Solution of the boundary layer problems for calculating the natural modes of riser-type slender structures

Chatjigeorgiou, IK

dc.contributor.author	Chatjigeorgiou, IK	en
dc.date.accessioned	2014-03-01T01:29:12Z
dc.date.available	2014-03-01T01:29:12Z
dc.date.issued	2008	en
dc.identifier.issn	0892-7219	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/19157
dc.subject	Boundary Layer	en
dc.subject.classification	Engineering, Ocean	en
dc.subject.classification	Engineering, Mechanical	en
dc.subject.other	Aerodynamics	en
dc.subject.other	Bending (deformation)	en
dc.subject.other	Boundary layers	en
dc.subject.other	Differential equations	en
dc.subject.other	Differentiation (calculus)	en
dc.subject.other	Drag reduction	en
dc.subject.other	Eigenvalues and eigenfunctions	en
dc.subject.other	Hydrodynamics	en
dc.subject.other	Lattice vibrations	en
dc.subject.other	Meteorology	en
dc.subject.other	Natural frequencies	en
dc.subject.other	Stiffness	en
dc.subject.other	Vibrations (mechanical)	en
dc.subject.other	Asymptotic approximations	en
dc.subject.other	Bending stiffness	en
dc.subject.other	Bending vibrations	en
dc.subject.other	Boundary layer problems	en
dc.subject.other	Clamped ends	en
dc.subject.other	Connections (structural)	en
dc.subject.other	Eigenvalue problem (EVP)	en
dc.subject.other	Governing equations	en
dc.subject.other	Mathematical formulations	en
dc.subject.other	Mode shapes	en
dc.subject.other	Natural modes	en
dc.subject.other	Perturbation approach	en
dc.subject.other	Rapid changes	en
dc.subject.other	Slender structures	en
dc.subject.other	Solution methodology	en
dc.subject.other	Static tensions	en
dc.subject.other	Difference equations	en
dc.subject.other	bending	en
dc.subject.other	boundary layer	en
dc.subject.other	eigenvalue	en
dc.subject.other	stiffness	en
dc.subject.other	structural analysis	en
dc.subject.other	structural component	en
dc.subject.other	tension	en
dc.subject.other	vibration	en
dc.title	Solution of the boundary layer problems for calculating the natural modes of riser-type slender structures	en
heal.type	journalArticle	en
heal.identifier.primary	10.1115/1.2786476	en
heal.identifier.secondary	http://dx.doi.org/10.1115/1.2786476	en
heal.identifier.secondary	011003	en
heal.language	English	en
heal.publicationDate	2008	en
heal.abstract	The present work treats the bending vibration problem for vertical slender structures assuming clamped connections at the ends. The final goal is the solution of the associated eigenvalue problem for calculating the natural frequencies and the corresponding mode shapes. The mathematical formulation accounts for all physical properties that influence the bending vibration of the structure including the variation in tension. The resulting model incorporates all principal characteristics, such as the bending stiffness, the submerged weight, and the function of the static tension. The governing equation is treated using a perturbation approach. The application of this method results in the development of two boundary layer problems at the ends of the structure. These problems are treated properly using a boundary layer problem solution methodology in order to obtain asymptotic approximations to the shape of the vibrating riser-type structure. Here, the term ""boundary layer"" is used to indicate the narrow region across which the dependent variable undergoes very rapid changes. The boundary layers adjacent to the clamped ends are associated with the fact that the stiffness (which is small) is the constant factor multiplied by the highest derivative in the governing differential equation. Copyright © 2008 by ASME.	en
heal.publisher	ASME-AMER SOC MECHANICAL ENG	en
heal.journalName	Journal of Offshore Mechanics and Arctic Engineering	en
dc.identifier.doi	10.1115/1.2786476	en
dc.identifier.isi	ISI:000255252600003	en
dc.identifier.volume	130	en
dc.identifier.issue	1	en