Question

The single degree of freedom model of a vehicle shown below will be used to obtain a first
approximation of the dynamic behavior of the entire vehicle. The mass m of the vehicle is
1200 kg when fully loaded and 400 kg when empty. The spring constant k is 400 kN/m and
the damping ratio ζ_f is 0.4 when the vehicle is fully loaded. The vehicle is traveling at 100
km/h over a road whose surface has a sinusoidally varying roughness with a spatial period
of 4.0 m. We also make the following assumptions about the behavior of the vehicle:
- As the vehicle moves forward at constant speed, only the vertical motion u(t) is relevant to the analysis.
- The tire is infinitely stiff, i.e., z(t) represents the motion of the axle of the vehicle.
- The tire remains in contact with the road.

• Compute (Using Matlab) the steady-state displacement transmissibility (DT) for the vehicle when it is:

1) fully loaded, and

2) empty, and plot the DT vs. r curves for both together.
• Estimate the vehicle velocity at which the DT (fully loaded) would be maximum.

1 cycle

Answer 1

niven tha M0Ho↓ vehicle ahe, Ful/. loade d 12.0 o ll speed ot the vehicle ^ - 43. b Sad se c 2

henFuy loaded ea 2.0 o F 1.32 9 | +12.104) 11.379 t-1', 3+9)し-e4o.yx1.399} 2 D.T - DT ,,S maximum Re8onance 0.2