Risk Engineering

Part I Analytical dynamic analysis.- Governing equation of motions.- Dynamic equilibrium.- Principle of virtual displacements (D'Alembert's principle).- Hamilton's principle through Lagrange's equations.- Momentum equilibrium.- Free vibrations for a single-degree-of-freedom (SDOF) system.- Undamped free vibration of SDOF system.- Damped free vibration of SDOF.- Deterministic and stochastic motions.- Category of motions.- Forced vibrations.- Forced vibration under harmonic excitations.- Forced vibration under complex periodical excitations.- Forced vibration under non-periodic excitations.- Forced vibration under random excitations.- Vibration of multi-degrees-of-freedom (MDOF) systems.- Solving eigenproblem for continuous systems - Rayleigh energy method.- Eigenvalues under the influence of axial loads.- Damping.- Types of damping and its effects.- Damping modeling.- Relationship among various expressions of damping.- Measuring damping.- Typical damping levels.- Comparison of cyclic response among structures made of elastic, viscous and hysteretic (viscoelastic) materials.- Nonlinear dynamics.- Sources of nonlinearities.- Solutions for nonlinear dynamic problems.- Eigenpairs, global-, local- and rigid body vibrations.- Structural response due to seismic excitation.- Part II Computer based dynamic analysis and modal testing.- Finite element methods for engineers.- One-dimensional element.- Two-dimensional element.- Three-dimensional element.- Isoparametric element.- Lumped and consistent mass.- Lumped and consistent mass.- Increasing FE accuracy.- Numerical integration for two- and three-dimensional element.- Meshing.- Sub-modeling.- Sub-structuring with superelement.- Take advantage of symmetry and anti-symmetry.- Mesh symmetry and anti-symmetry.- Using FEA for optimization.- Finite element application procedures.- Validation and verification.- Numerical techniques - direct time integration and modal superposition.- Explicit integration method - central difference method.- Implicit integration method.- Comparison between explicit and implicit integration method.- Computer system for improving numerical analysis efficiency.- Modal testing techniques.- Case studies of modal testing and eigen-analysis.- A ship deck structure with known excitations.- A large scale offshore jackup structure with unknown excitations.- Modal testing of a wind turbine using Laser-Doppler-Vibrometry.