Vibration control of a laminated com-posite plate subjected to blast loading

Bu sayısal çalışmada, bir kenarından ankastre olarak mesnetlenmiş konsol bir plağın üzerine etkiyen anlık basınç yükü nedeniyle oluşan titreşimler, plak üzerine yerleştirilmiş piezoelektrik uyarıcılarla kontrol edilerek sönümlenmiştir. Anlık basınç yükü modeli için zamana bağlı olarak üstel bir biçimde azalan Friedlander fonksiyonu kullanılmış ve bu fonksiyondaki parametreler için deneysel çalışmalardan elde edilen değerlerden yararlanılmıştır. Plağın sonlu eleman modelinin oluşturulması için bilinen semiloof kabuk eleman ile piezoelektrik etkilerin eklendiği semiloof kabuk sonlu eleman modeli kullanılmıştır. Sonlu eleman modelinin serbestlik derecesi yüksek olduğundan ve günümüzün modern kontrol yöntemlerinde yaygın olarak kullanılan durum denklemleriyle sistemin ifade edilmesi halinde serbestlik derecesinin ikiye katlanması nedeniyle sonlu eleman modelini indirgemek için mod toplama yöntemi ile indirgeme işlemleri yapılmıştır. Bu işlemler sonucunda elde edilen plak modelinin statik ve dinamik analizleri yapılmıştır. Plak aynı zamanda ANSYS yazılımı ile de modellenerek statik ve dinamik analizlerin sonuçları karşılaştırılmış ve bu sonuçların uyumluluğu gösterilmiştir. İndirgenmiş plak sonlu eleman modelinden sistemin durum denklemleri elde edilmiştir. Kararlılık sınırında bulunan sistemin kararlı olmasını garantilemek için optimum doğrusal regülatör problemi (optimal linear regulator problem, LQR) araştırılmıştır. Duyargalardan ölçülen deplasman değerlerini kullanarak sistemin durumlarını tahmin edecek gözleyicili bir kontrol sistemi ile oluşan yapısal titreşimler başarılı bir şekilde kontrol edilmiş ve sönümlenmiştir.Anahtar Kelimeler: Titreşim kontrolü, durum gözleyici, semiloof kabuk eleman, piezoelektrik, anlık basınç yükü.Plates and shells are the most widely used elements in aeronautics industry and the use of layered composite materials in the manufacturing of these parts is increasing. Layered composite materials, commonly used in aerospace structures, are chosen as plate material. Still, applications of smart structures which involve the use of piezoelectric parts not only in the desired shape changes of command and control surfaces of aeronautics and space structures, but also in vibration suppression, is one of the most popular research subjects. For this reason, static and dynamical analyses of these types of structural parts are very important. In this numerical study, vibrations of a cantilever composite plate subjected to blast loading are controlled and suppressed by the use of piezoelectric actuators. The dynamic responses of structures under blast loading have been investigated in many applications. Blast loading depends on magnitude and orientation of the blast pressure, geometry and size of the surface that the shock wave encounters and on the distance from the detonation source. Commonly, Friedlander exponential decay function can be used for expressing uniform time dependent blast loading which affects object surface through normal direction. Various parameters of the equation can be obtained from some of the experimental studies. Piezoelectric materials also have been investigated in many applications. Piezoelectric elements are used for controlling and suppression as preferred widely in recent years. The development of piezoelectric composite materials offers great potential for use in advanced aerospace structural applications. For a material to exhibit an anisotropic property such as piezoelectricity, its crystal structure must have no centre of symmetry. The piezoelectric effects can be seen as transformations between electrical and mechanical energy. That is linear piezoelectric constitutive equations include electromechanical coupling. Semiloof shell finite element including piezoelectric effects is used for finite element modeling of the plate. Semiloof shell element is one of the most efficient elements for solution of shells having arbitrary geometry and it accounts for both membrane and bending actions. Three displacement degrees of freedom at the corner and mid-side nodes are sufficient for defining the membrane action. The rotations at loof nodes are necessary to impart C1 continuity and account for bending action. Stiffness, mass and damping matrices which express the structural model are obtained from the semiloof shell finite element. In order to reduce the degrees of freedom of the finite element model, mode summation method is used with weighted modal vector including dominant modes in the dynamic behavior. Calculated results of the static and dynamic analyses of the plate are compared with those modeled by using Ansys software. A good agreement is observed. After noticing the good agreement between dynamic and static analysis, state-space equations are obtained from the reduced finite element model. The system of equation must satisfy the controllability condition in order to be taken under control. If this system is also desired to be controlled by using a state observer, it must satisfy the observability condition. Optimal linear quadratic regulator (LQR) problem has been investigated to guarantee the stability of the system on the stability edge due to neglecting structural damping. In this work, both piezoelectric pairs were used as actuators. This change doubled the force used in vibration suppression. In this case the voltages applied to the piezoelectric actuators are determined by employing state observer feedback control system which estimates all states by using displacements of some specific points of the plate. Structural vibrations due to blast loading have been successfully controlled and suppressed by using a state observer feedback control system. This study will provide noteworthy supports for experimental works in this area in the future. Vibration control of plates under different loads such as random or harmonic can be investigated by using different control strategies in experimentally or numerically. The influence of different boundary conditions and addition of stiffeners to the plate on structural vibrations and vibration control can also be investigated. Furthermore, some issues like nonlinear effects on plate deformations and adding structural damping are needed to be explored.Keywords: Vibration control, state observer, semiloof shell element, piezoelectric, blast loading

