Üniform eksenel akım etkisindeki elastik yapıların dinamik analizi için bir sınır eleman metodu

A boundary element method for dynamic analysis of elastic structures subjected to uniform axial flow

Özet

Akışkan taşıyan ya da eksenel bir akım içine daldırılmış elastik yapıların dinamik analizi için,lineer bir hidroelastik çözüm metodu sunulmuştur. Modal analiz tekniklerinden hareketlegeliştirilen metod, bağımsız iki analize dayanmaktadır: (i) yapısal sönüm ve dış kuvvetlerinyokluğunda elastik yapının dinamik karakteristiklerinin belirlenmesi ve (ii) yapının akışkanlatemastayken doğal modlarında hareket ettiği ve her bir modal formun, yapı ıslak yüzeyi üzerindekarşılık gelen bir basınç dağılımına neden olduğu varsayımları altında akışkan problemininçözülerek, etkileşim kuvvetlerinin hesaplanması. Akışkan-yapı sisteminin davranışı, hidrodinamikkuvvetlerin, yapısal sönüm ve var olan diğer dış yüklerle birlikte genelleştirilmiş hareketdenklemine etkitilmesiyle belirlenmektedir. Çözümün ilk aşaması ANSYS sonlu eleman yazılımıyla,ikinci aşama ise yapının elastik hareketlerinin akışkan ortamında neden olduğu pertürbasyonlarıtanımlayan potansiyel problemin, akışkan-yapı arayüzü üzerinde bir sınır integral denkleminedönüştürülmesiyle, sayısal olarak gerçekleştirilmektedir. Analizler sırasında, elastik yapınıngöreceli olarak yüksek frekanslarda titreştiği kabul edilerek, serbest yüzey dalgası etkileri ihmaledilmiş, ortaya çıkan serbest yüzey şartı ise imaj metodu kullanılarak doğrudan sağlanmıştır.Genelleştirilmiş eksu kütlesi, hidrodinamik sönüm ve hidrodinamik rijitlik formunda elde edilenetkileşim kuvvetleri, akışkan ortamının elastik yapı üzerindeki sırasıyla eylemsizlik ve titreşen yapıboyunca eksenel hareketiyle ilişkili Coriolis ve santrifüj etkilerini temsil etmektedir. Uçları basitbağlı silindirik bir kabuk üzerinde yapılan analizler, sunulan metodun güvenilirliğini ve etkinliğiniortaya koymaktadır.

Abstract

The dynamic interaction between an elastic struc- ture and a flowing fluid medium is an important as- pect in the design of various engineering applica- tions, such as flexible pipe lines conveying fluid,heat exchanger tubes in axial flow, inflatable damsin the presence of flowing water, etc. In all of thesesystems, fluid affects the dynamical behavior of thestructure strongly and in the extreme case maycause instability. A general 3-D hydroelastic method is presented forlinear dynamic analysis of structures subjected touniform axial flow. The developed numerical ap- proach is based on the fundamental principles oflinear hydroelasticity theory, where a weak couplingmethodology is preferred and co-use of finite ele- ment and boundary integral equation methods forelastic and fluid domains, respectively. By assumingthat the structure does not deform the fluid, but onlyaffects it through its elastic vibrations, the interestedproblem may also be taken as free or self-inducedvibrations of elastic structures under the influence ofhydrodynamic loads. The proposed numerical procedure is founded ontwo separate analysis: (i) evaluation of dynamiccharacteristics (natural frequencies and correspond- ing principal mode shapes) in the absence of anyexternal excitation and structural damping (vacuumanalysis), and (ii) by assuming that the elastic struc- ture preserves its in-vacuo mode shapes when incontact with fluid, and that each mode shape givesrise to a corresponding surface pressure distributionon the wet part of the structure, solution of the fluidproblem and calculation of the generalized fluid- structure interaction forces (wet analysis). In theformer stage, a standard finite element software(ANSYS) is adopted and in the latter one, the fluidproblem is converted to a boundary integral equa- tion over fluid-structure interface and solved nu- merically. In this investigation, it is assumed that thefluid is ideal (inviscid and incompressible) and itsmotion is irrotational. It is also assumed that theelastic structure vibrates at relatively high frequen- cies so that the effect of surface waves can be ne- glected. The resulting free surface condition is satis- fied implicitly by using method of images. Duringthe analysis, the interaction problem is consideredin two separate parts: (i) the vibration of the elasticstructure in a quiescent fluid and (ii) the disturbancein the main axial flow due to the oscillation of theelastic structure. Using the Bernoulli’s equation, the dynamic fluidpressure on the elastic structure is expressed interms of potential function, and interaction forcesare calculated from the pressure distribution overthe wetted surface of the structure, as generalizedadded mass, hydrodynamic damping and hydrody- namic stiffness coefficients, due to the inertia, Corio- lis and centrifugal effects of fluid, respectively. Bymerging the generalized structural matrices (massand stiffness) with the hydrodynamic matrices, aneigenvalue problem is obtained for the elastic struc- ture immersed in or containing flowing fluid, fromwhich the wet dynamic characteristics of the systemis obtained.In order to demonstrate the applicability of theproposed method, a circular cylindrical shell, simplysupported at both ends is studied. The cylindricalshell is considered, separately, with rigid andflexible extensions at its ends. A cylindrical shellwith rigid extensions corresponds to a finite length,flexible cylindrical shell connected to infinitely longrigid cylindrical baffles, of the same diameter as theshell at both ends and the cylindrical shell withflexible extensions coincides with one that isinfinitely long and periodically supported. To assess the influence of flowing fluid on thedynamic behavior of the shell structure, the non- dimensional eigenfrequencies are presented as afunction of the non-dimensional flow velocity. Theimaginary parts of the eigenfrequencies decreasewith increasing fluid velocity, and they reach zerovalues at certain axial fluid velocities, whichcorrespond to points of static divergence. Due to the gyroscopic conservative nature related with Coriolisforces, the cylindrical shell may regain stability withincreasing flow velocity and even for furthervelocities coupled mode flutter may also occur. Butboth of these are post-divergence behavior of theshell, involving large deformations and so cannot bedecided by a linear theory. In general, a very goodcomparison is obtained between the calculations ofthe present study and results found in the literature.