Eksenel akış etkisindeki plakların dinamik davranışlarının incelenmesi
Investigation of the dynamic behavior of flow induced plates
Yazar: FURKAN KUZGUN
Danışman: DOÇ. DR. BAHADIR UĞURLU
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü / Gemi İnşaat Mühendisliği Ana Bilim Dalı / Gemi İnşaatı ve Gemi Makineleri Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2020
Konu: Gemi Mühendisliği = Marine Engineering
Dizin: Akışkan-katı etkileşimi = Fluid-solid interaction ; Gemi inşaatı = Shipbuilding ; Serbest titreşimler = Free vibrations

Özet:
Yapı üstünde akışkanın neden olduğu etkileri saptamak ve etkilerin sebep olacağı bozunumları önlemek adına, dinamik etkileşimin kestirim uygulamalarına ihtiyaç duyulur. Gemi inşaatı, uçak, inşaat, vb geleneksel mühendislik alanları ya da biyomühendislik gibi görece yeni alanlarda akışkan-yapı etkileşimi kaynaklı problemlerin incelenmesi önemli olabilmektedir.
Temelinde bu çalışma, eksenel akış etkisinde düzlemsel basit bağlı plağın dinamik davranışını, lineer hidroeleastisite teorisinin ana ilkeleri doğrultusunda çözmeyi hedeflemiştir. Bu ilkeler doğrultusunda, farklı ortamlar için ayrı çözümler yapılmış ve çözümler birleştirilerek bütün bir sistem incelenebilmiştir. Problemde iki farklı sınır şartı çözümlerde uygulanmıştır. İlki, plağın akışkanda sonsuz derinlikte olacağı, bir diğeri ise ortamların etkileşimini sağlayan, akışkan-yapı arayüzündeki sınır şartıdır. Ayrıca akışkan ile etkileşimin plağın bir yüzeyinden olduğu kabul edilmiştir.  
Uygulanan çözüm yaklaşımı, yapısal sönüm ve dış kuvvetlerin yokluğunda elastik yapının dinamik karakteristiklerinin (doğal frekanslar ve karşılık gelen titreşim modları) belirlenmesi ve plak davranışının modal uzayda ifade edilmesi ile birlikte akışkan-plak etkileşiminin doğal modlar vasıtasıyla gerçekleştiği varsayımı ile akışkan probleminin çözülerek, etkileşim kuvvetlerinin kestirimi şeklindedir. Plak dinamik karakteristiklerinin tespit edildiği analizin 'kuru' safhası için sonlu eleman yöntemi Mindlin plak modeli üzerinde uygulanmış, akışkan-yapı etkileşim kuvvetlerinin hesaplandığı 'ıslak' safha içinse, etkileşim sonucunda ortaya çıkan akış alanını akışkan-yapı arayüzünde (plak yüzeyi) tanımlayan sınır integral denklem, sınır eleman yöntemiyle çözülmüştür. Akışkan ideal (viskoz olmayan ve sıkıştırılamaz) ve hareketi irrotasyonel kabul edilerek, yapının denge konumu etrafındaki küçük genlikli elastik titreşimlerinin akışkan ortamında neden olduğu hareketlenmeler (pertürbasyonlar), potansiyel akış modeliyle ifade edilmiştir. Akışkan ortamının sonsuza uzandığı varsayımıyla serbest yüzey etkileri ihmal edilmiştir.
Akışkan kuvvetleri ile yapısal hareket denkleminin çözümünden, yapı davranışında belirleyici rolü olan kararsızlık durumları ortaya çıktığı gözlemlenmiştir. Plakta gözlenen kararsızlıklar yapının giderek büyüyen genliklerde hareket ettiği anlamına gelmektedir. Bu sebepten kararsızlık durumlarının doğru tespiti için yapısal nonlineerliklerin çözüme katılması gerekmektedir. Ayrıca, tez kapsamındaki uygulamalar basit mesnetli plaklarla sınırlı kalmış olsa da, yöntem plağın tüm kenarı boyunca bağlı olduğu bütün sınır şartları için uygulanabilirdir. Bununla birlikte, konsol plak gibi belirli kenarların serbestçe hareket edebildiği sınır şartları için, serbest uçlarda oluşacak girdap etkilerini dikkate alabilen yeni bir akışkan-yapı etkileşim modeline ihtiyaç vardır.
Önerilen analiz yöntemi ile varılan sonuçların, ticari sonlu eleman yazılımları ve literatürde yer alan çalışmaların sonuçlarıyla uygunluk içerisinde olduğu saptanmıştır.

Abstract:
Understanding the behaviour of plate in fluid is an important task for engineering design process. In different engineering fields such as marine, civil, mechanical, aeronaustic and bioengineering is encountered with fluid structure interaction problem. Simulation of interaction problems help to predict structural deformation and structure dynamics for engineering applications. 
This thesis is aimed to examine the dynamic behaviour of a simple supported plate that is subjected to uniform axial fluid flow from one surface. Examined problem is based on linear hydroelasticity equations. It is facilitate to solve problem seperatly as fluid and structural stage. Thus, the solution of the interaction problem is made with different solution method. Furthermore, interaction of fluid and structure are made through help of kinematic boundary condition on plate surface. So, solutions is coupled  and solved as an one stage.