In-plane quasi-static compression deformation of Ti6Al4V double arrow-headed lattice structures fabricated by electron beam powder bed fusion process: Build orientation, scan speed and failure mechanism

Eren Z., Gokcekaya O., Nakano T., et al. In-plane quasi-static compression deformation of Ti6Al4V double arrow-headed lattice structures fabricated by electron beam powder bed fusion process: Build orientation, scan speed and failure mechanism. Journal of Materials Research and Technology 27, 6192 (2023); https://doi.org/10.1016/j.jmrt.2023.11.027.The 2D double arrow-headed (DAH) lattice structures, which are promising cellular structures for impact mitigation, remain relatively unexplored in terms of their compression response when manufactured using the powder bed fusion process with Ti6Al4V (Ti64) alloy. This study aims to investigate the effects of build orientation and beam scan speed of Electron Beam Powder Bed Fusion (PBF-EB) process on the energy absorption of 2D Ti64 DAH lattice structures. Additionally, potential microstructural variations due to adjusted process parameters can be linked to different levels of energy absorption. For the compressions, the lattice structures were manufactured at two build orientations (0° and 45°), using three different beam scan speeds: speed function (SF), low speed (LS), high speed (HS). In micro-characterizations, the unit cells of 0deg-LS exhibited the lowest micro-porosity level at 0.12 %. Based on KAM values, thin struts at unit cells had higher residual stresses than thick struts, contributing to the initiation of failure locations. The compressions revealed that the 0deg-LS group absorbed 21.6 % and 24 % more energy than 0deg-SF and 0deg-HS groups, respectively, at compressions of 33 %. 45° samples absorbed approximately 10 % more energy than 0° samples except HS groups. The lowest micro-porosity of 0deg-LS contributed to having the highest energy absorption among 0deg samples. As the residual stresses in KAM values did not differ strongly with varying beam speed, varied energy absorptions were not linked to them. An optimization of the numerical compressions helped obtain designs with higher energy absorption and less relative volume. This study provides valuable insights into Ti64 cellular applications constrained with 2D-type designs

Comparison of in-plane compression of additively manufactured Ti6Al4V 2D auxetic structures: Lattice design, manufacturing speed, and failure mode

