Prerequisite Mechanics, Mechanics of Solids. Mathematics: Linear differential equations. Matrix algebra. Complex analysis. Fourier analysis. Partial differential equations. Probability and Statistics.
Skills Required Microsoft Office (WORD, EXCEL, POWERPOINT), MATLAB, ANSYS.
Grading Homeworks 20% Mid-Term 20% Term paper 20% End-Term 40%
Books
Theory of Vibration with applications, 5th edition, W.T. Thomson. (TEXTBOOK)
Vibration Problems in Engineering, by S.Timoshenko. (TEXTBOOK)
Structural Dynamics : Vibrations and Systems, by Madhujit Makhopadhyay, Ane Books India. (Chapter 8)
Tutorial : Mechanical Vibrations, by S. Graham Kelly, Tata-McGraw Hill.
Tutorial : Textbook of Mechanical Vibrations, Rao V. Dukkapati and J. Srinivas, Prentice-Hall, India.
Reference : Principles of Naval Architecture, Volume 2.
Syllabus
Module – I Practical aspects of Vibration. Fatigue. Stress-Strain Diagram. The basic concept of structural vibration. Free and forced vibration of single degree of freedom system. Rotary Imbalance (static and dynamic). Whirling of rotating shafts. Torsional pendulum. Coulomb Damping.Viscous damping. Vehicle shock absorbers and silencers. Hysteresis damping. Vibration isolation.
Module –II Transient Vibrations. Free and forced vibration of multi-degree of freedom system. Eigen value analysis. Orthogonality of normal modes. Normal mode summation. Vibration absorber. Vibration instrumentation : strain gauge, load cell, accelerometer, oscilloscope, torsiongraph, transducer.
Module – III Vibration of continuous systems. Complexities in beam vibration : Timoshenko beam, intermediate fixities, multi-span beams, Stepped beams. Mode summation method. Classical methods. Energy Based methods. Rayleigh Ritz method: non-uniform beams.
Module – IV Radiation pressure. Added mass and its effect in ship hull vibration. Offshore structure vibrations. Vortex induced vibrations (VIV). Vibration induced in floating elastic structure like ship due to wave, propeller (PIV) and machinery. Ship Vibration Excitation Forces. Sloshing induced vibration, Baffle vibration. Hull resonance diagram. Vibration of machine and diesel engine shafts; Design of engine mounts. Machine alignment and balancing. Torsional vibration of rotating and reciprocating engines.
Module –V Random Vibrations. Non-linear Vibrations. Plate vibration.
Handouts : Empirical formulae for the evaluation of frequencies in ship hull vibration.
Tutorials There will be 13 tutorial hours in the semester. All tutorials will be scored in the class. Calculator is a must. Any student without it cannot attend the tutorial. Bring your laptop for computational tutorials. The student has to solve the tutorials in class. Programs must generate outputs for score.
Homeworks (20% marks) Each homework will be of 10 marks. There will be 4 homeworks in the semester. It has to be compulsorily done individually. It can be discussed with the instructor in the office hours. All homeworks are due in the office hours. All programming homeworks need to be run in front of the instructor to generate outputs. All written homeworks will be scrutinized and cross-questioned on the spot. The student will be graded immediately. There is penalty of 2 marks (out of 10) for late submission. Please find the 2016 homeworks below.
Term Paper Presentation (20% marks) : There will be self-made 12 teams of 5 members each. The students need to make their own teams and inform the instructor by the second week of September. The topics will be given before the mid-semester examination. The problem will be somewhat harder than the homeworks, and comparisons need to be shown with a recent journal publication (provided). One presentation per team and one 10-page report per team, are due in the 3rd week of November.
Please find the a few sample term papers below.