Articles de revues : « Conical shells »

1

Hien, Vu Quoc, Tran Ich Thinh, Nguyen Manh Cuong et Pham Ngoc Thanh. « FREE VIBRATION ANALYSIS OF JOINED COMPOSITE CONICAL-CONICAL-CONICAL SHELLS CONTAINING FLUID ». Vietnam Journal of Science and Technology 54, n^o 5 (19 octobre 2016) : 650. http://dx.doi.org/10.15625/0866-708x/54/5/7684.

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ABSTRACT A new continuous element (CE) formulation has been presented in this paper for the vibration analysis of three joined cross-ply composite conical shells containing fluid. The three joined cross-ply composite conical shells containing fluid can be considered as the general case for joined conical-cylindrical-conical, joined cylindrical-conical-cylindrical, joined cylindrical-conical-conical and joined conical-conical-cylindrical shells containing fluid. Governing equations are obtained using thick shell theory of Midlin, taking into account the shear deflection effects. The velocity potential, Bernoulli’s equation and impermeability condition have been applied to the shell-fluid interface to obtain an explicit expression for fuild pressure. The dynamic stiffness matrix has been built from which natural frequencies have been calculated. The appropriate expressions among stress resultants and deformations are extracted as continuity conditions at the joining section. A matlab program is written using the CE formulation in order to validate our model. Numerical results on natural frequencies are compared to those obtained by the finite element method (FEM) and validated with the available results in other investigations. This paper emphasizes advantages of CE model and the effects of the fluid level, semi-vertex angles and lamination sequences on the natural frequencies of joined composite conical-conical-conical shells.

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Y, Meish, et Meish V. « POSTULATION AND BUILDING OF A NUMERICAL ALGORITHM FOR SOLVING THE PROBLEMS OF THE DYNAMICS OF THE THEORY OF CONICAL SHELLS IN NONORTHOGONAL COORDINATE SYSTEM ». National Transport University Bulletin 1, n^o 46 (2020) : 211–17. http://dx.doi.org/10.33744/2308-6645-2020-1-46-211-217.

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The paper presents the formulation and numerical algorithm for solving problems of the dynamics of the theory of conical shells in a non-orthogonal coordinate system. The object of the study are conical shells, the equations of which are represented in non-orthogonal coordinate system. Purpose of the work is to formulate and construct a numerical algorithm for solving the problems of the dynamics of conical shells in a non-orthogonal coordinate system. The methods of research include the basic principles of the theory of shells to Tymoshenko's type and numerical methods. The formulation of problems and a numerical algorithm for studying the dynamic behavior of conical shells in a non-orthogonal coordinate system are considered. The results obtained in the work can be used in the design of elements of shell structures in the rocket, aircraft and shipbuilding industries. KEYWORDS: CONIC SHELL, DYNAMIC PROCESSES, NON-ORTHOGONAL COORDINATE SYSTEM, NUMERICAL METHODS

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Vinh, Le Quang, et Nguyen Manh Cuong. « Dynamic analysis of FG stepped truncated conical shells surrounded by Pasternak elastic foundations ». Vietnam Journal of Mechanics 42, n^o 2 (29 juin 2020) : 133–52. http://dx.doi.org/10.15625/0866-7136/14749.

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This research presents a continuous element model for solving vibration problems of FG stepped truncated conical shells having various material properties and surrounded by Pasternak foundations. Based on the First Order Shear Deformation Theory (FSDT) and the equations of the FGM conical shells, the dynamic stiffness matrix is obtained for each segment of the shell having constant thickness. The interesting assembly procedure of continuous element method (CEM) is employed for joining those segments in order to analyze the dynamic behavior of the FG stepped truncated conical shells an assembly procedure of continuous element method (CEM) is employed for joining those segments. Free vibrations of different configurations of FG stepped truncated conical shells on elastic foundations are examined. Effects of structural parameters, stepped thickness and elastic foundations on the free vibration of FG stepped truncated conical shells are also presented.

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Pang, Fuzhen, Chuang Wu, Hongbao Song et Haichao Li. « The free vibration characteristics of isotropic coupled conical-cylindrical shells based on the precise integration transfer matrix method ». Curved and Layered Structures 4, n^o 1 (27 novembre 2017) : 272–87. http://dx.doi.org/10.1515/cls-2017-0018.

