2014/2015

Vibration Theory and Applications

Tutorial III

1 An almond transporter in a processing plant consists of a horizontal vibrating

table forced by electrodynamic vibrators to move in an angle f as shown in the

figure. Assuming that the static friction is high and slipping of the almond on the

transporter surface is not possible, and the almond lose contact with the

transporter at its highest position and move along a free path until it hits the

transporter on its return from the lowest position. Assuming plastic contact, the

almond keeps moving with the transporter until the cycle is repeated. Clearly,

after every jump the almond moves to the right. Design a transporter for

transporting speed of 0.5m/s.

Ans. A=0.1797m, =0.59 rad.

2 A commercial-type vibration pickup has a natural frequency of 4.75 Hz and a

damping factor =0.65. What is the lowest frequency that can be measured with

(a) 1% error, (b) 2% error? (Q3.38, 3rd

edition)

Ans. (a) 15.9Hz, (b) 7.45Hz

3 An accelerometer, having an undamped frequency of 80 Hz and a damping

coefficient pf 8.0 n-s/M, is attached to a vibrating structure. When the structure

vibrates with an acceleration amplitude of 7.5m/s2 and a frequency of 50 Hz, the

instrument records the acceleration amplitude as 8.0 m/s2. Determine the

suspended mass and the spring constant of the accelerometer.

Ans. m = 0.014kg, k = 3527.2 N/m

4 The following figure represents a simplified diagram of a spring-supported

vehicle traveling over a rough road. Determine the equation for the amplitude of

W as a function of the speed and determine the most unfavourable speed.

Ans. m

kLv

2

5 A Turbine foundation floor, vibrating in the vertical direction, has an amplitude of

x=0.25 mm and frequency 30 Hz. A special telescope weighing w1=30N is

mounted on a light tripod of stiffness k1=90,000 N/m as shown below. It is used

to observe the foundation distortions on a scale weighing w2=10N and is mounted

on a base of stiffness k2=180,000 N/m. Assuming both are in phase, determine the

amplitude of the vibration of a mark on the scale that would be seen through the

telescope by an observer.

6 A large rotating machine causes the floor of a factory to oscillate sinusoidally. A

punch press is to be mounted on the same floor. The displacement of the floor at

the point where the punch press is to be mounted is measured to be y(t)=0.1sinbt

(cm). Using the base support method, calculate the maximum force transmitted to

the punch press at resonance if the machine in mounted on a rubber fitting of

stiffness, k = 40,000 N/m; damping, c = 900 N-s/m; and mass, m = 3000 kg.

Ans. 501.6 N