• Author / Uploaded
• Lin Yusheng

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2014/2015 Vibration Theory and Applications Tutorial II 1.

A slab door, 2m high, 0.75m wide, 40mm thick, and with a mass of 36kg, is fitted with an automatic door closer. The door opens against a torsion spring with a modulus of 10N-m/radian. Determine the necessary damping to critically dampen the return swing of the door. If the door is opened 90o and released, how long will it take until the door is within 1o of closing? Ans. t=5.36s.

2.

A 80 kg. piston-type air-compressor is producing an unbalanced horizontal force. To measure this, it was mounted onto a platform of mass M = 50kg that could vibrate horizontally without friction and had an elastic support with stiffness in the horizontal direction k = 3500N/m. At a running speed of 1150 rpm the measured horizontal vibration is 0.0005m. What is the unbalanced horizontal force, neglecting damping.

Ans. 942.7N 3

A slider of mass m = 1 kg travels in a cylinder with a velocity v = 80 m/s and engages a spring-damper system, as shown in figure below. If the stiffness of the spring is k = 40 N/mm and the damping coefficient is c = 0.2 kN-s/m, find the maximum displacement of the slider after engaging the spring and damper. How much time does it take to reach the maximum displacement? (Rao 2.52) Ans. Xmax = 0.1735 m, t = 0.0059 sec.

4

The following figure shows a simplified model of s mechanical tennis ball throwing machine. The ball is thrown by first giving an initial displacement to the block M and the ball m and then suddenly releasing them. The ball remains in contact with the block until x = 0, at which time the block engages the damper shown in the figure. (1) If M = 1 kg, m = 0.25 kg and k = 50 N/mm, find the initial displacement of the block and ball (x0) necessary in order to make the velocity of the ball equal to 25m/sec at the end of the first quarter cycle of motion. (2) If the damping coefficient of the damper is 30 N-s/M, find the response of the block during and after the first quarter cycle of motion. Ans. (1) 0.125 m, (2) x(t) = 0.125 cos(200t), x(t) = -0.1121e-15.004t sin (223.1028t)

5

A hydraulic shaker consists of a cylinder C, piston of mass m, and a spring k. A fluid fills the lower part, which is under a fluctuating pressure p = p0cost. Determine the force acting on the base, disregarding damping.

k   Ans. F  p0 A1  cos t 2   k  m 