Answer to Question #193733 in Mechanical Engineering for Lmeony

Question #193733

One of the wheels and leaf springs of an automobile, traveling over a rough road, is shown in Fig. For simplicity, all the wheels can be assumed to be identical and the system can be idealized as shown in Fig. The automobile has a mass of m1 = 1000 kg and the leaf springs have a total stiffness of k1 = 400 kN/m. The wheels and axles have a mass of m2 = 300 kg and the tires have a stiffness of k2− 500 kN/m. If the road surface varies sinusoidally with an amplitude of Y = 0.1 m and a period of l = 6 m, find the critical velocities of the automobile.


1
Expert's answer
2021-05-17T17:51:02-0400

The first frequency "f_1=\\frac{\\omega_1}{2\\pi}Hz=\\frac{14.5}{2\\pi}Hz"

The equation can be written in critical velocity term

"\\frac{s_1 (1000)}{3600}1\/6=\\frac{s_1}{21.6} \\implies s_1=49.6887 km\/h"


The second frequency "f_2=\\frac{\\omega_2}{2\\pi}Hz=\\frac{56.5}{2\\pi}Hz"

The equation can be written in critical velocity term

"\\frac{s_1 (1000)}{3600}1\/6=\\frac{s_1}{21.6} \\implies s_1=194.198 km\/h"


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