Analytical solutions to VBI system for non-simply supported boundary conditions

Matlab codes developed to calculate vehicle and bridge responses (displacement, velocity, and acceleration) for a theoretical vehicle bridge interaction (VBI) system for non-simply supported boundary conditions including both ends fixed, fixed simply supported, and one end fixed the other end free (cantilever) boundary condition. Both the vehicle and bridge damping effects and multiple bridge vibration modes are considered.
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 travelling speed is constant.
Limit: 1. Based on Bernoulli-Euler beam theory, 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, use with caution.
Note: Two forms of solutions are presented for cross-checking purposes, the numerical results for vehicle and bridge are almost the same, only allow for minor differences due to truncation issue existed in numerical calculations.