Question

8.9 An automobile with four wheels is about to pass over a speed bump as shown in the insert in Eigure 8.35a. The velocity of the vehicle at that time is 10 km/h. The vehicle is supported by a suspension system that consists of one coilover per wheel (a coilover is a combination of a shock absorber, or a damper, enclosed by a coil spring). The analytical model of the suspension system is illustrated in Figure 8.35b. The mass of the automobile carried by each wheel is 250 kg. The spring constant of the coilover is k = 50 000 N/m with a damping coefficient c. The damping effect by the flexible tires of the wheels is assumed to be negligible. Determine the following a. An estimate of the time required (in seconds) for either the front wheels or rear wheels to pass the speed bump. This time is considered to be small so as to justify the assumption that the disturbance to the suspension system of the vehicle by the speed bump is instantaneous. The cross- section of the speed bump is d -6 cm and w 18 cm as indicated in Figure 8.35a. b. The value of minimum damping coefficient c of the shock absorber for nonoscillatory motion of the vehicle after passing the speed bump c. The expression for the amplitude of vibration of the mass after the vehicle runs over the speed bump, and also the maximum amplitude of vibration of the mass. d. The time from the start of the vibration at which the amplitude of vibration is 1 mm. +y), amplitude Mass M Damper with damping coetficientc Spring with spring constant k Speed bump Wheel Figure 8.35 Vibration of a vehicle induced by passing over a speed bump. (a) A speed bump. (b) Analytical model of the suspension system.

Answer 1

Solution:

For non oscillatory vibration, the system needs to be critically damped.

Therefore $c_c=2\sqrt{kms}$

$c_c=2\sqrt{50000*250}$