(SEM V) THEORY EXAMINATION 2024-25 MECHANICAL VIBRATIONS

Subject Code: BME056

Subject Name: Mechanical Vibrations

Course: B.Tech (Semester V)

Maximum Marks: 70

Duration: 3 Hours

Exam Year: 2024–25

Sections: A, B, and C

SECTION A – Short Answer Questions (2 × 7 = 14 Marks)

Attempt all questions briefly.             Distinguish between periodic motion and harmonic motion.

Define degree of freedom.                  Define energy dissipation in viscous damping.

State the Orthogonality Principle.       What do you mean by static coupling?

Define whirling of uniform shaft.        What are vibration isolators?

SECTION B – Medium-Length Questions (7 × 3 = 21 Marks)

Attempt any three of the following.

Differentiate between torsional vibrations and damped vibrations with examples.

Define and explain acceleration measuring instruments with a suitable diagram.

Discuss Holzer’s method for determining natural frequencies of multi-rotor systems.

Explain the working of centrifugal pendulum absorbers with schematic diagram.

A rotor of 5 kg is mounted on a 0.01 m diameter shaft (length = 0.40 m).

CG is 0.02 mm off-center, rotation speed = 3000 rpm, E=1.96×1011 N/m2E = 1.96 × 10^{11} \, N/m^2E=1.96×1011N/m2.

Find amplitude of steady-state vibrations and dynamic force transmitted to bearings (neglect damping).

SECTION C – Long / Analytical Questions (7 × 5 = 35 Marks)

Attempt one part from each question.

Q3.

a. The cockpit of a firetruck (weight 2000 N) is attached to a telescoping boom (diagram shown).

Find the natural frequency of vibration in vertical direction.
b. Define energy dissipation in viscous damping.

Q4.

a. A machine weighing 3000 N is on a resilient foundation with static deflection = 7.5 cm.

Observed amplitude: 1 cm when base vibrates 0.25 cm at undamped natural frequency.

Find:

Damping constant

Dynamic force amplitude on base

Displacement amplitude of machine relative to base
b. Explain the working principle of displacement measuring instruments with sketch.

Q5.

a. For a 2-DOF spring–mass system (diagram provided):

Determine initial conditions for vibration in:
(i) First mode
(ii) Second mode
b. Define torsional vibration absorber and centrifugal pendulum absorber — state the difference.

Q6.

a. Using Rayleigh’s method, find lower natural frequency for given shaft system:

M1=100 kg,M2=50 kg,E=1.96×1011 N/m2,I=4.0×10−7 m4M_1 = 100 \, kg, M_2 = 50 \, kg, E = 1.96 × 10^{11} \, N/m^2, I = 4.0 × 10^{-7} \, m^4M1​=100kg,M2​=50kg,E=1.96×1011N/m2,I=4.0×10−7m4.
b. Define torsional vibrations of circular shafts.

Q7.

a. Define shaft with one disc (with and without damping).
b. Explain introduction to vibration analysis using MATLAB.

Key Topics for Preparation

Types of vibrations: Free, forced, damped, torsional

Degrees of freedom and system modeling

Viscous damping, energy dissipation, and damping ratio

Holzer’s method for multi-rotor systems

Whirling speed and critical speed of shafts

Natural frequency determination (Rayleigh’s method)

Vibration measurement instruments

Absorbers: Torsional and Centrifugal Pendulum

MATLAB-based vibration analysis

Study Tips

Practice numerical problems — amplitude, natural frequency, and damping.

Draw and label diagrams — especially for measuring instruments and spring–mass systems.

Revise formulas for natural frequency:

1. ωn=km,fn=12πkm\omega_n = \sqrt{\frac{k}{m}}, \quad f_n = \frac{1}{2\pi}\sqrt{\frac{k}{m}}ωn​=mk​​,fn​=2π1​mk​​

Memorize key principles — Orthogonality, Holzer’s method, Rayleigh’s method.

Prepare MATLAB basics for vibration analysis — data input, plotting, and frequency calculation.