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Abstract Based on the transfer matrix theory and precise integration method, the precise integration transfer matrix method (PITMM) is implemented to investigate the free vibration characteristics of isotropic coupled conicalcylindrical shells. The influence on the boundary conditions, the shell thickness and the semi-vertex conical angle on the vibration characteristics are discussed. Based on the Flügge thin shell theory and the transfer matrix method, the field transfer matrix of cylindrical and conical shells is obtained. Taking continuity conditions at the junction of the coupled conical-cylindrical shell into consideration, the field transfer matrix of the coupled shell is constructed. According to the boundary conditions at the ends of the coupled shell, the natural frequencies of the coupled shell are solved by the precise integration method. An approach for studying the free vibration characteristics of isotropic coupled conical-cylindrical shells is obtained. Comparison of the natural frequencies obtained using the present method with those from literature confirms the validity of the proposed approach. The effects of the boundary conditions, the shell thickness and the semivertex conical angle on vibration characteristics are presented.

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Zannon, Mohammad, et Hussam Alrabaiah. « Mathematical Formulation of Laminated Composite Thick Conical Shells ». Journal of Mathematics Research 8, n^o 4 (25 juillet 2016) : 166. http://dx.doi.org/10.5539/jmr.v8n4p166.

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The mathematical formulationof thick conical shells using third order shear deformation of thick shell theory are presented. The equations of motion are obtained using Hamilton’s principle. For present analysis, we consider shell's system transverse normal stress, rotary inertia and shear deformation.

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Kamaloo, Abbas, Mohsen Jabbari, Mehdi Yarmohammad Tooski et Mehrdad Javadi. « Nonlinear Free Vibrations Analysis of Delaminated Composite Conical Shells ». International Journal of Structural Stability and Dynamics 20, n^o 01 (29 novembre 2019) : 2050010. http://dx.doi.org/10.1142/s0219455420500108.

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This paper examines the nonlinear free vibration of laminated composite conical shells throughout the circumferential delamination. First, based on the energy method, the governing equation of motion for the shell was derived. To simplify the analysis, the nonlinear partial differential equations were reduced into a system of coupled ordinary differential equations using Galerkin’s method. Consequently, the results were obtained by the numerical methods. Finally, the effects of delamination, variations in the delamination length, conical shells characteristics, materials property and circumferential wave number on the nonlinear response of delaminated composite conical shells were examined. The results show that the presence of delamination leads to increase in the amplitude of oscillations for the shells. Besides, the increase in the delamination length and decrease of the circumferential wave number, number of layers, and half vertex angle of the cone and orthotropy bring about a decrease in the nonlinearity of delaminated composite conical shells. However, an increase of the middle surface radius of the shell leads to a reduction of the nonlinearity as well as an increase of the amplitude.

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Khadem, Siamak E., et Reza Nezamoleslami. « Investigation of the Free Vibrations of Composite Anisogrid Lattice Conical Shells Formed by Geodesically Spiral and Circumferential Ribs ». International Journal of Applied Mechanics 09, n^o 04 (16 mai 2017) : 1750047. http://dx.doi.org/10.1142/s1758825117500478.

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This paper focuses on the dynamic behavior of composite anisogrid lattice conical shells. Lattice composite conical shell consists of composite helical and circumferential ribs and thin outer skin. The free vibration analysis of anisogrid composite lattice conical shell is presented. A smeared method is employed to calculate the variable coefficients of stiffness of conical shell and more close to the realistic applications. The lattice part of conical shell is modeled as a beam, so in addition to the axial loads, ribs endure shear loads and bending moments. The first-order shear deformation shell theory is used to account for the effects of transverse shear deformations and rotary inertia. The current results are verified with 3D finite element model of conical shell by ANSYS Software and those reported in the literature. Some special cases as influences of geometric parameters of lattice part of shell, effects of boundary conditions and circumferential wave number on natural frequencies of the shell are discussed. It was concluded that employment of the smear method could be recommended for determining the coefficients of stiffness of the composite lattice conical shells with outer skin. Also increasing the vertex angle of cone increases the natural frequencies of conical shell.

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Alcaraz, Guillermina, Brenda Toledo et Luis M. Burciaga. « The energetic costs of living in the surf and impacts on zonation of shells occupied by hermit crabs ». Journal of Experimental Biology 223, n^o 16 (9 juillet 2020) : jeb222703. http://dx.doi.org/10.1242/jeb.222703.

