581. MATHEMATICAL FORMULATION OF INSTABILITY OF A SUBSEA SUSPENDENT PIPELINE. N. MESTANZADE 1 , L. YILMAZ 2  VIBROENGINEERING. JOURNAL OF VIBROENGINEERING. DECEMBER 2010. VOLUME 12, ISSUE 4. ISSN 1392-8716 459 581. Mathematical formulation of instability of a subsea suspendent pipeline N. Mestanzade 1 , L. Yilmaz 2 1 Atakoy Campus, Istanbul Kultur University, D225, Bakirkoy 34156/Istanbul-Turkey e-mail: n.mestanzade@iku.edu.tr 2 Technical University of Istanbul, Civil Engineering Faculty, Hydraulic Division, 80626, Maslak, Istanbul, Turkey e-mail: lyilmaz@itu.edu.tr (Received 20 September 2010; accepted 9 December 2010) Abstract: Lateral vibration of underwater suspended pipeline was investigated for the case of pipeline oscillation due to vortex shedding. Firstly, tension force was defined at the connection legs on sea bottom. To define the dynamical equation the analogy of the Mathieu equation was applied, meanwhile Ince-Strutt diagram was used for its solution. As a numerical example we used the behavior of pipeline in a project between Turkey and North Cyprus in the East Mediterranean Sea. Good agreement was found between the theoretical results and experimental data of Danish Hydraulic Institute (DHI). Keywords: Subsea pipeline, dynamic behavior, Ince-Strutt diagram, oscillation Symbols L 0 –Length of leg, m; L – Lengthening of leg, m; L – difference of lengthening, m ; x – maximum horizontal displacement of pipeline, m; F 0 – unite tension force in the leg, kN; F – Tension force in lengthening leg, kN; φ – Angle of displacement, grad; A k – cross-section of leg, m 2 ; F x – horizontal projection of F – tension force, kN; P – external wave force, kN;  – safety coefficient; u adm – permissible horizontal displacement; F adm – permissible tension force in the leg; ω – Cyclic frequency of structure, rad/s; θ – Frequency of the external force, rad/s; T – Period of structure, s; T 0 – period of the external force, s; g – Gravitation acceleration, m/s 2 ; ℓ – Length of the pipeline section, m; E – Modulus of elasticity, kN/mm 2 ;  – Poisson ratio; δ – Thickness of pipeline, m; R – External radius of pipeline, m; D – External diameter, m; ρ – density of HDPE material, kg/m 3 ; ρ 0 – density of water, kg/m 3 ; M – mass of structure plus added water mass on the one meter, N/m; I – moment of inertia of pipeline, m 4 ; EI – stiffness of pipeline structure, kN.mm 2 ; F k – Karman force; C k – non-dimensional Karman coefficient (for cylinders C k ≈1); S – area of the cross-section of pipeline; ω k – circular frequency of Karman vortex; T v – vortex shedding period; Γ – vortex of strength magnitude; U ∞ – incident velocity at the upstream end of the flow field; A – amplitude of pipeline displacement Ν – kinematical viscosity; Re – Reynolds number. Introduction: In this research, we defined oscillation of suspended subsea pipelines [1] by analogy with suspended bridges and offshore tension leg platforms [2,4,5,9]. In this research the brought to you by CORE View metadata, citation and similar papers at core.ac.uk provided by Journal of Vibroengineering