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

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

A METHOD BASED ON CLASSICAL LAMINATION THEORY TO CALCULATE STIFFNESS PROPERTIES OF CLOSED COMPOSITE SECTIONS

Structural deformation of composite wind turbine blades affect the aerodynamic performance of the rotor. To design better blades in terms of efficiency, aerodynamic performance and load mitigation, it is crucial to understand how blades act under operational loads. An interdisciplinary research should be conducted including composite structures and aerodynamics to analyze this interaction. This article focuses on the structural part and explains an easy to apply method to define sectional properties of a closed composite section. The method is based on Classical Lamination Theory (CLT) and it is assumed that the blade is a thin walled structure. Stress concentration and warping effects are ignored. During preliminary design phase, this method is useful to calculate bending and torsional stiffness values based on different lamination parameters and materials, it can also be used to investigate bending-torsion coupling effects. This article also includes parametric studies on NACA profiles using the method explained. This is the first phase of a study investigating aero-structure interaction in wind turbine blades and its effects on rotor performance

Nonlinear dynamic response of a composite cantilever plate exposed to blast load

Bu çalışmada mühendislik uygulamalarında pek çok kullanım alanı olan katmanlı kompozit plakların nonlineer dinamik davranışları parametrik olarak incelenmiştir. Çalışma esnasında dikdörtgen plak yapılar seçilmiştir. Plaklar konsol plak olarak mesnetlenmiş ve anlık basınç yükü altında test edilmiştir. Katmanlı kompozit konsol bir plağın lineer olmayan dinamik denklemleri türetilmiş ve çözülmüştür. Hareketin dinamik denklemleri virtüel iş ilkesi kullanılarak elde edilmiştir. Geometrik nonlineerlik etkileri ince plaklar için von Kármán büyük yer değiştirmeler teorisi kullanılarak hesaba katılmıştır. Uzay bölgesi için yaklaşık bir çözüm kabul edilmiştir. Zaman bölgesinde lineer olmayan diferansiyel denklemleri elde etmek için Galerkin yöntemi kullanılmıştır. Galerkin yönteminde kullanılan en uygun yaklaşım fonksiyonlarının belirlenmesi için öncelikle ANSYS sonlu eleman yazılımı kullanılarak lineer olmayan statik bir analiz yapılmıştır. Bu analiz sonuçlarına uygun yaklaşım fonksiyonları seçilmiştir. Yaklaşım fonksiyonlarının ilk terimi alınarak bağlı ve lineer olmayan diferansiyel denklemlerin çözümü için sonlu farklar yöntemi uygulanmıştır. En uygun zaman adımını tespit edebilmek için yakınsama çalışması yapılmıştır. ANSYS yazılımı kullanılarak serbest titreşim analizleri yapılmış, farklı mod şekilleri ile titreşim frekansları elde edilmiştir. Elyaf oryantasyonları değişiminin konsol plağın davranışı üzerindeki etkileri araştırılmıştır. Analizler konsol plak için en fazla birim uzamanın görüleceği kök noktası için yapılmıştır. İncelenen farklı oryantasyonlarda belirgin bir değişiklik gözlenmemiştir. Katman sayısının 5, 7 ve 9 olarak seçildiği diğer bir parametrik çalışma yapılmıştır. Bu çalışma sonucunda konsol plağın kökünde aynı basınç yükü altında x yönündeki birim uzamalarda büyük bir değişiklik görülmemiştir.Anahtar Kelimeler: Kompozit, konsol plak, anlık basınç yükü, sonlu farklar.Advanced laminated composites are used in several engineering fields such as space station structures, aircraft, automobiles and submarines. Because of their favorable weight-to-load ratio, plates are widely used by the aerospace industry. With the advent of the new composite material structures and their increased use in the aerospace industry, there is a need to reconsider the problem of the nonlinear dynamic behavior of laminated composite plates exposed to time-dependent pulses, such as sonic boom and blast loadings. This study deals with the derivation and the solution of nonlinear dynamic equations of a composite cantilever plate exposed to blast load. As it was clearly established, these pressure pulses reach the peak value in such a short time that the structure can be assumed to be loaded instantly and uniformly in the spanwise direction. The overpressure associated with the blast pulses can be described in terms of the modified Friedlander exponential decay equation. Friedlander decay function is used to approximate the air blast loading. Dynamic equations of the motion are derived by the use of the virtual work principle. Transverse shear stresses are ignored. The geometric nonlinearity effects are taken into account with the von Kármán large deflection theory of thin plates. An approximate solution is assumed for the space domain. The Galerkin Method is used to obtain the nonlinear differential equations in the time domain. In this study the displacement functions are chosen by considering the results of static large deformation analysis of laminated composite by using a commercial finite element code ANSYS 10.0 software. The plate is discretized using by the eight-node laminated shell elements (SHELL 91) with eight nodes which have geometric nonlinear capability. The finite difference method is applied to solve the system of coupled nonlinear equations. Comparisons of the transverse displacement-time and strain-time histories on the specific points of the plate are obtained. A methodology for simulating plate response subjected to blast load has been demonstrated. The results obtained from the finite element code (ANSYS) and the numerical solution used for these blast studies were compared here. Free vibration analyses are performed by using the ANSYS 10.0 software. Time step convergence studies were conducted on plates subjected to 1 kPa blast load. The convergence studies are the goal of a close proximity numerical solution. It was found that time increment of no more than 1.0 miliseconds were adequate for such a numerical solution. A FORTRAN program was described for automating the application of blast loads to a cantilever plate. All of these aspects were key preliminaries to the parametric studies conducted on blast loaded cantilever plates. Time-histories of normal strain in the x direction for the different points on the plate are performed and compared by using the ANSYS 10.0 software. The discrepancy would be a result of the effect of higher vibration modes on the plate response. Parametric studies are also applied for the cantilever plate. A comparison of different fiber orientations indicates that the plates had closely displacement and strain results for the chosen orientations. However, the 45/-45 oriented plate had the maximum displacement. Also, the effect of the thickness is examined. As a result, while the thickness of the plate increases, the amplitude of the transverse deflection in the z direction decreases, and the corresponding frequency increases. For the cantilever plate, the maximum normal strain occurs at clamped edge, but the maximum displacement occurs at the free-end of plate. So the analyses are performed for these specific points. In this study the in-plane stiffness is taken into account as a difference of the analysis made before. But the strain comparison results demonstrated that the nonlinear effects are negligible for the cantilever plate subjected to these loads. The analysis results show that the nonlinearity related to the first derivative of the deflection is effective on the strain variation. The maximum deflection is ten times of the plate thickness approximately. In this study, only one term is taken for each displacement function. Therefore, the contributions of the higher modes to the structural response are not included. A study can be performed for different boundary conditions and materials. The effect of the blast pressure character on the dynamic behavior can be investigated. Future studies may be devoted on these subjects. Keywords: Composite, cantilever plate, blast load, finite difference