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ABSTRACTCrashing waves create a hydrodynamic gradient in which the most challenging effects occur at the wave breaking zone and decrease towards the upper protected tide pools. Hydrodynamic forces depend on the shape of the submerged body; streamlined shapes decrease drag forces compared with bluff or globose bodies. Unlike other animals, hermit crabs can choose their shell shape to cope with the effects of water flow. Hermit crabs occupy larger and heavier shells (conical shape) in wave-exposed sites than those used in protected areas (globose shape). First, we investigated whether a behavioral choice could explain the shells used in sites with different wave action. Then, we experimentally tested whether the shells most frequently used in sites with different wave action reduce the energetic cost of coping with water flow. Metabolic rate was measured using a respirometric system fitted with propellers in opposite walls to generate bidirectional water flow. The choice of shell size when a large array of sizes are available was consistent with the shell size used in different intertidal sites; hermit crabs chose heavier conical shells in water flow conditions than in still water, and the use of heavy conical shells reduced the energetic cost of coping with water motion. In contrast to conical shells, small globose shells imposed lower energy costs of withstanding water flow than large globose shells. The size and type of shells used in different zones of the rocky shore were consistent with an adaptive response to reduce the energetic costs of withstanding wave action.

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Yan, Yi Xia, Wei Fang Xu, Xi Cheng Huang, Gang Chen et Zhi Ming Hao. « Numerical Simulation on Drop Test of the Conical Shell ». Applied Mechanics and Materials 44-47 (décembre 2010) : 2341–45. http://dx.doi.org/10.4028/www.scientific.net/amm.44-47.2341.

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The drop test for the thin 2A12 conical shells was developed on a drop hammer. The dynamical responses, typical deformation histories and failure mode of the shells were presented. The drop impact response of the thin conical shells were numerically simulated and analyzed in detail by using the explicit, nonlinear transient dynamic code, LS-DYNA. In the calculation, the material plastic behavior of the conical shells was described by Johnson-Cook constitutive relationship, which includes the effects of the strain rate, strains harden and temperatures soften. The deformation and failure model of the conical shell obtained from the numerical simulation were consistent well with the experiment. It was shown that the calculation method, material model and the failure criterion were available. The test and numerical simulation results were all shown that the failure mode was different because of the different drop height.

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Hagihara, Seiya, et Noriyuki Miyazaki. « Bifurcation Buckling Analysis of Conical Roof Shell Subjected to Dynamic Internal Pressure by the Finite Element Method ». Journal of Pressure Vessel Technology 125, n^o 1 (31 janvier 2003) : 78–84. http://dx.doi.org/10.1115/1.1533801.

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Cylindrical tanks with conical roof shells are utilized as oil storage tanks and for some containment vessels. It is known that conical roof shells and torispherical shells subjected to static internal pressure buckle into a displaced shape with circumferential waves caused by an instability condition commonly called bifurcation buckling. It can be important to obtain the dynamic bifurcation buckling load in designing conical roof shells. In this paper, the bifurcation buckling pressure is calculated for dynamic pressure during accident conditions as characterized by step pressure loading, ramp pressure loading and pulse pressure loading. The minimum bifurcation buckling pressure is shown to be a linear function of radius-to-thickness ratio R/h of the shell in a linear fashion on a logarithmic scale. The minimum bifurcation buckling pressure is minimum for conical roof shells subjected to the step loading. The minimum dynamic bifurcation buckling pressure for step loading is about half of the static bifurcation buckling pressure.

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Kang, Jae-Hoon, et Arthur W. Leissa. « Three-Dimensional Vibration Analysis of Thick, Complete Conical Shells ». Journal of Applied Mechanics 71, n^o 4 (1 juillet 2004) : 502–7. http://dx.doi.org/10.1115/1.1767843.

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A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (not truncated) conical shells of revolution. Unlike conventional shell theories, which are mathematically two-dimensional (2D), the present method is based upon the 3D dynamic equations of elasticity. Displacement components ur,uz, and uθ in the radial, axial, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the r and z-directions. Potential (strain) and kinetic energies of the conical shells are formulated, the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four-digit exactitude is demonstrated for the first five frequencies of the conical shells. Novel numerical results are presented for thick, complete conical shells of revolution based upon the 3D theory. Comparisons are also made between the frequencies from the present 3D Ritz method and a 2D thin shell theory.

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Bakhtiari, Mehrdad, Aouni A. Lakis et Youcef Kerboua. « Nonlinear Vibration of Truncated Conical Shells : Donnell, Sanders and Nemeth Theories ». International Journal of Nonlinear Sciences and Numerical Simulation 21, n^o 1 (25 février 2020) : 83–97. http://dx.doi.org/10.1515/ijnsns-2018-0377.

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AbstractNonlinear free vibration of truncated conical shells has been investigated for three different shell theories; Donnell, Sanders and Nemeth to investigate the effect of their simplifying assumptions. The displacement field of a finite element model that was obtained from the exact solution of equilibrium equations of Sander’s improved first-approximation theory is used to define the nonlinear strain energy of conical shells. Employing generalized coordinates method the equations of motion are derived and subsequently the amplitude equation of nonlinear vibration of conical shells was developed. The amplitude equation is solved for multiple cases of isotropic materials. Linear and nonlinear free vibration results are validated against the existing studies in scientific literature and demonstrate good accordance. The validated model is used to investigate effects of different parameters including circumferential mode number, cone-half angle, length to radius ratio, thickness to radius ratio and boundary conditions for the nonlinear vibration of conical shells.

