South Valley University Mechanical Vibrations

Faculty of Engineering 3rd

year 2014 / 2015

Mechanical Department Mid-Term Exam, Time: 2 Hours

Answer Two Questions Only. Question One:

1. Explain with sketch the main steps of Vibration Analysis. 2. Distinguish between transient, steady-state, and total solutions. 3. An automobile moving over a rough road can be modeled considering (a) weight of the car body,

passengers, seats, front wheels, and rear wheels; (b) elasticity of tires (suspension), main springs, and

seats; and (c) damping of the seats, shock absorbers, and tires. Develop three mathematical models of

the system using a gradual refinement in the modeling process.

4. Find the natural frequency of the system shown in Fig. with and without the springs k1 and k2 in the middle of the elastic beam.

5. A spring-mass system has a natural frequency of 10 Hz. When the spring constant is reduced by 800 N/m, the frequency is altered by 45

percent. Find the mass and spring constant of the original system.

Question Two:

1. Explain simple Harmonic Motion, degree of freedom and magnification factor.

2. Write short notes on: free vibration, forced vibration, logarithmic decrement, damping and resonance.

3. Derive the expression for the equivalent spring constant that relates the applied force F to the resulting displacement x of the system shown in Fig.

2. Assume the displacement of the link to be small.

4. The maximum velocity attained by the mass of a simple harmonic oscillator is 10 cm/s, and the period of oscillation is 2 s. If the mass is

released with an initial displacement of 2 cm, find (a) the amplitude, (b)

the initial velocity, (c) the maximum acceleration, and (d) the phase angle.

5. The ratio of successive amplitudes of a viscously damped single-degree-of-freedom system is found to be 18:1. Determine the ratio of successive amplitudes if the amount of damping is (a) doubled, and (b)

halved.

Question Three:

1. Classify different types of damping? 2. 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.

3. A slider-crank mechanism is used to impart motion to the base of a spring-mass-damper system, as shown in Fig.. Approximating the base motion y(t) as a series of harmonic functions, find the response

of the mass for r = 10 cm, l = 1 m, and = 100 rad/s. m = 1 kg, c = 10 N-s/m, k = 100 N/m.

With my best wishes Dr. Nouby M. Ghazaly