Analytical solutions to VBI system (simply supported boundary condition) considering both vehicle and bridge damping effects and multiple bridge vibration modes

Published: 22-09-2020| Version 5 | DOI: 10.17632/m4z6mkwt6k.5
Zhenhua Shi,
Nasim Uddin


Matlab codes developed to calculate vehicle and bridge responses (displacement, velocity, and acceleration) for a theoretical vehicle bridge interaction (VBI) system (simply supported boundary condition) reestablished to consider both the vehicle and bridge damping effects and multiple bridge vibration modes. Hypothesis: Multiple bridge dynamic information may be extracted from the vehicle that travels on it. Assumption: 1. The magnitude of the vehicle acceleration signal (gravitational direction) is negligible compared to the gravitational acceleration constant (g), say <10%. Analytical solutions will be invalid if this condition is not reasonably met, say >20%; 2. Uniformly distributed bridge property (mass, damping, section stiffness); 3. Vehicle traveling speed is constant. Limit: 1. The bridge is considered as the Bernoulli-Euler beam, flexure effects caused by shear forces, rotary inertial forces, and axial forces are not considered; 2. For zero initial conditions of bridge and vehicle only; 3. Other flaws may also apply. Note: Two forms of solutions are presented for cross-checking purposes, choose either SSB_dvb.m or SSB_dvb_check.m, the results for vehicle and bridge should be the same, but allow for minor differences due to truncations of numerical calculation.