Dynamic Reliability Calculation of Bridge Based on Quasi-non-integrable-Hamiltonian System Theory

To improve the computation efficiency of bridge dynamic reliability, kinetic energy and potential energy of a railway bridge with nonlinear characteristics were expressed in the modal space, and the generalized momentum, the generalized velocity, the Hamiltonian function and the quasi-Hamiltonian system equation were established based on the quasi-Hamiltonian system theory. A quasi-non-integrable-Hamiltonian equation for a railroad concrete bridge was derived just considering its lateral and torsion displacements, and the backward Kolmogorov (BK) equation governing conditional reliability function and its corresponding quantitative boundary and initial conditions were obtained, and the central finite difference method was introduced to calculate the BK equation. The case research results show that the dynamic reliability of a nonlinear bridge structure and the peak value of probability density decrease as the primary energy increases, while they increase as the limit energy raises; and the contrastive analysis results of railway bridges with different spans are agreed with the actual situations, illustrating that the dynamic reliability calculation of railway bridges based on the quasi-non-integrable-Hamiltonian system theory is feasible.