Eren Z., Gokcekaya O., Balkan D., et al. Comparison of in-plane compression of additively manufactured Ti6Al4V 2D auxetic structures: Lattice design, manufacturing speed, and failure mode. Materials and Design 241, 112885 (2024); https://doi.org/10.1016/j.matdes.2024.112885.The metal-based 2D auxetic lattice structures hold the potential for multifunctional tasks in aerospace applications. However, the compression response of those manufactured by powder bed fusion process is underexplored. This study proposes a comprehensive comparison of in-plane quasi-static compression performance of 2D auxetic lattice structures, utilizing three designs (anti-tetrachiral (ATC), double arrow-headed (DAH), and tree-like re-entrant (TLR)), manufactured with stiff Ti6Al4V by the electron beam powder bed fusion process (PBF-EB) with various manufacturing speeds. The results revealed unique failure patterns and superior energy absorptions among 2D lattice structures in the literature. TLR design enhanced energy absorption by overcoming failures between DAH columns and exhibited the lowest standard deviations in specific energy absorption (SEA) values (9.75 %–12.62 %). Besides, Kernel average misorientation (KAM) values followed the order of DAH, TLR, and ATC, and inversely correlated with SEA values. ATC structures with the lowest KAM outperformed DAH and TLR by 47.5 % and 6.44 %, respectively. Scan speed variations affected SEA and porosity values differently for each lattice design while exhibiting similar microstructure characteristics. The findings in this study propose a significant contribution to the development of aerospace sandwich structures where harsh environments exist and employment of 2D topologies are required

Evaluation of metabolic profiles of Saanen goats in the transition period

ΔΕΝ ΔΙΑΤΙΘΕΤΑΙ ΠΕΡΙΛΗΨΗHealthy Saanen goats (n=30) in periparturient period were used in the present study. Blood samples were collected 21, 14 and 7 days before parturition, at the time of birth and postpartum days 7, 14 and 21. Non-esterifiedfatty acids (NEFA), betahydroxy butyric acid (BHBA), Total protein (TP), albumin (ALB), blood urea nitrogen (BUN), creatinine (CREA) aspartate amino transferase (AST), gamma glutamyl transferase (GGT), sorbitol dehydrogenase (SDH), glucose (GLU), cholesterol (CHOL), triglyceride (TG), calcium (Ca), phosphorus (P), and magnesium (Mg) levels were evaluated. During the study period, NEFA, SDH, CREA levels increased and CHOL and TG levels decreased at time of parturition. When the changes of parameters in prepartum and postpartum period were compared, the concentrations of NEFA, CHOL, GLU, TG, Ca were higher (p <0.001) in prepartum period;however BHBA, Mg, ALB, GGT, AST, TP, P, BUN, SDH and CREA concentrations were detected to be higher (p <0.001) in postpartum period. Metabolic Profile Test based on biochemical parameters evaluated in our study would be beneficial for diagnosis, prevention and control of diseases such as pregnancy toxemia, hypocalcemia, infertility in goats