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Hien, Vu Quoc, Tran Ich Thinh et Nguyen Manh Cuong. « Free vibration analysis of joined composite conical-cylindrical-conical shells containing fluid ». Vietnam Journal of Mechanics 38, n^o 4 (20 décembre 2016) : 249–65. http://dx.doi.org/10.15625/0866-7136/6954.

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A new continuous element (CE) formulation has been presented in this paper for the vibration analysis of cross-ply composite joined conical-cylindrical-conical shells containing fluid. Governing equations are obtained using thick shell theory of Midlin, taking into account the shear deflection effects. The velocity potential, Bernoulli's equation and impermeability condition have been applied to the shell-fluid interface to obtain an explicit expression for fluid pressure. The dynamic stiffness matrix has been built from which natural frequencies have been calculated. The appropriate expressions among stress resultants and deformations are extracted as continuity conditions at the joining section. A matlab program is written using the CE formulation in order to validate our model. Numerical results on natural frequencies are compared to those obtained by the Finite Element Method and validated with the available results in other investigations. This paper emphasizes advantages of CE model, the effects of the fluid filling and shell geometries on the natural frequencies of joined composite conical-cylindrical-conical shells containing fluid.

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Gao, Cong, Jiajun Zheng, Fuzhen Pang, Jiawei Xu, Haichao Li et Jibing Yan. « Prediction of Time Domain Vibro-Acoustic Response of Conical Shells using Jacobi–Ritz Boundary Element Method ». Acoustics 6, n^o 2 (31 mai 2024) : 523–40. http://dx.doi.org/10.3390/acoustics6020028.

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Considering the lack of studies on the transient vibro-acoustic properties of conical shell structures, a Jacobi–Ritz boundary element method for forced vibro-acoustic behaviors of structure is proposed based on the Newmark-β integral method and the Kirchhoff time domain boundary integral equation. Based on the idea of the differential element method and the first-order shear deformation theory (FSDT), the vibro-acoustic model of conical shells is established. The axial and circumferential displacement tolerance functions are expressed using Jacobi polynomials and the Fourier series. The time domain response of the forced vibration of conical shells is calculated based on the Rayleigh–Ritz method and Newmark-β integral method. On this basis, the time domain response of radiated noise is solved based on the Kirchhoff integral equation, and the acoustic radiation characteristics of conical shells from forced vibration are analyzed. Compared with the coupled FEM/BEM method, the numerical results demonstrate the high accuracy and great reliability of this method. Furthermore, the semi-vertex angle, load characteristics, and boundary conditions related to the vibro-acoustic response of conical shells are examined.

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Lin, Jie, Chao Deng et Jia Chu Xu. « Nonlinear Dynamic Buckling of FGM Shallow Conical Shells under Triangular Pulse Impact Loads ». Advanced Materials Research 460 (février 2012) : 119–26. http://dx.doi.org/10.4028/www.scientific.net/amr.460.119.

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In this paper, nonlinear dynamic buckling of FGM shallow conical shells under the action of triangular pulse impact loads are investigated. The nonlinear dynamic governing equation of symmetrically FGM shallow conical shells is built. Using Galerkin method, the nonlinear dynamic governing equation is solved, and the nonlinear dynamic response equation of symmetrically FGM shallow conical shells is obtained. The Runge-Kutta method is introduced to numerically solve the nonlinear dynamic response equation and the impact response curve is achieved. Budiansky-Roth motion criterion expressed by the displacement of the peak of the shell is employed to determine the critical impact buckling load. The influences of geometric parameters and gradient constants on impact buckling are discussed as well.

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Krivenko, Olga, et Petro Lizunov. « Vibrations of launch vehicle fairings with conical shape ». Strength of Materials and Theory of Structures, n^o 109 (11 novembre 2022) : 66–71. http://dx.doi.org/10.32347/2410-2547.2022.109.66-71.

