CE 216 Random Vibrations and Structural Reliability Analyses

Credits: 3:0

October 2020-February 2021

Instructor: C S Manohar

Background

Uncertainties are ubiquitous in structural engineering. Civil engineering structures are to be designed for loads created by environmental actions like earthquakes and wind. These actions are exceptionally uncertain in their manifestations. Materials used in civil engineering constructions also display wide scatter in their engineering properties. Structural engineering activities, on one hand, lead to increase in societal wealth, and, on the other hand, these activities also make society vulnerable to risks. A structural engineer is accountable for the decisions that he takes. A hallmark of professionalism is to quantify the risks and benefits involved. The subjects of random vibrations and structural reliability offer a rational framework to quantify uncertainties mathematically. The subjects combine theories of probability, random variables and random processes with principles of structural mechanics and form the basis on which modern structural design codes are developed. The present course aims to introduce the basics of the random vibration and structural reliability analyses procedures. The course would provide the necessary groundwork to embark upon research in this field.

Syllabus

Review of probability: probability space, random variables, functions of random variables, sequence of random variables and limit theorems for sums, products and extremes. Review of random processes: stationarity, ergodictiy, power spectrum and autocovariance. Calculus of random processes. Input-output relations for linear systems. Stochastic steady state. Level crossing and first passage problems. Extreme value distributions. Reliability index based analyses: FORM and SORM. Monte Carlo simulations and variance reduction. Reliability of existing structures.

 

Pre-requisites

 

  • Basics of vibration analysis
  • It would helpful if the prospective registrants possess background in probability/statistics.

 

Books on Probability, Random variables and Random processes 

 

  • A Papoulis, 1991, Probability, random variables and stochastic processes, 3rd Edition, McGraw-Hill, New York.
  • J R Benjamin and C A Cornell, 1970, Probability, statistics and decisions for civil engineers, John Wiley, New York.
  • A H S Ang & W H Tang, 2006, Probability concepts in engineering and design, Volume 1 - Basic concepts, John Wiley, NY.

 

Books on Random Vibrations

 

  • N C Nigam, 1983, Introduction to random vibrations, MIT press, Cambridge
  • Y K Lin, 1967, Probabilistic theory of structural dynamics, McGraw-Hill, New York.
  • D E Newland, 1993, An introduction to random vibrations, spectral and wavelet analysis, Longman, Singapore.
  • Y K Lin and G Q Cai, 1995, Probabilistic structural dynamics, McGrw-Hill, New York.
  • T T Soong and M Grigoriu, 1993, Random vibration of mechanical and structural systems, Prentice Hall, Englewood Cliffs.
  • V V Bolotin, 1984, Random vibration of elastic system, Martinus and Nijhoff Publishers, The Hague.

Books on Structural Reliability

  • H O Madsen, S Krenk and N C Lind, 1986, Methods of structural safety, Prentice Hall, Englewood Cliffs, NJ.
  • P Throft-Christensen & Y Murotsu, 1986, Application of structural systems reliability theory, Springer Verlag, Berlin.
  • R E Melchers, 1999, Structural reliability: analysis and prediction, 2nd Edition, John Wiley, Chichester.
  • A H S Ang & W H Tang, 1984, Probability concepts in engineering planning and design, Volume II Decision, Risk & reliability, John Wiley, NY.
  • E Leporati, 1979, The assessment of structural safety, Research Studies Press, Oregon.
  • Haldar, A., and Mahadevan, S. (2000). Reliability assessment using stochastic finite element analysis. John Wiley and Sons, New York.
  • Haldar, A., and Mahadevan, S. (2000). Probability, reliability and statistical methods in engineering design. John Wiley and Sons, New York.
  • Ranganathan, R. (1999). Structural reliability analysis and design. Jaico Publishing House, Mumbai.

 

Books on probabilistic structural mechanics

 

  • C (Raj) Sundararajan, 1995, Probabilistic structural mechanics handbook, Chapman and Hall, NY.
  • I Elishakoff, 1983, Probabilistic methods in theory of structures, John Wiley, New York.
  • V V Bolotin, 1969, Statistical methods in structural mechanics, Holden-Day, San Fransisco.
  • G Augusti, A Baratta & F Casciati, 1984, Probabilistic methods in structural engineering, Chapman Hall, NY.
  • M Tichy and M Vorlicek, 1975, Statistical theory of concrete structures, Irish University Press, Shannon.
  • K Veng Yuen, 2010, Bayesian methods for structural dynamics and civil engineering, Wiley, Chichester.

Recommended general reading

 

  • N N Taleb, 2010, The black swan: the impact of highly improbable, Penguin.
  • N N Taleb, 2004, Fooled by randomness: the hidden role of chance in life and in market, Random house, New York.

Course Objectives:

  • Provide a brief review of mathematical tools for quantifying uncertainties using theories of probability, random variables and random processes.
  • To develop theories for propagation of uncertainties in vibrating structures.
  • To develop the theory of methods of structural reliability based on concept of reliability indices. This includes discussions on FORM and SORM.
  • To introduce methods of random vibration and reliability analysis using Monte Carlo simulations that includes discussion of variance reduction techniques and RSM.
  • To provide the necessary background to carry out reliability based design.
  • To prepare the ground for research students to undertake research in this field.

 

Video resource http://nptel.iitm.ac.in/courses/105108080/  [NPTEL course on Stochastic Structural Dynamics by C S Manohar]