Random spectrum excitation samples of a road surface profile are investigated. The displacements

velocities

accelerations of a vehicle and a bridge structure are discussed using certain samples. The road excitations are numerically simulated by the random phase cosine method of the power spectral density. The vehicle bridge system responses are obtained using the vehicle bridge differential equations for different road surface profiles. It is concluded that the random phase has critical effects on the road surface profile curve shape

and the power spectral density on the curve value. The random samples possesses the same statistical characteristics. The system response values are affected more by the road surface profiles

and the response shapes are affected more as the vehicle velocity varies. Some engineering advice is proposed based on the numerical calculation with the different random excitation inputs for their significant differential responses.