Syllabus
Unit 1
Recap of SDOF, response to simple harmonic motion, Response to non-periodic motions, impulse response, step response, convolution and Du Hamel integrals, Numerical methods: Runge-Kutta method, Normal mode analysis, response to initial conditions.
Unit 2
Modelling of multi-degree freedom system, stiffness and flexibility influence coefficients, beat phenomenon, response to simple harmonic motion, damped vibration, static and dynamic coupling, principal coordinate, decoupling, Rayleigh’s proportionality damping, vibration absorber. response to periodic and non-periodic motions, modal analysis (mode – synthesis method).
Unit 3
Vibration of continuous: Free vibration of string, bar, shaft and beam. Free vibration analysis of basic structural members with different boundary conditions, analytical and approximate solutions, response of basic structural members to periodic and non-periodic forces, mode synthesis, approximate solutions. Application of Continuous vibration in Aerospace problems.
Objectives and Outcomes
Requisite(s): 23AEExxx AIRCRAFT STRUCTURES 1
Course Objectives
To make students to understand and appreciate the importance of vibrations in mechanical design of dynamically active parts that operate in vibratory conditions by deriving equations of motion and solution methods for free and forced vibratory systems.
Course Outcomes
CO1: Know how to obtain response to Initial conditions or forced excitations.
CO2: Obtain equations of motion for MDOF systems and obtain normal modes.
CO3: Calculate the response of MDOF systems for any excitations.
CO4: Derive equation of motion for continuous (1D) systems like beam, bar and shaft.
CO5: Estimate natural frequencies and mode shapes of the continuous system.
CO-PO Mapping
PO/PSO |
PO1 |
PO2 |
PO3 |
PO4 |
PO5 |
PO6 |
PO7 |
PO8 |
PO9 |
PO10 |
PO11 |
PO12 |
PSO1 |
PSO2 |
PSO3 |
CO |
CO1 |
3 |
3 |
2 |
2 |
– |
– |
– |
– |
– |
– |
– |
2 |
3 |
2 |
– |
CO2 |
3 |
3 |
2 |
2 |
– |
– |
– |
– |
– |
– |
– |
2 |
3 |
2 |
– |
CO3 |
3 |
3 |
1 |
1 |
3 |
– |
– |
– |
3 |
1 |
– |
2 |
3 |
2 |
– |
CO4 |
3 |
3 |
3 |
3 |
– |
– |
– |
– |
– |
– |
– |
2 |
3 |
2 |
– |
CO5 |
3 |
3 |
3 |
3 |
3 |
– |
– |
– |
3 |
1 |
– |
2 |
3 |
2 |
– |
Text Books / References
Text Book(s)
W. T. Thomson, “Theory of vibrations with applications,”, 5th Edition, Pearson, 2008.
Reference(s)
Leonard Meirovitch, “Elements of vibration Analysis,” Tata McGraw Hill, 1986.
Leonard Meirovitch, “Fundamentals of vibration,” McGraw Hill, 2001.
S. S. Rao, “Mechanical vibrations,” Pearson, 2010.