Dynamic Analysis of Non-Linear Structures by the Method of Statistical Quadratization: (57 Lecture Notes in Engineering)

This text deals with a new technique for the dynamic analysis of nonlinear structures. A special feature is the technique of equivalent quadratization, which allows engineers to deal with complex nonlinear problems in a systematic manner. The applicability of this method is especially important for dealing with offshore structures which are exposed to nonlinear forces due to waves. The reader is expected to have a fundamental knowledge of calculus and some background in the area of random variables and stochastic processes. The book is intended for engineers and applied scientists who deal with nonlinear vibrations and have particular interest in the area of offshore engineering.

Table of Contents:
1: Introduction.- 1.1 Introduction.- 1.2 Aim of Study.- 1.3 TLP Model.- 1.4 Environmental Loads.- 1.5 Literature Review of TLP Analyses.- 1.6 Scope of Study.- 2: Equivalent Stochastic Quadratization for Single-Degree-of-Freedom Systems.- 2.1 Introduction.- 2.2 Analytical Method Formulation.- 2.3 Derivation of Linear and Quadratic Transfer Functions.- 2.4 Response Probability Distribution.- 2.5 Response Spectral Density.- 2.6 Solution Procedure.- 2.7 Example of Application.- 2.8 Summary and Conclusions.- 3: Equivalent Stochastic Quadratization for Multi-Degree-of-Freedom Systems.- 3.1 Introduction.- 3.2 Analytical Method Formulation.- 3.3 Derivation of Linear and Quadratic Transfer Functions.- 3.4 Response Probability Distribution.- 3.5 Response Spectral Density.- 3.6 Solution Procedure.- 3.7 Reduced Solution Analytical Method.- 3.8 Example of Application.- 3.9 Summary and Conclusions.- 4: Potential Wave Forces on a Moored Vertical Cylinder.- 4.1 Introduction.- 4.2 Volterra Series Force Description.- 4.3 Near-Field Approach for Deriving Potential Forces.- 4.4 Linear Velocity Potential.- 4.5 Added Mass Force.- 4.6 Linear Force Transfer Functions.- 4.7 Quadratic Force Transfer Functions.- 4.8 Transfer Functions for Tension Leg Platform.- 4.9 Summary and Conclusions.- 5: Equivalent Stochastic Quadratization for Tension Leg Platform Response to Viscous Drift Forces.- 5.1 Introduction.- 5.2 Formulation of TLP Model.- 5.3 Analytical Method Formulation.- 5.4 Derivation of Linear and Quadratic Transfer Functions.- 5.5 Response Probability Distribution.- 5.6 Response Spectral Density.- 5.7 Axial Tendon Force.- 5.8 Solution Procedure.- 5.9 Numerical Example.- 5.10 Summary and Conclusions.- 6: Stochastic Response of a Tension Leg Platform to Viscous and Potential Drift Forces.- 6.1Introduction.- 6.2 Analytical Method Formulation.- 6.3 Numerical Results.- 6.4 Summary and Conclusions.- 7: Summary and Conclusions.- Appendix A: Gram-Charlier Coefficients.- A.1 Introduction.- A.2 Gram-Charlier Coefficients.- Appendix B: Evaluation of Expectations.- B.1 Introduction.- B.2 Expectations Involving Quadratic Nonlinearity.- B.3 High Order Central Moments.- Appendix C: Pierson-Moskowitz Wave Spectrum.- Appendix D: Simulation Methods.- D.1 Introduction.- D.2 Linear Wave Simulation.- D.3 Linear Wave Force Simulation.- D.4 Drag Force Simulation.- D.5 Quadratic Wave Force Simulation.- References:.