Bir uçak dış yükü yapısının dinamik davranışının incelenmesi /
Yazar: HALİT S TÜRKMEN
Danışman: DOÇ.DR. ZAHİT MECİTOĞLU
İstanbul Teknik Üniversitesi / Fen Bilimleri Enstitüsü
Derece: Yüksek Lisans, 1993
Konu: Uçak Mühendisliği = Aircraft Engineering
Dizin: Bomba adaptörleri = Bomb adapters ; Dinamik davranış = Dynamic behavior ; Dış basınç = External pressure ; Savaş uçakları = Fighter aircrafts

Özet:
ÖZET Birinci bölümde adaptör yapısının titreşimlerinin öneminden bahsedilmiştir. Bu bölümde yapı genel olarak tanıtılmış ve buna benzer yapılar ile ilgili çalışmalardan örnekler verilmiştir. İkinci bölümde adaptör yapısını meydana getiren yapı elemanları tanıtılmıştır. Bu yapı elemanlarının analizlerinin yapılabilmesi için kullanılan yaklaşımlar ele alınmıştır. Yapının büyük çoğunluğunu meydana getiren kabuklar hakkında geniş ölçüde bilgi verilmiş ve kullanılan varsayımlar anlatılmıştır. Yapının diğer kısımlarını meydana getiren çubuklar ve kirişler ele alınmış ve çubuk ve kiriş yapılar için yapılan kabuller anlatılmıştır. Yapılan kabullerin ışığı altında tüm yapı elemanları için potansiyel ve kinetik enerji ifadeleri elde edilmiştir. Yapının dinamik analizi için Hamilton prensibi yazılmıştır. Üçüncü bölümde adaptör yapısının modellenmesinde faydalanılan sonlu elemanlar metodu anlatılmıştır. Yapının dinamik analizi için Hamilton prensibinden faydalanılarak sonlu eleman formülü elde edilmiştir. Adaptör yapısının modellenmesinde kullanılan sonlu elemanlardan bahsedilmiştir. Adaptör yapısının modellenmesinde ve dinamik analizinde kullanılan I-DEAS yazılımı tanıtılmıştır. Yapının modellenmesinde kullanılan elemanların katılık ve kütle matrislerinin elde edilmesinde nasıl bir yol izlendiği anlatılmıştır. Dördüncü bölümde adaptörün temel parçalarının sonlu elemanlar ile modellenmesinde nasıl bir yol izlendiği ve sayısal çözüm tekniği anlatılmıştır. Beşinci bölümde sonuçlar üzerinde durulmuştur. Yapının serbest titreşim frekansları ve mod şekilleri ilk altı mod için elde edilmiştir. Ara takviyelerin, gövde bağlantı ve taşıma profillerinin ve yükleme durumunun titreşim frekanslarını ne şekilde etkilediği ele alınmıştır. Vll

Abstract:
DYNAMIC BEHAVIOR OF AN EXTERNAL STORAGE OF AIRCRAFT SUMMARY In this thesis, the free vibration of a bomb adapter structure has been reviewed in detail. The bomb adapter is a structure that consists of shells, beams and rods. This bomb adapter carries bombs and rockets as loads. In the first chapter, the importance of the vibration of the adapter structure has been highlighted. In this chapter, the structure has been introduced briefly. Also several studies related to the cylindrical shell structures have been reviewed. Additionally, several studies about stiffened shell structures have been presented. In the second chapter, the structural components those form the adapter have been introduced. The assumptions which are used for analyzing similar structures have been reviewed. The most of the adapter structure has been consisted of shells. Therefore, the shell structures have been reviewed. The basic equations which describe the behavior of a thin elastic shell were originally derived by Love in 1888. These equations, together with the assumptions upon which they are based, form a theory of thin elastic shells which is commonly referred to as Love's first approximation. In this chapter, the basic differential equations of the first approximation have been derived using, as a basis, E. Reissner's version of the Love theory. In the three dimensional theory of elasticity, the fundamental equations occur in three broad categories. Thus, it has been recalled that in elasticity we have equations of motion which are obtained from a balance of the forces acting on some fundamental element of the medium considered, that we have strain-displacement relations which are obtained from a strictly geometrical consideration of the process of deformation, and that we have the constitutive law of elasticity which is introduced in order to provide a relationship between the stresses and the strains in the elastic medium. However, the solution of problems in the three-dimensional theory of elasticity involves vast complications. Thus, a group of simplifying assumptions that provide a reasonable description of the behavior of thin elastic shells was proposed by Love and has led to the development of a subclass of the theory of elasticity known as the theory of thin elastic shells. Love's first approximation to the theory of thin elastic shells is based upon the following postulates: vm1. The shell is thin. 2. The deflections of the shell are small. 3. The transverse normal stress is negligible. 