500 KW Rüzgar Türbini İçin Ana Şaft Tasarımı Ve Analizi

Konferans Bildirisi -- Teorik ve Uygulamalı Mekanik Türk Milli Komitesi, 2013Conference Paper -- Theoretical and Applied Mechanical Turkish National Committee, 2013Bu çalışmada, 500 kW güç üreten bir rüzgar türbinin ana şaftının tasarımı ve yapısal analizleri yapılmıştır. Ana şaftın boyutlandırılmasında yorulma kriterlerinin esas alınması gerekmektedir. Ana şaftın yorulmaya ait yük durumu ise literatürde bulunan ampirik formüller kullanılarak hesaplanmıştır. Yorulma analizlerinde şaftı çevrimsel yüklerle zorlayan rotor ağırlığının yanında rüzgar kesmesi ve kule blokaj etkisi vb. sebeplerle ortaya çıkan değişken eğilme momenti ve tork değerleri de hesaba katılmıştır. Ana şaftın kritik kesitlerindeki çap hesabı, ASME Eliptik yorulma kriteri kullanılarak sonsuz ömre göre yapılmıştır. Ana şaftın tasarımındaki kritik bölgeler şaftın yataklandığı bölge ve şaftın dişli kutusuna bağlandığı bölgedir. Ayrıca, kontrol amaçlı olarak Uluslararası Elektroteknik Komisyonu’nun (International Electrotechnical Commision) yayınlamış olduğu IEC 64100-1 standardında belirtilen yükleme şartları için ana şaftın statik analizleri ANSYS 14.5 sonlu elemanlar yazılımı kullanılarak gerçekleştirilmiştir. Şaftın sonlu eleman modeli SOLID185 elemanlar kullanılarak oluşturulmuştur. Ayrıca, ana şaft - göbek bağlantı elemanlarının analizi de bu çalışma kapsamında yapılmıştır. Sayısal ve analitik yöntemler kullanılarak elde edilen deformasyon ve gerilme sonuçları karşılaştırılmış ve iyi bir uyum olduğu görülmüştür.In this paper, the main shaft which is one of the important structural parts for a 500 kW wind turbine has been designed. The fatigue criteria has been based on sizing the main shaft. The main shafts critic desing loads have been calculated by empirical formulas which are on the literatures. Oscillation moments of the torque and the flexural moments which is created by wind share, and effect of tower, etc. have been envisaged for analytical and numerical studies. In this study, the main shaft has been designed for infinite life using with ASME Elliptic criteria. There are two critic areas which are supported and connected to the gear box. In addition Iternational Electrotechnical Commision (IEC) 64100-1 standards have been based on the critic design load cases. The main shaft and the fasteners are modeled using the finite element method. The finite element model of the shaft is designed using with SOLID185 elements. Its static analysis have been achieved with using ANSYS 14.5 software. Also a comparison of two different approximations have been mentioned in this paper. The values of analitic and numerical of deplacement and stress are compared each

Otobüslerde Kullanılan Plastik Yakıt Tanklarının Statik Ve Dinamik Analizler Yardımıyla Dayanımının İncelenmesi

Konferans Bildirisi -- Teorik ve Uygulamalı Mekanik Türk Milli Komitesi, 2015Conference Paper -- Theoretical and Applied Mechanical Turkish National Committee, 2015Günümüzde, otobüslerde kullanılmakta olan konvansiyonel metal yakıt tankları yerini plastik yakıt tanklarına bırakmaktadır. Bu makalede, plastik yakıt tanklarının, statik ve dinamik analizlere dayalı, bilgisayar destekli, geliştime-tasarım projesinn bir kısmı sunulmuştur. Öncelikle, plastik malzemenin mekanik özelliklerini bulmaya yönelik kupon testleri gerçekleştirilmiştir. Statik analizlerde yakıt tankına eşdeğer yükler uygulanmıştır. Dinamik analizler ise zamanla değişen yük, yakıt ve tankın atalaet momentleri göz önüne alınmış ve modal transient analiz yöntemi kullanılmıştır. Statik analizlerde, eşdeğer statik yükleme yaklaşımı kullanılmaktadır. Yapılan dinamk analizlerde, akışkan akustik elemanlar kullanılarak modellenmiştir. Yakıt tankı farklı doluluk oranları için incelenerek karşılaştırılmış ve sonuçları bu bildiride paylaşılmıştır.Nowadays, the conventional metal fuel tanks used in buses are being replaced with plastic fuel tanks. In this paper, a part of the project which aims to develop a computer aided methodology for developing/designing of the plastic fuel tanks based on static and dynamic analysis is presented. Coupon tests are first conducted to acquire the mechanical properties of the plastic material. In the static analysis, equivalent static loads are applied to the fuel tanks. In the dynamic analysis, the time varying loading and the inertia of the fluid and fuel tanks are taken into account using modal transient analysis. Fluid which is in the tank is modeled with acoustic approach in dynamic analysis. In this paper, different fullness ratios of the fuel tank are investigated and both results are compared each other