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Vibrations of launch vehicle conical fairings are investigated. Fairings are simulated using thin conic shells. The modal analysis of a thin elastic shell is based on the use of the developed finite element model of an inhomogeneous shell. In general, the technique makes it possible to investigate the geometrically nonlinear deformation, stability, and post-buckling behavior of a wide class of thin elastic shells. The modal analysis of the structure is implemented at each step of the static thermomechanical load. The subspace iteration method is used to determine the spectrum of the lowest vibration frequencies of shells of an inhomogeneous structure. The shell behavior analysis method is based on the relations of the three-dimensional theory of thermoelasticity and uses the finite element moment scheme. A thin elastic shell is simulated by a universal solid isoparametric finite element. The parameters of natural vibrations of conical shells of revolution with different thicknesses are investigated. Comparison of the calculation results obtained by the finite element moment scheme with the data of other authors shows a fairly good agreement between the solutions.

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de Souza, V. C. M., et J. M. F. Saraiva. « Analysis of Free Vibrations of Conical Shells Using Donnell’s Approximations ». Applied Mechanics Reviews 48, n^o 11S (1 novembre 1995) : S84—S89. http://dx.doi.org/10.1115/1.3005087.

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The free vibrations of conical shells, having two open rigidly clamped edges, are investigated by using a variational development of the equations of motion based upon the Classical Shell Theory, and results are compared with those obtained by using Donnell’s approximation in the development of these equations. Through suitable examples, the validity of Donnell’s approximation to compute natural frequencies and mode-shapes of conical shells is shown.

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XIAO, Weiwei, Siqi LIU, Xiaolin HUANG, Xiaojun WU et Xusheng YUAN. « Vibration Analysis of Porous Functionally Graded Material Truncated Conical Shells in Axial Motion ». Mechanics 30, n^o 2 (23 avril 2024) : 123–34. http://dx.doi.org/10.5755/j02.mech.34592.

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In this study, a vibration equation for axially moving truncated conical thin shells made of functionally gradient materials with uniformly and non-uniformly distributed pores has been established based on classical thin shell theory. The free vibration and dynamic response solutions are obtained using the Galerkin method. The effects of axial velocity, half cone angle, ceramic material mass composition, material component index, and internal porosity on the free vibration and dynamic response of mentioned shells were analyzed and discussed. The results show that the increase of axial velocity, half cone angle, and material composition index all decrease the natural frequency of the truncated conical shell but amplify its dynamic response, and the rise of the mass fraction of the ceramic material increases the natural frequency of the truncated conical shell but reduces the dynamic response. The results also demonstrate that compared with non-uniformly distributed pores, the effects of uniformly distributed pores on the shells’ dynamic responses are more evident under axial motion.

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Lizunov, Petro, Eduard Kriksunov et Oleksandr Fesan. « Оscillations of closed conical shells with complex rotation ». Strength of Materials and Theory of Structures, n^o 105 (30 novembre 2020) : 127–32. http://dx.doi.org/10.32347/2410-2547.2020.105.127-132.

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The paper consider a system of two closed conical shells connected by a central rigid insert rotating in opposite directions in a central force field with a constant angular velocity around the axis of symmetry of the system. The shell element is subjected to a load consisting of gravitational and inertial forces, but at large values of the angular velocity of the system, the gravitational loads can be neglected. The gyroscopic interaction between the rotational portable motion of the system and the relative elastic oscillations of the elements is a source of excitation of precession oscillations, which may be resonant or unstable. Occurring when changing the axis of orientation of the system gyroscopic moment causes the appearance of alternating stresses, which significantly affect the strength and reliability of the shells. Such problems arise in construction engineering, mechanical engineering, aircraft construction, space engineering and other sectors of the economy. The main load acting on the elements of such systems are significant centrifugal forces of inertia, which significantly affect the strength characteristics of structures. Taking into account the periodicity of the right-hand side and the coefficients of the system of resolving equations, with the help of the projection method it is possible to reduce the resolving equations to the system of ordinary differential equations, which approximately replaces the original one. The solution of the obtained system of equations makes it possible to determine the forms of oscillations and forces in a composite conical shell at various parameters of the shell and the ratios of the velocities of the shell's own rotation and the rotation of its center of mass.

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Kang, Jae-Hoon, et Arthur W. Leissa. « Free Vibrations of Thick, Complete Conical Shells of Revolution From a Three-Dimensional Theory ». Journal of Applied Mechanics 72, n^o 5 (20 janvier 2005) : 797–800. http://dx.doi.org/10.1115/1.1989355.

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A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, complete (not truncated) conical shells of revolution in which the bottom edges are normal to the midsurface of the shells based upon the circular cylindrical coordinate system using the Ritz method. Comparisons are made between the frequencies and the corresponding mode shapes of the conical shells from the authors' former analysis with bottom edges parallel to the axial direction and the present analysis with the edges normal to shell midsurfaces.

