JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD

Pre-requisites

Probability & Statistics, Kinematic of machinery and Dynamics of machinery.

Course Objectives

The main objective of course is to present fundamentals to a modern treatment of

vibrations, placing the emphasis on analytical developments and computational solutions. This course will provide the detail knowledge about nonlinear and random vibration with fault diagnosis of machinery using vibration signature analysis.

Course Outcomes

After completing this course, students should be able to:

• Apply tools from probabilistic modeling to analyze dynamic systems while accounting for variability and uncertainties that are inevitably present in real engineered systems.
• Classify random excitations as stationary or non‐stationary
• Discuss important properties of random processes
• Define and compute power spectral density functions
• Compute auto‐and cross‐correlation functions, and relate them to power spectral
• Density functions Describe the dynamic response of a multi‐degree‐of‐freedom system to a stochastic excitation
• Quantify the distributions of peak loads and peak responses from a system subject to stochastic excitation

UNIT - I

Probability Theory: Random Vibrations - Probability distribution and density functions - Excreted values - Conditional probability - Characteristic and log characteristic functions - Chebyshev inequality - Functions of random variables.

UNIT - II

Random Processes - I: Concept of stationary and ergodicity - Evolutionary nono stationary process - Auto and cross correlation and covariance Functions - Mean square limit, differentiability and inerrability - Spectral decomposition.

UNIT - III

Random Processes - II: Power spectral and cross spectral density Factions - Wiener - Khintchine relations - Properties of Gaussian. Poisson and Markov processes –Fokker - Planck Equation - Broad band and narrow band random processes - white noise.

UNIT - IV

Random Vibrations - I: Response of linear single and multi - degree of freedom systems to stationary excitation - Response of continuous systems - Normal mode method.

UNIT - V

Random Vibrations - II: Level crossing, peak and envelop statistics - First excursion and fatigue.

TEXT BOOKS:

• 1. Probabilistic Methods in the Theory of Structures by Lishakoff, I John Wiley, New York, 1983.
• 2. An Introduction to Random Vibrations and Spectral Analysis by Newland and D. E Longman Inc., New York, Second Edition, 1984. R19 M.Tech. ENGG. DESIGN

REFERENCE BOOKS:

• 1. Introduction to Random Vibrations by Nigam, N.C., MIT Press, Cambridge, Massachusetts, 1983.
• 2. Applications of Random Vibrations by Nigam, N.C. and Narayanan, S., Narosa Publications, 1995. R19 M.Tech. ENGG. DESIGN M. TECH. I Year I Sem. (ENGG. DESIGN)