Topics to be covered include:

• Theory of Random Processes [Specification of Random Processes; Stationary (Homogeneous) Random Processes; Expected Values: Moments; Differentiation and Integration of a Random Process; Spectral Representation of a Random Process; Non-stationary (evolutionary) Random Processes];
• Some Important Random Processes [Gaussian, Poisson, and Markov Random Processes];
• Further Properties of Random Processes [Threshold Crossings; Peak Distribution; Envelope Distribution; First-Passage Time; Maximum Value of a Random Process in a Time Interval];
• Linear Structures with Single Degree of Freedom (SDOF) [System Response to Random Excitation; Weakly Stationary Excitations; Non-stationary Excitations]; Linear Structures with Multiple Degrees of Freedom (MDOF) [General Analytical Framework];
• Structural Failures Resulting from Dynamic Response and Related Topics [First-Excursion Failures; Fatigue Failures];
• Response of Nonlinear Structural Systems [Method of Equivalent Linearization – Hysteretic Systems]

• Nigam, N.C.(1983), Introduction to Random Vibration, MIT Press.
• Soong, T.T. and M. Grigoriu (1993), Random Vibration of Mechanical and Structural Systems, P T R Prentice-Hall, Inc.
• Lutes, L.D. and S. Sarkani (2004), Random Vibrations: Analysis of Structural and Mechanical Systems, Elsevier.
• Roberts, J.B. and P.D. Spanos (1990), Random Vibration and Statistical Linearization, John Wiley & Sons Ltd.

Prerequisites

• Structural Dynamics
• Elements of Probability Theory
• Elements of Methods of Applied Mathematics (e.g. Fourier Theory; Ordinary Differential Equations; Applied Linear Algebra)

Teaching and learning methods

• Lectures are given using the blackboard and are supplemented with handouts.
• Certain homework problems require programming using MATLAB.

Assessment and grading methods

• Around 4 homework assignments (60%);
• Take-home final exam (40%)