Free vibrations of stiffened circular cylindrical shells

Tez (Doktora) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1988Thesis (Ph.D.) -- İstanbul Technical University, Institute of Science and Technology, 1988Yapısal titreşimler hava ve uzay araçlarının yorulma dayanımı vb araç. içindeki mekanik ve elektronik aksamın sağlıklı olarak çalışması bakımından oldukça önemlidir. Yapının dinamik davranışının belirlenmesi için serbest titreşimlerin incelenmesi gerekmektedir. Bu çalışmada uçak ve roketlerin yarı-monokok gövde yapıları göz önünde bulundurularak bir takım takviye kirişleri ve çerçevelerle desteklenmiş silindirik kabuk yapının doğal -.frekansları ve mod şekilleri incelenmiştir. Kabuk yapı için birinci mertebe Love yaklaşımına dayalı ince kabuk teorisi kullanılmıştır. Hareketin varyasyonel denklemi Hamilton ilkesi yardımıyla yazılmıştır. Takviye parçalarının katkısı ortotropik malzeme yaklaşımıyla kapsama alınmıştır. Serbest titreşim probleminin çözümüne sonlu elemanlar yöntemiyle yaklaşım yapılmıştır. Bu amaçla izo- parametrik bir eleman olan sekiz düğüm noktalı semiloo-f eleman kullanılmıştır. Karakteristik matris denklem elde edilerek Sturm dizisi özellisine dayalı bisection yönte miyle özde>3erler elde edilmiştir. özvektörler tersiterasyonla bulunmuştur. Uçlarından kesme diya-f rami arıyla mesnetlenmi ş takviyeli silindirik yapıların doğal -frekansları ve mod şekilleri belirlenmiştir. Dolu dikdörtgen kesitli takviye parçalarıyla desteklenmiş bir silindirik kabuk için.frekansların takviye aralıklarıyla ve takviye parçalarının boyutlarıyla demişimi incelenmiştir. İkinci bir çalışma olarak pro-fii kesitli takviye kirişi ve çerçeveler kullanılmış ve -frekansların takviye aralıklarıyla, silindirik kabuğun boyu ile demişimi araştırılmıştır. Ayrıca üzerinde dikdörtgen şeklinde bir oyuk ve kalınlık artışı bulunan takviyeli silindirik kabukların doğal frekansları elde edilmiştir.The importance of structural vibration to the operation o-f electronic and mechanical equipment, and to the strength o-f structural elements in a missile or aircraft, rests on the -fact that it supplies one of the environmental conditions in which these items must operate. The major adverse e-f-fects o-f vibration on these items are the shortening of life due to wearing or metal fat i que and the production of spurious actuations or signals which preclude proper performance of the component. Vibration of aircraft and missiles is produced by a complicated system of forces and dynamic loads. Some of these forces are applied to the structure of the vehicle by other solid bodies, such as the ground or the engines. Such forces are localised and are propagated mechanically through the vehicle by its structural members. Aerodynamic forces are aplied to the structure by the surrounding air and are spatially distributed over the surfaces of the vehicle. Thin shell structures are used in many branches of technology, such as aerospace engineering, building construction, mechanical. engineering, ship building, chemical engineering, and nuclear reactor engineering. The theory of shells is therefore an important, "'«hject in structural mechanics. A three dimensional linear elasticity analysis is undoubtedly the most accurate linear analysis possible, especially for very thick shells. However, even today with large-capacity, high-speed computers available, such an analysis is seldom used in structural dynamics except in the case of simple geometrical configurations such as a cylinder or sphere. In practice, linear thin shell equations are commonly used and the most of them are based on Kirchhof f -Love hypothesis E33. On the other hand, some theories were presented in order to improve Love's first approximation shell theory [11-143. Some shear theories has been developed considering to be inconsistent to omit the transverse shear strains in the Love second- approximation theory C 20-22 3. VI i Plate and shell type structures stiffened with beam type elements are extensively utilised in the constructions of aircraft, missile and ship. The analyses of stiffened shells may he conveniently divided into two categories; those which consider the stiffeners to be closely spaced in order to average or "smear" the stiffening effects over the surface of shell, and those which consider the stiffeners as discrete elements. A considerable body of literature dealing with the dynamics of stiffened and unstiffened shell structures has devoloped over last 35 years. An extensive review of the available literature