Minia University Mechanical Vibrations

Faculty of Engineering Postgraduate Msc. 2012

Automotive & Tractors Eng. Dept. Time: 3 Hrs.

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Assume any missing data Maximum: 100 marks

Part A (20 x 2 = 40 marks) Answer ALL Questions.

Question One: 1. Explain with a neat sketch the main steps of Vibration Analysis. 2. A light rigid rod of length L is pinned at one end

0 and has a body of mass m attached at the other

end. A spring and viscous damper connected in

parallel are fastened to the rod at a distance a

from the support. The system is set up in a

horizontal plane: a plan view is shown.

Assuming that the damper is adjusted to provide

critical damping, obtain the motion of the rod as

a function of time if it is rotated through a small

angle , and then released. Given that = 2 and the undamped natural frequency of

the system is 4 rad/sec, calculate the displacement 2 sec after release. Explain the

term logarithmic decrement as applied to such a system and calculate its value

assuming that the damping is reduced to 85% of its critical value.

Question Two:

1. Write short notes on: free vibration, forced vibration, self-excitation vibration, logarithmic decrement, damping and resonance.

2. A 50-kg block moves between vertical guides as shown in Fig. The block is pulled 40mm down from its

equilibrium position and released. For each spring

arrangement, determine: a) the period of the vibration, b)

the maximum velocity of the block, and c) the maximum

acceleration of the block.

3. Figure shows a simple model of a motor vehicle that can vibrate in the vertical direction while traveling over a rough road. The

vehicle has a mass of 1200 kg. The suspension system

has a spring constant of 400 kN/m and a damping

ratio of = 0.5. If the vehicle speed is 20 km/hr, determine the displacement amplitude of the vehicle.

The road surface varies sinusoidally with an

amplitude of Y = 0.05 m and a wavelength of 6 m.

Part B (3 x 20=60 marks) Answer THREE Questions only.

Question Three:

1. Classify different types of damping? 2. Explain simple Harmonic Motion, degree of freedom and magnification factor. 3. A vibrating system is defined by the following parameters:

m= 5kg , k= 200N/m, c=3N.sec/m. Determine:

a- the damping factor b- the natural frequency of damped vibration c- logarithmic decrement

Minia University Mechanical Vibrations

Faculty of Engineering Postgraduate Msc. 2012

Automotive & Tractors Eng. Dept. Time: 3 Hrs.

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d- the ratio of two consecutive amplitudes e- the number of cycles after which the original amplitude is reduced to 30%.

Question Four:

1. What are the most common machinery problems that cause vibration? 2. A two-wheel trailer is drawn over an undulating surface in such a way that the

vertical motion of the tyre may be regarded as

sinusoidal, the pitch of the undulations being 5 m. The

combined stiffness of the tyres is 170 kN/m and that of

the main springs is 60 kN/m; the axle and attached parts

have a mass of 400 kg, and the mass of the body is 500

kg. Find (a) the critical speeds of the trailer in km/h and

(b) the amplitude of the trailer body vibration if the

trailer is drawn at 50 km/h and the amplitude of the

undulations is 0.1 m.

Question Five:

1. Classify different types of vibrations? 2. Distinguish between transient, steady-state, and total solutions. 3. The block shown to the right rests on a frictionless

surface. Find the response of the system if the block is

displaced from its static equilibrium position 15 cm to

the right and released from rest. m = 4.0 kg, b = 0.25

N/(m/s), k1= 1.5 N/m, k2 = 0.50 N/(m/s).

Question Six:

1. What are the main causes of vibration?

2. A reciprocating pump, weighing 150 lb, is

mounted at the middle of a steel plate of thickness

0.5 in., width 20 in., and length 100 in., clamped

along two edges as shown in Fig. During operation

of the pump, the plate is subjected to a harmonic

force, F(t) = 50 cos62t lb. Find the amplitude of

vibration of the plate.

Question Seven:

1. What are the advantages and disadvantages of vibration? 2. A structure is modelled by the three degree of freedom system shown. Determine the

highest natural frequency of free vibration and the associated mode shape.

With my best wishes Dr. Nouby M. Ghazaly