Introduction to Vibrations, Basic terminologies.
Introduction to Vibrations: – Types of Vibrations, Definitions and Terminologies, Simple Harmonic Motion (S.H.M.), Principle of Super Position Applied to SHM, Beats, Fourier Theorem, Numerical Example Problems.
Single Degree of Freedom Un-damped Free Vibrations
Single Degree of Freedom Un-damped Free Vibrations: Spring Mass Systems, Methods of Analysis, Natural frequencies of Simple Mechanical Systems, Springs in Series and Parallel, Effect of Mass of Spring on natural Frequency, Torsional and Transverse Vibrations, Numerical Example Problems.
Single Degree of Freedom Damped Free Vibrations
Single Degree of Freedom Damped Free Vibrations: Types of Damping, Analysis and Derivations for Single Degree of Freedom system with Viscous Damping Over, Critical and Under damped Systems, Logarithmic Decrements, Numerical Example Problems.
Single Degree of Freedom of Forced Vibrations
Single Degree of Freedom of Forced Vibrations: Analysis of Forced Vibration System with Harmonic Excitation, Magnification Factor, Rotating and Reciprocating Unbalances, Support Excitation / Motion, Force and Motion Transmissible, Energy Dissipated due to Damping, Numerical Example Problems.
Two Degrees of Freedom Systems
Two Degrees of Freedom Systems: Principle Modes of Vibrations, Normal Mode and Natural Frequencies, Simple Spring Mass Systems (Without and with Damping), Masses on Tightly Stretched Strings, Double Pendulum, Torsional Systems, Combined Rectilinear and Angular Systems, Geared Systems. Un-damped dynamic vibration absorber, Numerical Example Problems.
Multi Degree of Freedom Systems
Multi Degree of Freedom Systems: Introduction, Maxwell’s Reciprocal Theorem, Influence Coefficients, Rayleigh’s Method, Dunkerley’s Method, Stodola Method, Holzer’s Method, Orthogonality of Principal Modes, Method of Matrix Iteration, Numerical Example Problems.
Continuous Systems: Vibration of String, Longitudinal Vibration of Bars/Rods, Torsional Vibration of Rods, Transverse Vibration – Euler Equation for Beams. Numerical Example Problems.