Introduction to Wavelets
History of Wavelets
Fourier transform
Random Vibration
Wavelet Analysis
A brief review of wavelet properties
Vibration Analysis of SDOF and MDOF Systems in Wavelet Domain
Wavelet based discretization of ground motions
Time-frequency characteristics of wavelets
Formulation of SDOF system equation in wavelet domain
Wavelet basis function for ground motion process
Wavelet domain stochastic response of SDOF system
Statistical parameters and non-stationary peak responses
Wavelet domain stochastic response of MDOF system
Ground Motion Characterization and PSA Response of SDOF system
Characterization of ground motions
PSA response spectrum
Time history simulation by Runge-Kutta fourth-order method
Fixed base analysis of a tank
Basic assumptions
Equations of motion
Numerical study
Ground motion characterization
Validation – PSA response
Validation – structural response
Wavelet analysis – structural response
Wavelet based analysis of linear MDOF system
Description of the model
Equations of motion
Wavelet domain formulation of tank-liquid-foundation system
Wavelet based non-stationary system responses
Solution of transfer functions
Expected largest peak response
Numerical Example
Impulsive response
MDOF analysis results
Wavelet based non-stationary vibration analysis of a simple nonlinear system
Nonlinear system
Duffing oscillator
Perturbation method
Solution of Duffing equation
Nonlinear system subjected to random vibration
Wavelet based probabilistic analysis
Model and soil nonlinearity
General equations of Motion
Equations based on yield conditions
Transfer functions
Response of the structure
Probability evaluation
Validation and results
General applications
B-WIM NOR signal analysis
Bridge and vehicle model
Wavelet analysis of experimental NOR data
Stiffness degradation analysis
Description of the analytical model
Numerical approach to wavelet based damage detection
Finite element model
Wavelet based analysis of numerical results
Soil-structure-soil interaction analysis
Responses at tank base
Finite element model of the system
Biography
Dr Pranesh Chatterjee has earned undergraduate and postgraduate degrees in civil engineering and subsequently adoctorate in engineering from Jadavpur University, India. Dr Chatterjee took up post-doctoral fellowship in structural mechanics at Katholieke Universiteit te Leuven in Belgium and then was selected as prestigious Pierse Newman Scholar at University College Dublin in Ireland. He is working as Manager of Plasticity and Tribology group of Tata Steel Europe in the Netherlands. He is active in research and publication of research works.
"I believe that this book will be an important contribution in the area of structural dynamics, particularly pertaining to civil engineering. …the content is crisp yet highly comprehensive and most importantly explains wavelet from a civil engineering outlook."
—Mira Mitra, Associate Professor, Department of Aerospace Engineering, Indian Institute of Technology Bombay, Mumbai, India






