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

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

by M.G. Donley, Pol Spanos

Paperback(Softcover reprint of the original 1st ed. 1990)

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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.

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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.- 1.4.1 Methods to Compute Viscous Forces.- 1.4.2 Methods to Compute Potential Forces.- 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.- 4.3.1 Fluid Flow Boundary Value Problem.- 4.3.2 Perturbation Expansion.- 4.4 Linear Velocity Potential.- 4.5 Added Mass Force.- 4.6 Linear Force Transfer Functions.- 4.6.1 Wave Diffraction Force.- 4.6.2 Wave Diffraction Moment.- 4.6.3 Hydrodynamic Buoyancy Force.- 4.6.4 Comparison to Morison’s Equation.- 4.7 Quadratic Force Transfer Functions.- 4.7.1 Wave Elevation Drift Force.- 4.7.2 Wave Elevation Drift Moment.- 4.7.3 Velocity Head Drift Force.- 4.7.4 Velocity Head Drift Moment.- 4.7.5 Body Motion Drift Forces and Moment.- 4.7.6 Numerical Examples for Fixed Vertical Cylinder.- 4.8 Transfer Functions for Tension Leg Platform.- 4.8.1 Modification of Cylinder Transfer Functions.- 4.8.2 Numerical Example 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.- 6.1 Introduction.- 6.2 Analytical Method Formulation.- 6.3 Numerical Results.- 6.3.1 Response to Quadratic Drag Force.- 6.3.2 Response to Quadratic Wave Elevation/Velocity Head Force.- 6.3.3 Response to Quadratic Body Motion Force.- 6.3.4 Response to Combined Viscous and Potential Quadratic Forces.- 6.3.5 Evaluation of Newman’s Approximation.- 6.3.6 High Frequency Axial Tendon Force.- 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:.

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