Forced transient vibration analysis of a multi-cracked bridge model under moving loads by means of Green's functions

The forced transient vibration of a multi-cracked bridge model under moving loads is investigated in this work based on Green's function method, and Euler-Bernoulli beam model is used to establish the dynamic model of the bridge. Parameters of a bridge are chosen based on civil engineering standards in this study, and moving loads correspond to real vehicle weights whose values are obtained from civil engineering standards. Laplace transform is used to eliminate the time variable in the dynamic model and transform the dynamic model into a dynamic equation without time variable in the complex space, and the eigenfunction expansion method is used to solve the transformed dynamic equation. In the eigenfunction expansion process, a special mode shape function is used in this study to simplify the solution process. The forced transient vibration of the uncracked bridge model under multiple moving loads is first derived, and the transfer matrix method is used to derive the analytical solution of the dynamic response of the multi-cracked bridge model based on the response of the uncracked bridge model. In the numerical solution part, the present solution is verified by comparison with the result in the literature. Effects of the crack depth and bridge depth-span ratio on the first natural frequency of the beam is revealed by numerical calculation. Effects of vehicle types, loads, numbers of vehicles, vehicle spacing, and crack depths and locations on the forced transient response of the mid-span displacement of the bridge model are investigated. Effects of bridge depth-span ratios, vehicle speeds, load locations, and crack depths on the quasi-steady-state response of the bridge model are discussed. Parameter analyses for relations of the depth-span ratio and crack depth with the mid-span displacement are included, and confidence intervals for quadratic fit coefficients reach 95% in these parameter analyses, which indicates that the quadratic fit formula fits well with the present solution. Results of this study can be extended for diverse numerical simulations and experimental studies related to cracked bridge models under moving loads.