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Question:
The suspension of a car of mass 1500 kg can be idealised as the mass-spring-damper system shown in Figure Q1, where all four springs and dampers for the wheels are represented as one equivalent spring and damper. The tyres can be considered to be very stiff compared to the suspension springs. It is driven along a rough road where the bumps can be modelled as sinusoidal displacements.
The total vertical displacement of the tyre from peak to trough of each bump is 0.02 m, and the distance between successive peaks in the road is 15 m. The dampers together have an equivalent damping constant of 24 kNs/m. Vibration tests of the car revealed the natural frequency of the car to be 11 rad/s.
(a) Find the combined stiffness of the suspension and also the damping factor.
(b) Determine the steady state amplitude of vibration of the car body in mm if it is travelling at 30 kph on the rough road.
(c) Also determine the amplitude of the vertical acceleration of the car at this speed.
(d) Determine the force acting on the car body through the springs and dampers when it is travelling at 80 kph.
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