Dynamic Analysis of Non-Linear Structures by the Method of Statistical Quadratization

by M.G. Donley, Pol Spanos

Overview

1. 1 Introduction As offshore oil production moves into deeper water, compliant structural systems are becoming increasingly important. Examples of this type of structure are tension leg platfonns (TLP's), guyed tower platfonns, compliant tower platfonns, and floating production systems. The common feature of these systems, which distinguishes them from conventional jacket platfonns, is that dynamic amplification is minimized by designing the surge and sway natural frequencies to be lower than the predominant frequencies of the wave spectrum. Conventional jacket platfonns, on the other hand, are designed to have high stiffness so that the natural frequencies are higher than the wave frequencies. At deeper water depths, however, it becomes uneconomical to build a platfonn with high enough stiffness. Thus, the switch is made to the other side of the wave spectrum. The low natural frequency of a compliant platfonn is achieved by designing systems which inherently have low stiffness. Consequently, the maximum horizontal excursions of these systems can be quite large. The low natural frequency characteristic of compliant systems creates new analytical challenges for engineers. This is because geometric stiffness and hydrodynamic force nonlinearities can cause significant resonance responses in the surge and sway modes, even though the natural frequencies of these modes are outside the wave spectrum frequencies. High frequency resonance responses in other modes, such as the pitch mode of a TLP, are also possible.

Product Details

ISBN-13:	9783540527435
Publisher:	Springer Berlin Heidelberg
Publication date:	08/24/1990
Series:	Lecture Notes in Engineering , #57
Edition description:	Softcover reprint of the original 1st ed. 1990
Pages:	172
Product dimensions:	6.69(w) x 9.61(h) x 0.02(d)

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 Shastic 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 Shastic 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 Shastic 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: Shastic 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:.