Dynamic Behavior of a Stiffened Laminated Conical Shell under Hygrothermal Loads

The dynamic behavior of a stiffened composite laminated conical thin shell under hygrothermal loads is studied numerically. The governing equations of truncated conical shell are based on the Donnell-Mushtari theory of thin shells including the transverse shear deformation and rotary inertia. The extension-bending coupling is taken into account in the equations. The composite laminated conical shell is also reinforced at uniform intervals by elastic rings andlor stringers. The stiffening elements are relatively closely spaced, and therefore the stiffeners are "smeared out" along the conical shell. The inhomogeneity of material properties because of moisture and temperature is taken into account in the constitutive equations. The equations of laminated composite conical shell are solved by the use of finite difference method The effect of moisture is examined on the dynanlic behavior. The accuracy of results is tested by certain earlier results and an agreement is found

Dynamic Response of Composite Cylindrical Shells to Shock Loading

In this paper, dynamic response of composite cylindrical shells subjected to shock loading is studied analytically. The equations of motion are based on Sanders theory of thin shell. The effects of transverse shear deformation and rotatory inertia are taken into account. The circular cylindrical thin shell with simply supported ends is subjected to a shock load, represented by an axially symmetric moving load at a constant speed along the longitudinal direction. The governing equations are solved analytically using the Assumed-Modes Method. The influences of geometrical parameters and composite material properties of circular cylindrical shells on the dynamic response are studied

Nonlinear Structural Response of Laminated Composite Panels Subjected to Blast Loadings

\u27This paper presents a theoretical analysis and correlation with numerical results of the displacement time histories of laminated composite panels exposed to normal blast shock waves. Nonlinear dynamic equations of the cylindrically curved laminated panels are derived by the use of the Lagrange equations in the frame of Love\u27s theory of thin shells. The governing equations of the laminated curved panel are solved by Runge-Kutta method. In addition, ANSYS finite element software is used to obtain displacement time history numerically. The effect ofloading conditions and geometrical properties is examined on the dynamic behavior