JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

UNIT - I

Free Vibration of Single-Degree-of-Freedom-System: Importance of the Study of Vibration; Basic Concepts of Vibration - Elementary Parts of Vibrating Systems, Number of Degrees of Freedom, Discrete and Continuous Systems; Classification of Vibration - Free and Forced Vibration, Undamped and Damped Vibration, Linear and Nonlinear Vibration, Deterministic and Random Vibration; Vibration Analysis Procedure, Spring Elements, Mass or Inertia Elements, Damping Elements, Harmonic Motion, Harmonic Analysis. Introduction, Free Vibration of an Undamped Translational System, Free Vibration of an Undamped Torsional System, Response of First Order Systems and Time Constant, Rayleigh s Energy Method, Free Vibration with Viscous Damping, Graphical Representation of Characteristic Roots and Corresponding Solutions, Parameter Variations and Root Locus Representations, Free Vibration with Coulomb Damping, Free Vibration with Hysteretic Damping, Stability of Systems

UNIT - II

Vibration Under Harmonic Forcing Conditions: Introduction, Equation of Motion, Response of an Undamped System Under Harmonic Force, Response of a Damped System Under Harmonic Force, Response of a Damped System Under F(t)=F0eit , Response of a Damped System Under the Harmonic Motion of the Base, Response of a Damped System Under Rotating Unbalance, Forced Vibration with Coulomb Damping, Forced Vibration with Hysteresis Damping, Forced Motion with Other Types of Damping, Self-Excitation and Stability Analysis, Transfer-Function Approach.

UNIT - III

Vibration Under General Forcing Conditions: Introduction, Response Under a General Periodic Force, Response Under a Periodic Force of Irregular Form, Response Under a No periodic Force, Convolution Integral, Response Spectrum, Laplace Transform, Numerical Methods, Response to Irregular Forcing Conditions Using Numerical Methods

UNIT - IV

Two-Degree - and Multi-Degree-of-Freedom Systems: Introduction, Equations of Motion for Forced Vibration, Free Vibration Analysis of an Undamped System, Torsional System, Coordinate Coupling and Principal Coordinates, Forced-Vibration Analysis, Semi-definite Systems, Self-Excitation and Stability Analysis Modeling of Continuous Systems as Multi- degree-of-Freedom Systems, Using Newton s Second Law to Derive Equations of Motion, Influence Coefficients - Stiffness Influence Coefficients, Flexibility influence Coefficients, Inertia Influence Coefficients; Potential and Kinetic Energy Expressions in Matrix Form, Generalized Coordinates and Generalized Forces, Using Lagrange s Equations to Derive Equations of Motion, Equations of Motion of Undamped Systems in Matrix Form, Eigen

R16 B.TECH AERONAUTICAL ENGG.

value Problem, Solution of the Eigen value Problem, Expansion Theorem, Unrestrained Systems, Free Vibration of Undamped Systems, Forced Vibration of Undamped Systems Using Modal Analysis, Forced Vibration of Viscously Damped Systems, Self-Excitation and Stability Analysis

UNIT - V

Continuous Systems: Introduction, Transverse Vibration of a String or Cable, Longitudinal Vibration of a Bar or Rod, Torsional Vibration of a Shaft or Rod, Lateral Vibration of Beams, The Rayleigh-Ritz Method.

TEXT BOOKS:

• 1. Rao, S.S., Mechanical Vibrations, Fifth Edition, Prentice-Hall, 2011.
• 2. Thomson, W.T., Theory of vibrations with applications, CBS Publishers, Delhi.
• 3. Meirovitch, L., Fundamentals of vibrations, McGraw Hill International Edition, 2001.

REFERENCES:

• 1. Leissa, A.W., Vibration of continuous system, The McGraw-Hill Company, 2011.
• 2. Inman, D.J., Vibration Engineering, Third Edition, Prentice Hall Int., Inc., 2001,
• 3. Kelly, S.G., Schaum’s Outline of The Theory and Problems of Mechanical Vibrations, Schaum’s Outline Series, McGraw-Hill, 1996. R16 B.TECH AERONAUTICAL ENGG.