Random Vibration : Mechanical, Structural, and Earthquake Engineering Applications

Section I Basic Probability Theory Introduction Background of Random Vibration Fundamental Concept of Probability Theory Random Variables Functions of Random Variables Systems and Functions Sums of Random Variables Other Functions of Random Variables Design Considerations Central Limit Theorems and Applications Section II Random Process Random Processes in the Time Domain Definitions and Basic Concepts Stationary Process Correlation Analysis Random Processes in the Frequency Domain Spectral Density Function Spectral Analysis Practical Issues of PSD Functions Spectral Presentation of Random Process Statistical Properties of Random Process Level Crossings Extrema Accumulative Damages Section III Vibrations Single-Degree-of-Freedom Vibration Systems Concept of Vibration Periodically Forced Vibration Response of SDOF System to Arbitrary Forces Response of SDOF Linear Systems to Random Excitations Stationary Excitations White Noise Process Engineering Examples Coherence Analyses Time Series Analysis Random Vibration of MDOF Linear Systems Modeling Direct Model for Determining Responses Normal Mode Method Nonproportionally Damped Systems, Complex Modes Modal Combination Section IV Applications and Further Discussions Inverse Problems Introduction to Inverse Problems System Parameter Identification Vibration Testing Failures of Systems 3sigma Criterion First Passage Failure Fatigue Considerations on Reliability Design Nonlinear Vibrations and Statistical Linearization Nonlinear Systems Nonlinear Random Vibrations Monte Carlo Simulations References Index