The objective of this course is to develop methods for 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 question of propagation of uncertainties in the inputs to the response variables of interest and also considers questions on 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.
Probability space.
Conditional probability.
Random variables.
Probability distribution and density functions; expectations.
Commonly occurring random variables. Sequence of random variables and limit theorems.
Random processes and classifications.
Stationary and ergodicity.
Power spectral density function and auto – covariance functions.
Gaussian, Poisson and Poisson pulse processes.
Mean square derivatives and integrals.
Examples on models for earthquake and wind loads.
Review of input output relations in time and frequency domains for linear time invariant systems.
Uncertainty propagation under stationary and nonstationary excitations. SDOF and MDOF systems.
Structural failure under random vibrations.
Level crossing problems.
First passage time.
Models for peaks and envelopes.
Extreme value distributions.
Narrow band processes and clumping effects.
Applications to response spectrum based methods in earthquake engineering and gust factor approach in wind engineering.
Fatigue failure.
Estimation of expected life time under random loading.
Introduction to Monte Carlo simulation methods.
Simulation of random variables and random processes.
Problem of variance reduction.
Application to models for uncertainty propagation and reliability analysis.

Other Resources

Course Curriculum

Definition of probability measure and conditional probability Details 55:42
Scalar random variables-1 Details 57:7
Scalar random variables-2 Details 55:44
Multi-dimensional random variables-1 Details 56:11
Multi-dimensional random variables-2 Details 56:53
Random processes-1 Details 57:10
Random processes-2 Details 56:58
Random processes-3 Details 54:36
Random processes-4, Random vibrations of sdof systems-1 Details 54:30
Random vibrations of sdof systems -2 Details 57:23
Random vibrations of sdof systems -3 Details 56:9
Random vibrations of sdof systems-4 Details 56:11
Random vibrations of mdof systems-1 Details 55:36
Random vibrations of mdof systems-2 Details 56:21
Random vibrations of mdof systems-3 Details 56:48
Random vibrations of mdof systems-4 Details 54:13
Failure of randomly vibrating systems-1 Details 55:42
Failure of randomly vibrating systems-2 Details 56:16
Failure of randomly vibrating systems-3 Details 55:24
Failure of randomly vibrating systems-4 Details 55:45
Markov vector approach-1 Details 53:49
Markov vector approach-2 Details 57:46
Markov vector approach-3 Details 57:13
Markov vector approach-4 Details 56:59
Markov vector approach-5, Monte Carlo simulation approach-1 Details 57:6
Monte Carlo simulation approach-2 Details 56:18
Monte Carlo simulation approach-3 Details 55:34
Monte Carlo simulation approach-4 Details 56:20
Monte Carlo simulation approach-5 Details 55:28
Monte Carlo simulation approach-6 Details 54:1
Monte Carlo simulation approach-7 Details 52:20
Probabilistic methods in earthquake engineering-1 Details 54:38
Probabilistic methods in earthquake engineering-2 Details 55:19
Probabilistic methods in earthquake engineering-3 Details 54:4
Probabilistic methods in earthquake engineering-4 Details 54:44
Fatigue failure & Vibration energy flow models Details 54:39
Problem solving session-1 Details 51:18
Problem solving session-2 Details 53:54
Problem solving session-3 Details 55:9
Problem solving session-4 Details 55:46

This Course is provided by IISc Bangalore as part of NPTEL online courses.

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