Unit 1

Introduction to vibration, undamped vibration, natural frequency, damped vibration, viscous damped system, under, over and critically damped system, logarithmic decrement, Coulomb damping, response to initial condition, response to simple harmonic motion, rotating unbalance, base excitation, whirling of shafts, vibration measuring instruments, response to periodic motion

Unit 2

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, beat phenomenon, response to simple harmonic motion, damped vibration, static and dynamic coupling, principle coordinate, decoupling, Rayleigh’s proportionality damping, vibration absorber.

Unit 3

Modeling of multi-degree freedom system, stiffness and flexibility influence coefficients, modeling of beam and portal members, response to periodic and non-periodic motions, modal analysis (mode – synthesis method), Vibration of continuous: Free vibration of string, bar, shaft and beam.

Course Objectives

• To make students to understand and appreciate the importance of vibrations in mechanical design of machine parts that operate in vibratory conditions by deriving equations of motion and solution methods for free and forced vibratory systems

Course Outcomes

• CO1: Derive equation of motion for systems under translational and rotational motions.
• CO2: Know how to obtain response to Initial conditions or forced excitations.
• CO3: Derive equations of motion for MDOF systems and obtain normal modes.
• CO4: Know how to obtain response of MDOF systems for any excitations
• CO5: Derive equation of motion for continuous (1D) systems and obtain natural frequencies and normal modes.

CO – PO Mapping

Textbook(s)

• W. T. Thomson, “Theory of vibrations with applications,” Pearson, 1997.

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.

Evaluation Pattern