until 1973 was given by Leissa C343. Some of the recent works and the detailed information related with the importance and classification of vibrations in aircrafts and missiles was also given in the introduction. The aim of this work was to investigate the free vibrations of the stiffened circular cylindrical shell structures parametrical ly. The circular cylindrical shells having a rectangular cutout and thickness discontinuity have been considered. Love's first- approximation theory is used for the shell structure. The effects of stiffeners are treated with orthotropic material approach and takig into account the eccentricity of stiffeners. The shear diaphragm end conditions are considered. The rest of the thesis has been organised as four chapters. In chapter 2» the fundamental equations of el astodynamics are derived. Problems of continuum mechanics have different but equivalent and interdependent global, local and variational formulations. All the formulations have their natural origin in global formulations established through the fundamental axioms of continuum mechanics. These axioms are expressed as conservation of mass, balance of momentum, balance of moment of momentum, conservation of energy, principle of entropy, conservation of charge, Faraday's law of induction and Ampere's law. The basic axioms are valid for all materials irrespective of their constitution. It is therefore expected that their mathematical expressions generally are not sufficient to predict uniquely the behaviour of all subtances under prescribed boundary and initial conditions» In order to fake account of the nature of different materials, some additional relations as known constitutive equations, are required..Furthermore, in the shell theory, certain assumptions must be made in order to reduce the shell geometry from three-dimensional one to a two-dimensional one. In the classical theory of small displacements of thin shells the assumptions that were made by Love may be summarised as fol lows s Thickness of the shell is small vi 1 1 compared with the other characteristic dimensions. Strains and displacements are suf f icientl y small so that, the first-order terms may be retained only in the strain- displacements relations» The theory is physically linear. fit point on the normal of the shell is on same normal of the deformed shell and its distance to middle surface of the shell remains unchanged. The transverse normal stress is small compared with other normal stress components and may be neglected. Under these assumptions and using the basic -axioms and constitutive relations we obtain the following strain energy expression for the shell structure Et Wk - - - - - t Et3 Î4 Shell constructions stiffened by means of discrete stringers and rings may be more efficient from weight standpoint than to use a sufficiently thick single- layered construction. The composite structure must be represented as a combination of the shell elements and stiff ener elements each having its own equations of motion and coupled to each other by equations of continuity. If the stiffeners are relatively closely spaced, it becomes desirable to simplify the analysis by considering them to be approximated by a stiffening sheet with certain bending, twisting and extensional properties. This representation can be accurately made for the purpose of determining free vibration frequencies and mode shapes, but not stress resultants. In order to obtain a theory that remains within the framework of the theory of the shell, we must make certain assumptions about the stiffeners. We assume that the stiffeners are concentrated along curvilinear coordinates. The stiffener dimensions are assumed as small compared to the principal radii of curvature of the shell. The normal strains in the stiffener and in the sheet are equal at their contact point. The stiffness of the stiffeners in-plane direction, perpendicular to their coordinates is equal to zero. The stiffeners carry torsional moment on account of their torsional rigidity. With these assumptions, the stiffener strain energy per unit middle surface area is, x EA a> i EA ss W«.- / \ c.1- / ^ e «» ''-' ır*r - '»n"ai3Kla! ?