JNTUA B.Tech. R20 Regulations

########## JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY ANANTAPUR B.Tech (ME) - IV-I Sem L T P C 3 0 0 3 (20A03702b) MECHANICAL VIBRATIONS (Professional Elective-IV) Course Objectives:

- ● Demonstrate basic concepts and definitions of mechanical vibrations. To write equation of motion for discrete spring-mass systems with different configuration using classical and energy methods.
- ● To train the students about basic concepts of forced vibrations, vibration transmissibility and isolation and seismic instruments. Further to understand about various vibration control methods.
- ● To familiarize the students about two degree freedom system and various types of vibration absorbers.
- ● To analyze the two degree and multi degree of freedom systems.

After successful completion of the course, the student will be able to

########## Course Outcomes:

- ● Find natural frequency of un-damped single degree freedom systems
- ● Analyze the two degree freedom systems with and without damping
- ● Calculate transmissibility and isolation
- ● Solve problems on vibration absorber
- ● Calculate natural frequencies of multi degree freedom system
- ● Measure vibration parameters
- ● Use mechanical exciters and electro dynamic shaker

UNIT I Single Degree Freedom Systems Un-damped free vibration: Classical method, Energy method, Single Degree Freedom Systems: Un-damped free vibration: Classical method, Energy method, Single Degree Freedom Systems: equivalent systems, torsional systems. Damped free vibration- Viscous damping, under damping, critical damping, over damping. Coulomb damping, equivalent damping coefficient. Simple problems. Dunkerley's lower bound approximation, Critical speed of Whirling of shafts: Transverse vibrations: of shafts: Transverse vibrations: shafts.

########## UNIT II Forced vibrations of Single Degree Freedom Systems

Steady state forced vibration, sources of excitation, impressed harmonic force, resonance impressed force due to unbalance, motion excitation, transmissibility and isolation, performance of different type of isolators, power absorbed by viscous damping.

########## UNIT IIITwo Degree Freedom Systems:

Formulation of Equation of motion, Natural frequencies and modes of vibration by classical method, coupled pendulum, forced vibration, dynamic vibration absorber.

########## UNIT IVMulti Degree Freedom Systems:

Lagrangian method for formulation of equation of motion Influence co- efficient method, Lumped mass and distributed mass systems, Stodola method, Holzer's method, model analysis of free and forced vibrations.

########## UNIT VVibration measurement and Applications

Transducers: variable resistance transducers, Piezoelectric transducers, electro dynamic transducers and linear variable differential transformer transducer; Vibration pickups: vibrometer, accelerometer, velometer and phase distortion; Frequency-measuring instruments; Vibration exciters- Mechanical exciters and electro dynamic shaker.

########## Textbooks:

- 1. Singiresu S. Rao, Mechanical Vibrations, 6/e, Pearson Education, 2018.
- 2. G.K.Groover, Mechanical Vibrations, Nemchand& Bro, 8/e, 2009.

########## Reference Books:

- 1. L. Meirovich, Elements of Vibrations Analysis, Tata McGraw Hill, 1986.
- 2. S. Graham Kelly, Mechanical Vibrations, Tata McGraw Hill, 1996
- 3. William Thomson, Theory of Vibrations with Applications, 5/e, Pearson, 2008
- 4. William Weaver, Timeoshenko, and Young, Vibration Problems in Engineering, 5/e, John Wiley, 2013.