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Tong, Liyong, B. Tabarrok et Tsun Kuei Wang. « BENDING ANALYSIS OF ORTHOTROPIC CONICAL SHELLS ». Transactions of the Canadian Society for Mechanical Engineering 17, n^o 2 (juin 1993) : 215–28. http://dx.doi.org/10.1139/tcsme-1993-0013.

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Using Donnell type shell theory a simple and exact procedure is presented for bending analysis of orthotropic conical shells under various loads. The solution is in the form of a power series in terms of a particularly convenient coordinate system, and its convergence radius is obtained.

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Bagheri, H., Y. Kiani et M. R. Eslami. « Free vibration of joined conical-conical shells ». Thin-Walled Structures 120 (novembre 2017) : 446–57. http://dx.doi.org/10.1016/j.tws.2017.06.032.

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Ruili, Zhang, Yang Zhichun et Gao Yang. « The flutter of truncated conical shell subjected to internal supersonic air flow ». Multidiscipline Modeling in Materials and Structures 10, n^o 1 (3 juin 2014) : 18–35. http://dx.doi.org/10.1108/mmms-12-2012-0030.

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Purpose – The purpose of this paper is to propose a new approach to determine the aeroelastic instability of truncated conical shells. In the proposed approach the governing equation of flutter for a truncated conical shell is established using Love's thin shell theory and the quasi-steady first-order piston theory. Design/methodology/approach – The derivatives in both the governing equations and the boundary conditions are discretized with the differential quadrature method, and the critical flutter chamber pressure is obtained by eigenvalue analysis. Findings – The influence of the shell geometry parameters, such as semi-cone angle, radius-thickness ratio and length-radius ratio, on the critical flutter chamber pressure is studied. Results are also presented to indicate the stabilizing effects of aerodynamic damping and the destabilizing effects of the curvature correction term of piston theory on flutter of truncated conical shell. Originality/value – The present approach is an efficient method for the free vibration and flutter analysis of truncated conical shells due to its high order of accuracy and less requirement of virtual storage and computational effort.

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Hart, E. L., et O. O. Semencha. « Computer simulation of the effect of annular inclusions on the stress concentra-tion in thin-walled cylindrical and conical shells with circular openings ». Technical mechanics 2023, n^o 4 (14 décembre 2023) : 60–75. http://dx.doi.org/10.15407/itm2023.04.060.

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Shell structures are used in various industries, such the aerospace industry, the oil and gas industry, power engineering, mechanical engineering, construction, etc. Due to their design or manufacturing features, their integrity may be disrupted by the presence of various openings, around which local stresses develop. Finding ways to reduce stress concentrations around openings is an important problem in deformable solid mechanics. This paper presents the results of a computer simulation and a finite-element analysis of the stress and strain field of thin-walled cylindrical and truncated conical shells with circular openings in the presence of annular inclusions around them made of a material whose properties differ from the main material of the shells. The effect of the elastic modulus of an inclusion and its geometric parameters on the stress and strain concentration in the vicinity of the openings was studied. Several inclusion materials and inclusion widths were considered. An annular inclusion made of a homogeneous material and located in the shell plane was considered. Stress and strain intensity distributions in the local stress concentration zones were calculated. A comparative analysis of the results obtained for cylindrical and conical shells was carried out. The study showed that the presence of a “soft” homogeneous annular inclusion makes it possible to reduce the stress concentration around the opening by ~13–35% depending on the inclusion width and elastic modulus both for a cylindrical and a conical shell. Certain combinations of the geometric and mechanical parameters of the inclusion give rise to a “mechanical” effect, which consists in shifting the stress concentration zone from the opening edge to the inclusion – shell material interface. For conical shells, due to their geometric features, a “conical” effect occurs: the stresses increase not only in the vicinity of the opening-weakened zone, but also near the cone basis.

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AWREJCEWICZ, J., V. A. KRYSKO et T. V. SHCHEKATUROVA. « TRANSITIONS FROM REGULAR TO CHAOTIC VIBRATIONS OF SPHERICAL AND CONICAL AXIALLY-SYMMETRIC SHELLS ». International Journal of Structural Stability and Dynamics 05, n^o 03 (septembre 2005) : 359–85. http://dx.doi.org/10.1142/s0219455405001623.

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By the variational principle, the chaotic vibrations of deterministic geometrically nonlinear elastic spherical and conical axially symmetric shells with non-homogeneous thickness subjected to a transversal harmonic load are analyzed. The material of the shells is assumed to be isotropic and of the Hookean type. Inertial forces tangent to the averaged surface and inertia of rotation of the cross-section are neglected. By the Ritz procedure, the original PDEs are transferred to the ODEs (Cauchy problem), which are then solved by the fourth-order Runge–Kutta method. In the numerical studies, scenarios of transitions from harmonic to chaotic states for vibrations of flexible spherical and conical shells are detected. Various vibrational states for different combinations of the following control parameters: shell's deflection arrow, the amplitude and frequency of the exciting force, number of modes considered, boundary conditions, and the thickness and shape of the shell cross-section are studied. By adjusting the above parameters, we can detect the transition of a continuous system to the lumped one, and the transition from the harmonic to chaotic vibrations.