In this thesis, it is assumed that the presence of the structure in the fluid did not cause any deterioration in the fluid domain. The interaction with fluid just took place with natural mode shapes of the plate.  So, the problem could be considered as the dynamic analysis investigation of the plate that vibrates with natural mode under the fluid domain.
Presented numerical procedure is founded on two separate analysis. The first analysis is made to get the result of the natural frequencies and corresponding principal mode shapes in dry state (condition that no fluid effect). Structural damping and environmental forces are neglected in the solution of dry state. In the second analysis, the fluid force values is calculated according to dynamic values of plates in dry state. These forces would impact separately to acceleration, speed and deformation expressions of the equation of motion. So, the two system could be expressed as one system.
In first solution of problem, a code study is made in the Matlab software program to calculate the dynamic values of plate (natural frequency values and mode shapes) in dry state. The code provide generalized finite element solution to get results of plate's dynamic values for any aspect ratio and thickness of plate in simple supported condition. The dynamic values are calculated with eigenvalue and eigenvector solutions. Eigenvalues give a results of plate's natural frequencys and eigenvector give a results of mode shapes corresponding to natural frequencys. Dry state of solutions are made in basis of Mindlin plate theory. 
The Mindlin plate theory is defined as the thick plate theory. It causes wrong results in thin plate solutions because of the shear-locking problem. The reduced integration method is included to the generalized finite element solution to deal with shear-locking problem for the solutions of thin plates of the Mindlin plate theory.
Mesh elements are necessary for the solution of the finite element method. The mesh elements are created as linear isotropic finite elements that have four nodes at each corner and each node has three degrees of freedom. The dynamic values of dry state are compared with the Ansys software program results. Shell181 type elements are used in Ansys software program. These elements are classified as linear isotropic type elements in Ansys. In addition, the convergence criteria of the natural frequency (in dry state) values are examined according to the increasing number of mesh elements.
First boundary condition employed in the system is that surface normal direction velocities at the interface between fluid and structure are equal. It is mean that the elastic vibration movements of the structure at the direction of the surface normal excite the fluid domain with the same velocity at the interface between fluid and structure. The other boudary condition, the plate is considered to be located at an infinite depth in the fluid. With this assumption, the effect of structure movement is considered to be zero at the infinite boundary of the fluid.
The fluid is assumed ideal (inviscid and incompressible) and its motion is irrotational. Small elastic vibrations move the fluid domain and that movement cause perturbation velocities. Perturbation velocities are assumed to be expressed as the potential gradient in this thesis. Using the Bernoulli's equation, the dynamic fluid pressure is expressed in terms of potential function, so that the fluid-structure interaction forces are calculated from pressure distribution on the wetted surface, as generalized added mass, hydrodynamic damping and hydrodynamic stiffness, due to the inertial, Coriolis and centrifugal effects of fluid, respectively. By merging the generalized structural matrices (mass and stiffness) with the hydrodynamic matrices, an eigenvalue problem is obtained, from which the dynamic characteristics of the structure is achived. 
In second solution of problem, a boundary integral solution is created to determine the changes in the fluid perturbations caused by the elastic vibrations of the structure. A boundary integral solution is made for Laplace equation under the given boundary conditions. So, potential values at the wetted surface are obtained.
The structure is exposed to the added-mass effect only in the quiescent fluid. Corilousis and centrifugal effects are revealed with the flowing flow in addition to the added-mass. Added-mass increases the inertia value of the structure; so, it causes a decrease in the frequency values. The centrifugal effect causes negative elasticity to the plate and its effect decreases all frequency value. Corilousis effect is responsible to plate damping and it plays important role for the plate instabilitys.
The centrifugal effects may completely remove the elasticity of the structure at a certain fluid velocity. The state of the plate at this velocity is expressed as a static instability (divergence). The plate does not vibrate in the mode that causes the static instability situation, but, displacements are so high at this mode. In this thesis, static instability is observed in the first mode of the plate.
The other type instability emerge in flowing fluid is the dynamic instability (couple mode flutter). In this thesis, first and second modes are coupled in a certain flow velocity (after the static instability condition) and so, it is caused the dynamic instability. Coriolis forces are the main effects to emerge the dynamic instability because which have a responsible of damping on the structure. When fluid velocity increase, damping effect tends to gradually decrease. At certain velocity, transfared energy to the plate from fluid is reach to positive value. At this stage, the plate vibrates at first two modes but the plate vibration is large. This post-divergence behavior, however, can be considered purely theoretical, since the linearity assumption becomes obsolete after the onset of divergence.
Static and dynamic instabilities have large deformations. This could exceed the linear limits of the plates. For this reason, to determine behavior of the plate's instability conditions with the linear structural assumption is obsolete. For this reason, it would be more appropriate to determine the plate's instability behaviors by including structural nonlinearities to the solutions. Beside of this, the presented method is not valid for all types of plate supports. In cantilever plates, for example, an energy transfer mechanism from flow to plate is developed and the present fluid model should be modified to consider the accompanying vortices.
The response of fluid-structure systems to any external excitation (wave forces, propulsion forces, etc.) could be analyzed, by adopting the mathematical model with using the computed wet dynamic characteristics. Comparison are made with result the literature and commercial finite element program for several characteristic (wet frequencies, dry frequencies, dry mode shapes) that clearly show the reliability and effectiveness of the method.