Question

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.

Answer 1

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

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