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Krasovsky, Vasily, et Alexey Karasev. « Properties of numerical solution of the deformation and stability problem in shallow conical shells under external pressure ». Roads and Bridges - Drogi i Mosty 15, n^o 2 (30 juin 2016) : 117–35. http://dx.doi.org/10.7409/rabdim.016.008.

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The paper presents an analysis of a numerical solution in the ANSYS software to three problems related to determination of deformations and stability of closed shallow conical shells under external pressure: 1) linear (bifurcation) problem of determining the critical pressure; 2) geometrically non-linear problem of shell deformation and buckling to determine the limit pressure using axisymmetric finite elements (FE); 3) solution to the same problem as set out in 2, yet using 4-node shell elements. The solutions presented in the paper concern the stationary state of a simply supported and fixed shell. Shallow conical shells are applied as load bearing and protective elements of bridge structures.

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Nacy, Somer M., Mohammad Qasim Abdullah et Malik M. Ali Abdulhadi. « FREE VIBRATION ANALYSIS OF STIFFENED CONICAL SHELL ». Journal of Engineering 8, n^o 03 (1 septembre 2003) : 263–75. http://dx.doi.org/10.31026/j.eng.2002.03.01.

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This paper presents a procedure for the free vibration analysis of stiffened conical shell by the finite element method. The element used is a modified eight-node superparametric shell element. The effects of the number and cross-section area of stiffeners on the conical shells were analyzed. The results showed that increasing the number of stiffeners and their cross-'i'ectional area tend to increase the natural frequency of the conical shell. These results are iompared with available research results and those obtained from MSC\NASTRAN .

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SOFIYEV, A. H., E. SCHNACK, V. C. HACIYEV et N. KURUOGLU. « EFFECT OF THE TWO-PARAMETER ELASTIC FOUNDATION ON THE CRITICAL PARAMETERS OF NONHOMOGENEOUS ORTHOTROPIC SHELLS ». International Journal of Structural Stability and Dynamics 12, n^o 05 (octobre 2012) : 1250041. http://dx.doi.org/10.1142/s0219455412500411.

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A theoretical analysis is presented for determining the free vibrational and buckling characteristics of the nonhomogeneous, orthotropic, thin-walled, circular cylindrical and conical shells under a hydrostatic pressure and resting on a two-parameter elastic foundation. The basic relations have been obtained for the orthotropic truncated conical shell, the Young's moduli and density of which vary continuously in the thickness direction. By applying the Galerkin method, the buckling hydrostatic pressure and dimensionless frequency parameter of the homogeneous and nonhomogeneous orthotropic truncated conical shells with or without elastic foundations are obtained. Finally, the effects of the Winkler and Pasternak-type elastic foundations, the variations of shell characteristics, the effects of the nonhomogeneity and orthotropy on the critical parameters have been studied. The results are presented in tables, figures and compared with other works.

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Tarn, Jiann-Quo, Yung-Ming Wang et Shi-Horng Chang. « Theory of Multilayered Anisotropic Shells Based on an Asymptotic Variational Formulation ». Journal of Mechanics 14, n^o 4 (décembre 1998) : 173–82. http://dx.doi.org/10.1017/s1727719100000204.

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ABSTRACTA general theory for multilayered anisotropic elastic shells is developed in an asymptotic variational framework of 3-D elasticity. The generic shell continuum considered is heterogeneous through the thickness. It is shown that the classical laminated shell theory based on Love's assumption arises naturally as the first-order approximation to the 3-D theory. Higher-order corrections can be determined by solving the 2-D shell equations hierarchically. The associated edge conditions at each level of approximation are derived. Various types of shells such as shells of revolution, conical shells, spherical shells, circular cylindrical shells can be treated within the context.

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SINGH, S., B. P. PATEL et Y. NATH. « POSTBUCKLING BEHAVIOR OF CROSS-PLY LAMINATED CONICAL AND JOINED CONICAL-CYLINDRICAL SHELLS SUBJECTED TO THERMO-MECHANICAL LOADS ». International Journal of Structural Stability and Dynamics 07, n^o 03 (septembre 2007) : 543–53. http://dx.doi.org/10.1142/s0219455407002393.