- b b Eîy adding the stiff ener strain energy to the strain energy of the shell and applying the Hamilton's principle, the variational equation -for dynamical problem is obtained £W - «ST = 0 ' where W is the total strain energy of the stiffened shell per unit middle surface area and T is the kinetic energy o-f the sti-f-fened shell structure expressed as = *J eû^dv V The shear diaphgram end conditions -for a closed circular cylindricall shell o-f -finite length L, is mentioned as follows v = w = M" = NM = 0 for >i = 0, L Finite element analysis of thin shells has received considerable attention during recent years and a number of thin shell finite elements have been derived. The analysis of the problem formulated in chapter 2, is based on the semi 1 oof element developed by Irons C613. The element is non-conforming and basically adopts the well-known isoparametric S-noded parabolic model» Each node has three associated displacement components and some measure of C1 continuity is provided by the introduction of normal rotation variables of discrete points (Loof nodes) on the element periphery. The patch test is passed for plane elements with straight sides, and rigid body motions are satisfied exactly for any combinations of elements of any geometry. Kirchhoff 's assumptions of shell theory is applied as the transverse shears are constrained to be zero at selected points, chosen to be the Gaussian quadrature positions. These shear constraints are then employed to eliminate certain nodal variables. Bince the el merit does not accomodate lateral shear, it is restricted to thin shell situations. A variation in thickness in invidual elements and a thickness discontinuity between adjacent elements can be readily handled. Sharp edges, curved sides and surfaces, and multiply-connected regions are all allowed. Discretising the structure with the semi loof elements and applying the Hamilton's principle, following matrix equation is obtained -for the dynamic problems MQ + KQ = P If it. is assumed that, there is no external -force, P, and the displacements, G are harmonics, the dynamical problem reduces to the following real symmetric general eigenvalue problem to determinate the natural -frequencies and mode shapes o-f a structure CK - Q^MIQ = 0 where S"2 is the natural -frequency. This type of eigenvalue problems may be reduced to standard form using the Cholesky factorisation of M K0 = ftS20 If the mass matrix is not positive definite, the factorisation of the stiffness matrix may be used. The eigenvalues of the standard problem are determined by the method of bisection applied to the Sturm sequence. This method enables one to compute the eigenvalues lying a specified range without having to compute any other. Chapter four is devoted to the applications. The effects of the spacings and dimensions of stringer and rings on the natural frequencies of the stiffened circular cylindrical shell structures are investigated. Two different stiffened circular cylindrical shell models are used for parametric works. The first of them is stiffened by the stringers and/or rings with rectangular cross section and the other one is stiffened by the stringers- and/or rings with profile shape cross section. Both of the models used in application are discretised with 24 semiloof quadrilateral element, resulting 88 nodes and 376 degrees of freedom. The computer program has been coded in FORTRAN IV language. All the numerical computations are done on IBM 4341 digital computer. Evaluation of the results and the recommendations are presented at the last chapter. One may summarise them as follows: - Although in this work stiffeners are assumed to be "distributed" over the whole surface of the shell, the prediction of the natural frequencies is satisfactory. While the number of the elements increases, the results converge to the frequencies obtained experimental ly. - The results of the parametric works made by MODEL İ may be expressed ass The natural frequencies of the stringer stiffened shell are smaller than those of the unstiffened shell. When the stringers have been used together with the rings, it has been XI found that the -frequencies increase with the number of the stringers and are higher than those of the unstif f ened shell structure. If the number of stringers is hold to be constant, the frequencies- may exhibit increasing or decreasing -for different modes while the number of rings increases. - The results obtained MODEL 2 shows that in the stringer stiffened shell, increasing of the number of stringers causes increasing of the natural frequencies. The variations are generally linear. The changing of the frequencies with the number of rings has been found to be of different character. While the frequencies corresponding to some modes increases, some ones decreases. The variation may be also of different character. DoktoraPh.D