(SEM V) THEORY EXAMINATION 2023-24 MECHANICAL VIBRATIONS

Course: B.Tech (Mechanical Engineering)

Semester: V

Subject Code: KME057

Subject Title: Mechanical Vibrations

Total Marks: 100

Duration: 3 Hours

Exam Type: Theory (Written)

Section A – Short Answer Questions (10 × 2 = 20 Marks)

Students must attempt all questions in brief.
These questions test conceptual understanding of fundamental vibration concepts.

What is meant by Frequency?                                      What are the effects of vibration?

Define damping.                                                           What is meant by forced vibrations?

Write a short note on simple harmonic motion.        Write short notes on D’Alembert’s principle.

Define Single Degree of Freedom system.                Define Multi-degree of Freedom system.

Define Critical speed of shafts.                                   Define the principle of vibration absorber.

These questions are designed to assess your grasp of key mechanical vibration principles such as frequency, damping, forced motion, and dynamic systems

Section B – Descriptive Questions (3 × 10 = 30 Marks)
 

Attempt any three questions. Each carries 10 marks.

Define Vibrations of systems with viscous damping and explain with a suitable example.

Define Harmonic excitation with viscous damping and explain steady-state vibrations.

Write short notes on:

(i) Vibration isolators

(ii) Vibration dampers

Apply Newton’s Second Law to derive equations of motion for a vibrating body.

Explain undamped free and forced vibration of multi-degree freedom systems.

 These questions deal with the application of damping, isolation, and motion laws in real-world vibration problems, such as machinery design and engine balancing.

Section C – Long Answer / Problem-Based Questions (5 × 10 = 50 Marks)

Attempt one part from each of the following questions (Q3–Q7).

Q3. Vibration Fundamentals

a. A cantilever beam carries a mass M at its free end. A mass m falls from height h onto M and adheres without rebounding.

Determine the resulting transverse vibration of the beam (diagram provided on page 1).

Figure shows E = Young’s Modulus, I = Moment of Inertia, and k = 3EI/l³.
b. Explain the classification of vibration with examples (free, forced, damped, undamped, linear, non-linear).

Q4. Applied Vibration Systems

a. A reciprocating pump (150 lb) is mounted at the center of a steel plate (0.5 in thick, 20 in wide, 100 in long) clamped on two sides.

Under operation, the pump exerts a harmonic force F(t) = 50 Cos(62.832t) lb.

Find the amplitude of vibration of the plate.
b. Define vibration measuring instruments with a neat sketch and working principle.

Q5. Natural Frequency and Absorbers

a. Find the natural frequencies and mode shapes of a spring-mass system constrained to move vertically (diagram shown on page 2).
b. Define the principle of vibration absorber and explain undamped dynamic vibration absorber.

Q6. Multi-Degree Freedom Systems

a. Find the stiffness influence coefficients of the given mechanical system (as per figure on page 2).
b. Estimate the fundamental natural frequency of a simply supported beam carrying three identical, equally spaced masses.

Q7. Rotating Shafts and Critical Speed

a. A shaft carries a rotor (100 lb) with an eccentricity of 0.1 in, rotating at 1200 rpm.

Find (a) the steady-state whirl amplitude, and (b) the maximum whirl amplitude during start-up.

Given: Shaft stiffness = 2 × 10⁵ lb/in, damping ratio = 0.1.
b. Define secondary critical speed of shafts.

 Important Concepts Covered

Free, forced, and damped vibrations                                      Viscous damping and harmonic excitation

D’Alembert’s principle and Newton’s motion equations        Vibration isolation and absorbers

Multi-degree freedom and mode shapes                               Critical speed and resonance in shafts

Measuring instruments and beam vibration

FAQs

Q1. What is damping?
Damping is the resistance that reduces vibration amplitude over time due to energy loss (e.g., friction, material resistance).

Q2. What are vibration isolators?
Vibration isolators are devices (springs, pads, mounts) used to reduce the transmission of vibration from machines to the foundation.

Q3. What is critical speed?
It is the speed at which the system’s natural frequency matches the rotational speed, causing resonance and large amplitude vibrations.

Q4. What is D’Alembert’s principle?
It states that dynamic equilibrium can be achieved by introducing an inertial force equal to mass × acceleration, acting opposite to the direction of motion.

Q5. What is a vibration absorber?
A vibration absorber is an auxiliary mass-spring system added to a machine or structure to minimize unwanted vibrations.