Stochastic Structural Dynamics

Instructor: Prof. C. S. Manohar, Department of Civil Engineering, IISc Bangalore.

The objective of this course is to develop methods for the analysis of structures subjected to dynamic loads which are random in nature. Structures under the action of wind or earthquake loads are typical of such problems. The course introduces the application of probability, random variables and random processes to model uncertainties in dynamic loads. The response analysis considers the question of propagation of uncertainties in the inputs to the response variables of interest and also considers questions on the reliability of vibrating systems under dynamic loads. The course mainly deals with linear time invariant systems. A brief introduction to random vibration analysis of nonlinear systems is also provided. Solution strategies include analytical techniques and Monte Carlo simulation procedures.

Mod-01 Lec-01 Definition of probability measure and conditional probability.
Mod-01 Lec-02 Scalar random variables-1.
Mod-01 Lec-03 Scalar random variables-2.
Mod-01 Lec-04 Multi-dimensional random variables-1.
Mod-01 Lec-05 Multi-dimensional random variables-2.
Mod-02 Lec-06 Random processes-1.
Mod-02 Lec-07 Random processes-2.
Mod-02 Lec-08 Random processes-3.
Mod-02 Lec-09 Random processes-4, Random vibrations of sdof systems-1.
Mod-03 Lec-10 Random vibrations of sdof systems -2.
Mod-03 Lec-11 Random vibrations of sdof systems -3.
Mod-03 Lec-12 Random vibrations of sdof systems-4.
Mod-04 Lec-13 Random vibrations of mdof systems-1.
Mod-04 Lec-14 Random vibrations of mdof systems-2.
Mod-04 Lec-15 Random vibrations of mdof systems-3.
Mod-04 Lec-16 Random vibrations of mdof systems-4.
Mod-05 Lec-17 Failure of randomly vibrating systems-1.
Mod-05 Lec-18 Failure of randomly vibrating systems-2.
Mod-05 Lec-19 Failure of randomly vibrating systems-3.
Mod-05 Lec-20 Failure of randomly vibrating systems-4.
Mod-06 Lec-21 Markov vector approach-1.
Mod-06 Lec-22 Markov vector approach-2.
Mod-06 Lec-23 Markov vector approach-3.
Mod-06 Lec-24 Markov vector approach-4.
Mod-06 Lec-25 Markov vector approach-5, Monte Carlo simulation approach-1.
Mod-07 Lec-26 Monte Carlo simulation approach-2.
Mod-07 Lec-27 Monte Carlo simulation approach-3.
Mod-07 Lec-28 Monte Carlo simulation approach-4.
Mod-07 Lec-29 Monte Carlo simulation approach-5.
Mod-07 Lec-30 Monte Carlo simulation approach-6.
Mod-07 Lec-31 Monte Carlo simulation approach-7.
Mod-08 Lec-32 Probabilistic methods in earthquake engineering-1.
Mod-08 Lec-33 Probabilistic methods in earthquake engineering-2.
Mod-08 Lec-34 Probabilistic methods in earthquake engineering-3.
Mod-08 Lec-35 Probabilistic methods in earthquake engineering-4.
Mod-09 Lec-36 Fatigue failure & Vibration energy flow models.
Mod-10 Lec-37 Problem solving session-1.
Mod-10 Lec-38 Problem solving session-2.
Mod-10 Lec-39 Problem solving session-3.
Mod-10 Lec-40 Problem solving session-4.