Syllabus

Module I – Single-Degree-of-Freedom Systems (9 hours)

Free Vibration of Single-Degree-of-Freedom Systems: Underdamped Critically damped Overdamped Coulomb damping Hysteretic damping Harmonically Forced Vibration of Single-Degree-of-Freedom Systems: Undamped system Viscously damped system Harmonic excitation Vibration isolation Multifrequency excitations General periodic excitations Energy Harvesting Transient Vibration of Single-Degree-of-Freedom Systems: Convolution integral Response due to general excitation and Base excitation Laplace Transform Shock Spectrum Vibration isolation for short duration pulses

Module II – Multiple-Degree-of-Freedom Systems (7 hours)

Multiple-Degree-of-Freedom System Vibrations: Normal modes Natural frequencies and mode shapes Proportional damping General Viscous Damping Modal Analysis for Undamped systems and systems with general damping Finite Difference method for system of equations Energy-Based Approaches: Virtual Work Lagrange’s equation Kinetic Energy, Potential Energy, and Generalized force

Module III – Continuous Systems (8 hours)

Vibration of Continuous Systems: Vibrating string Longitudinal vibration of rods Torsional Vibration of Rods Euler equation for beams Systems with repeated identical sections Mode-Summation Procedures for Continuous Systems (Beams): Mode summation method Normal modes of constrained structure Mode-acceleration method Component-mode synthesis

Module IV – Classical Methods (8 hours)

Classical Methods: Rayleigh method Dunkerley’s Equation Rayleigh-Ritz method Holzer Method Myklestad’s method for beams Element Stiffness and Mass Global Stiffness and Mass for beam element Vibration involving beam elements

Module V – Random Vibrations (4 hours)

Random Vibrations: Frequency response function Probability distribution Correlation Power spectrum and Power spectral density Fourier Transforms FTS and response

To provide the fundamentals of vibrations.

To analyse single degree of freedom systems and multiple degree of freedom system.

To analyse continuous systems subjected to vibration.

To learn classical methods of vibration analysis.
and To understand fundamentals of random vibrations.

Students will develop skills in mathematical modelling of vibrations.

Students will formulate and solve vibrations of bodies with multiple degree of freedoms.

Students will analyse complex problems involving random vibrations.

Students will analyse continuous beams, rods for vibration.

Students will engineer ways to reduce vibration in structures.

S. Graham Kelly, Mechanical Vibrations: Theory and Applications, Cengage Learning , 2012

William T. Thomson and Marie Dillon Dahleh., Theory of Vibrations with Application, Pearson Education India , 2008

Singiresu S. Rao, Mechanical Vibrations, Pearson Inc. , 2018

Earthquake Engineering and Engineering Vibration

Journal of Sound and Vibration

Journal of Vibration and Acoustics