4. Normals to the reference surface of the shell remain normal to it and undergo no change in length during deformation. The rest of the adapter structure consists of beams and rods. Beams and rods are assumed to be one dimensional structures. Therefore, the cross section of these structures moves as a rigid plate. This movement consists of a translational displacement and a rotation. Equations of motion have been derived by using Hamilton's principle Hamilton's principle states that the actual path followed by a dynamical process is such as to make 8j(n-T)dt = 0 That is, the integral of (n - T) takes an extremum value which can be shown to be a minimum. In the third chapter, the method for modeling the adapter structure has been explained in detail. The structure of adapter has been modeled by using the finite elements method. The basic structural components of adapter have been discretized using appropriate finite elements. A finite element is a subregion of a discretized continuum. It is of finite size and usually has a simpler geometry than that of the continuum. The finite-element method enables us to convert a problem with an infinite number of degrees of freedom to one with a problem with a finite number in order to simplify the solution process. Although the original applications were in the area of solid mechanics, its usage has spread to many other fields having similar mathematical bases. In any case it is a computer-oriented method that must be implemented with appropriate digital computer programs. The finite-element approach yields an approximate analysis based upon an assumed displacement field, a stress field, or a mixture of these within each element. The assumption of displacement functions is the technique most commonly used. The following steps suffice to describe this approach: 1. The continuum is divided into a finite number of subregions of simple geometry. 2. Key points were selected on the elements to serve as nodes, where conditions of equilibrium and compatibility are to be enforced. 3. Displacement functions are assumed within each element so that the displacements at each generic point are dependent upon nodal values. IX4. Strain-displacement and stress-strain relationships are satisfied within a typical element. 5. Stiffness and equivalent nodal loads were determined for a typical element using work or energy principles. 6. Equilibrium equations are determined, and these equations are solved. It is required that, in fact, a solution technique which is numerically stable, easily programmed and can be adapted to a wide range of problem types without excessive interference by the user. From a structural viewpoint the finite element method provides the most satisfactory solution technique in this category. The essence of the finite element method involves dividing the structure into a suitable number of small pieces called finite elements. The intersections of the sides of the elements occur at nodal points or nodes and the interfaces between element are called nodal lines and nodal planes. For structural problems involving static or dynamic applied loads it will be defined the behavior of the structure in terms of displacements and/or stresses. Within each of the elements it is needed to select a pattern or shape for the unknown displacement or stress. In the case of a displacement field the shape function defines the behavior of displacements within an element in terms of unknown quantities specified at the element nodes. These nodal values are known as nodal connection quantities and allow the deformation behavior in one element to be communicated to adjacent elements. For free vibration analysis of the adapter structure, the equation of motion has been obtained by using Hamilton principle. This equation has been obtained as follows: MQ+KQ=0 For a specific element type (beam, plate, shell, etc.), the shape functions are identical for each element. Thus, a given element need only be programmed once and the computer can repeat the operations specified for one, general, element as often as required. Finite elements which were used for modeling of adapter structure have been introduced. These are shell, beam, rod, rigid, and mass elements. Two different types shell elements have been used: Quadrilateral and triangle. The derivation of element equations for one-dimensional structural element has been considered in this section. These elements can be used for the analysis of bar type systems like planar trusses, beams, continuous beams, planar frames, grid systems and space frames.A rod element is a bar which can resist only axial forces (compressive or tensile) and can deform only in the axial direction. It will not be able to carry transverse loads or bending moments. In the two dimensional analysis, each of the two nodes can have components of displacement parallel to X and Y axis. In three dimensional analysis, each node can have displacement components in X, Y and Z directions. A beam element is a bar which can resist not only axial forces but also