AO4077 Theory of Vibrations Syllabus:
AO4077 Theory of Vibrations Syllabus – Anna University PG Syllabus Regulation 2021
COURSE OBJECTIVES:
This course will enables students
1. To get insight into the basic aspects of vibration theory.
2. This course presents the principles of dynamics and energy methods pertaining to structures.
3. This course provides a platform for better understanding of the approximate methods for aerospace structures.
4. To get insight into the dynamic responses of the large systems.
5. To get insight into the basic aspects of aero-elasticity.
UNIT I SINGLE DEGREE OF FREEDOM SYSTEMS
Simple harmonic motion, definition of terminologies, Newton’s Laws, D’Alembert’s principle, Energy methods. Free and forced vibrations with and without damping, base excitation, and vibration measuring instruments.
UNIT II MULTI-DEGREES OF FREEDOM SYSTEMS
Two degrees of freedom systems, Static and dynamic couplings, eigen values, eigen vectors and orthogonality conditions of eigen vectors, Vibration absorber, Principal coordinates, Principal modes. Hamilton’s Principle, Lagrange’s equation and its applications.
UNIT III VIBRATION OF ELASTIC BODIES
Transverse vibrations of strings, Longitudinal, Lateral and Torsional vibrations. Approximate methods for calculating natural frequencies.
UNIT IV EIGEN VALUE PROBLEMS & DYNAMIC RESPONSE OF LARGE SYSTEMS
Eigen value extraction methods – Subspace hydration method, Lanczos method – Eigen value reduction method – Dynamic response of large systems – Implicit and explicit methods.
UNIT V ELEMENTS OF AEROELASTICITY
Aeroelastic problems – Collar’s triangle of forces – Wing divergence – Aileron control reversal – Flutter.
TOTAL: 45 PERIODS
REFERENCES
1. Timoshenko, S. “Vibration Problems in Engineering”, John Wiley & Sons, Inc., 2018.
2. Meirovitch, L. “Elements of Vibration Analysis”, New Delhi, McGraw-Hill Education, 2014.
3. Thomson W.T, Marie Dillon Dahleh, “Theory of Vibrations with Applications”, Harlow, Essex Pearson 2014
4. F.S. Tse., I.F. Morse and R.T. Hinkle, “Mechanical Vibrations”, Prentice-Hall of India, 1985.
5. Rao.J.S. and Gupta.K. “Theory and Practice of Mechanical Vibrations”, New Delhi, New Age International, 1999.
6. Fung, Y.C., “An Introduction to the Theory of Aeroelasticity”, Dover Publications., Mineola, N.Y., 2008.