Stochastic Structural Dynamics in Earthquake Engineering

Abstract

1 - Stochasticity in Engineering Systems Basic Principles of Stochastic Structural Dynamics Classification of Problems Concluding Remarks Problems. 2 - Random Variable and Stochastic Processes Introductory Remarks The Concept of Probability Random Variables Transformations of Random Variables Some Useful Probability Distributions Stochastic Processes Non-stationary, Stationary and Ergodic Stochastic Processes Statistical Descriptors of Stationary-Ergodic Stochastic Processes Linear Transformations of Stationary-Ergodic Stochastic Processes Normal-Gaussian Stochastic Processes Envelopes and Extremes of Narrow Band Stochastic Processes Non-stationary Stochastic Processes Problem Classification Concluding Remarks Problems. 3 - Single DOF System Response to Random Input Introductory Remarks Description of the Problem The Single Degree-of-Freedom Oscillator Random Response of the Sdof System Solution in the Frequency Domain Design Aspects for Simple Frame Structures Under Random Loads Extreme Values of Random Dynamic Response Concluding Remarks Problems. 4 - Multiple DOF System Response to Random Input Introductory Remarks Principles of Stochastic Dynamic Analysis for Mdof Systems Two-dof Linear Oscillator Subjected to White-noise Excitation The Role of Cross-correlation of Load Components Principles of Stochastic Analysis of Continuous Dynamic Systems Concluding Remarks Problems. 5 - Nonlinear Oscillators under Stochastic Excitation Introductory Remarks Sources of Nonlinearity and Problem Classification Linear Oscillators Subjected to Non-normal Stationary Loading Nonlinear Oscillators Subjected to Normal Stationary Loading Concluding Remarks Problems. 6 - Response of Continuous Systems to Random Input Introductory Remarks Continuous Systems in Structural Dynamics Propagation of Seismically Induced Waves Perturbation Method for Random Continuous Media Numerical Simulation of Random Fields in Continuous Media Numerical Examples Concluding Remarks Problems. 7 - Random Field Simulations Introductory Remarks Monte-Carlo Simulations Numerical Realizations of Random Fields The Kanai-Tajimi and High-Pass Filters Response Spectra Concluding Remarks Problems. 8 - Numerical Methods in Stochastic Dynamics Introductory Remarks Classification of Numerical Methods Perturbation Method Stochastic Boundary Element Method Stochastic Finite Element Method Applications to Earthquake Engineering Numerical Examples Problems. 9 - Risk Analysis of Structures Introductory Remarks Some Basic Concepts in Reliability Risk Analysis Development of the Methodology Fragility Curves Concluding Remarks Problems. Appendix A - Basic Concepts in Structural Dynamics Appendix B - Solutions to Problems