transverse loads and bending moments. In the analysis of planar beams, each of the two nodes of an element will have two translational displacement components (parallel to X and Y axes) and a rotational displacement (in the plane XY). For a space beam element, each of the two ends is assumed to have three translational displacement components (parallel to X, Y and Z axes) and three rotational displacement components (one in each of the three planes XY, YZ and XZ). It will be argued by many shell experts that when it is compared the exact solution of a shell approximated by flat facets to the exact solution of a truly curved shell considerable differences in the distribution of bending moments, etc., occur. This is undoubtedly true, but for simple elements the discretization error is approximately of the same order and excellent results can be obtained with the flat shell element approximation. In a shell, the element will be subject, generally, both to bending and 'in-plane' forces. For a flat element these cause independent deformations, provided the local deformations are small, and therefore the ingredients for obtaining the necessary stiffness matrices are available. In the division of an arbitrary shell into flat elements only triangular elements can be used. Although the concept of the use of such elements in the analysis has been suggested as early as 1961. The success of such analysis was hampered by the luck of a good stiffness matrix for triangular plate elements in bending. Some shells, for example those with general cylindrical shapes, can be well represented by flat elements of rectangular or quadrilateral shape. With good stiffness matrices available for such elements the progress here has been more satisfactory. For many practical purposes the flat element approximation gives very adequate answers and indeed permits an easy coupling with edge beam and rib members. A linear shell element consists of a plate bending and a plane stress element. For a shell element, each node can have three translational displacement components in X, Y and Z directions and three rotational displacement components one in each of the three planes XY, YZ and XZ. XIIn the fourth chapter, modeling of the adapter structure and solution technique have been mentioned. In the free vibration analysis of the adapter structure with finite elements method, the I-DEAS software has been used. I-DEAS software consists of drafting, solid modeling, finite element modeling and system dynamic analysis families. In this thesis, solid modeling and finite element modeling families have been used. The adapter structure has been modeled as a surface in the solid modeling family. Then this surface has been divided into quadrilateral and triangle shell elements in the finite elements modeling family. One dimensional stiffening structures have been modeled by using beam and rod elements. Bombs and some connecting parts have been modeled by using mass elements. The adapter body-launcher connection points have been modeled by using rigid elements. The finite element model of adapter has been restrained at two nodes where the adapter is connected to the aircraft wing. The free vibration analysis of adapter has been done in the I-DEAS finite element modeling model solution task. The adapter structure has been analyzed for five different stiffening cases. However, adapter structure has been analyzed with various bombs and rocket loads. For each case, the first six mode shapes and frequencies have been obtained. For the free vibration analysis of adapter structure, the simultaneous vector iteration method has been used. The vector iteration method assumes that the natural frequencies are distinct and well separated such that, oI<©2< <©". In the simultaneous vector iteration technique, it is applied to the eigenproblem in standard form, that is The method converges to the highest eigenvalue of A. Therefore the stiffness matrix K is expressed in the form K = LlJ and the mass matrix is expressed in the form A = L'MLT. In the fifth chapter, the natural frequencies and mode shapes of adapter structure has been obtained for different stiffening and load cases. In the case of removal of some stiffeners, it has been observed decrease in the natural frequencies. In the case of removal bombs and rockets, it has been observed increase in the natural frequencies. These natural frequencies' values have been presented in a table. Mode shapes have been presented in the figures. First mode shape shows those lateral vibrations. The other mode shapes show that extensional vibrations. XllThe natural frequencies obtained in the result of free vibration analysis of adapter structure can be used determining the fatigue life of the structure. However, knowledge of these characteristics is necessary for the determination of structural integrity. xiu