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Using Green's strains based on Sanders' approximation, the postbuckling behavior of cross-ply laminated composite conical and joined conical-cylindrical shells subjected to thermo-mechanical loads are studied employing the semi-analytical finite element method. The formulation is based on the first-order shear deformation theory and the field consistency principle. The Newton–Raphson iteration technique coupled with the displacement control method is used for the solution of nonlinear governing equations to trace the pre- and post-buckling equilibrium paths. A small magnitude load spatially proportional to the linear buckling mode shape is employed as asymmetric perturbation to initiate the bifurcation of the shell deformation. The influence of semi-cone angle and number of circumferential waves on prebuckling/postbuckling characteristics of cross-ply laminated conical and joined conical-cylindrical shells are investigated.

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Efremova, G., et V. Ryabov. « Stability of conical shells ». Transactions of the Krylov State Research Centre 4, n^o 386 (2018) : 11–19. http://dx.doi.org/10.24937/2542-2324-2018-4-386-11-19.

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Safarov, I. I., M. Kh Teshaev, Sh R. Axmedov, S. A. Boltayev et Sh N. Almuratov. « Intrinsic oscillations of viscoelastic three-layer truncated conical shell ». Journal of Physics : Conference Series 2388, n^o 1 (1 décembre 2022) : 012002. http://dx.doi.org/10.1088/1742-6596/2388/1/012002.

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Abstract Conical shells are used in rocket engineering, construction, aircraft engineering and shipbuilding. The purpose of the present work is to carry out a technique, algorithm and programs for obtaining resonant frequencies and waveforms for circular viscoelastic three-layer conical shells. On the basis of the Lagrange variation equation integral-differential equations of own vibrations are obtained. Based on the method of finite elements, a method for solving the problem of eigen-wear oscillations of the truncated three-layer shell with handedly and freely resting edges was carried out. The problem comes down to solving algebraic equations a large order. Obtained a frequency equation with complex output parameters. The proper oscillations of truncated conical shells are investigated, some characteristic features are revealed. Solving the frequency equation by the Muller method, complex roots are determined. It is established that as the elastic modulus of the shell increases, the real and imaginary parts of the natural frequencies increase accordingly. Paying attention to the rheological properties allows you to increase the values of frequency up to 15%.

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Thai, Duc-Kien, Tran Minh Tu, Le Kha Hoa, Dang Xuan Hung et Nguyen Ngọc Linh. « Nonlinear Stability Analysis of Eccentrically Stiffened Functionally Graded Truncated Conical Sandwich Shells with Porosity ». Materials 11, n^o 11 (6 novembre 2018) : 2200. http://dx.doi.org/10.3390/ma11112200.

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: This paper analyzes the nonlinear buckling and post-buckling characteristics of the porous eccentrically stiffened functionally graded sandwich truncated conical shells resting on the Pasternak elastic foundation subjected to axial compressive loads. The core layer is made of a porous material (metal foam) characterized by a porosity coefficient which influences the physical properties of the shells in the form of a harmonic function in the shell’s thickness direction. The physical properties of the functionally graded (FG) coatings and stiffeners depend on the volume fractions of the constituents which play the role of the exponent in the exponential function of the thickness direction coordinate axis. The classical shell theory and the smeared stiffeners technique are applied to derive the governing equations taking the von Kármán geometrical nonlinearity into account. Based on the displacement approach, the explicit expressions of the critical buckling load and the post-buckling load-deflection curves for the sandwich truncated conical shells with simply supported edge conditions are obtained by applying the Galerkin method. The effects of material properties, core layer thickness, number of stiffeners, dimensional parameters, semi vertex angle and elastic foundation on buckling and post-buckling behaviors of the shell are investigated. The obtained results are validated by comparing with those in the literature.

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Khatri, K. N. « Vibration Control of Conical Shells Using Viscoelastic Materials ». Proceedings of the Institution of Mechanical Engineers, Part C : Journal of Mechanical Engineering Science 206, n^o 3 (mai 1992) : 167–78. http://dx.doi.org/10.1243/pime_proc_1992_206_113_02.

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The vibration and damping analysis of multi-layered conical shells incorporating layers of viscoelastic materials in addition to elastic ones, the former causing dissipation of vibratory energy, is the subject matter of this paper. The analysis given herein uses Hamilton's variational principle for deriving equations of motion of a general multi-layered conical shell. In view of the correspondence principle of linear viscoelasticity which is valid for harmonic vibrations, the solution is obtained by replacing the moduli of viscoelastic layers by complex moduli. An approximate solution for axisymmetric vibrations of multi-layered conical shells with two end conditions—simply supported edges and clamped edges—is obtained by utilizing the Galerkin procedure. The damping effectiveness in terms of the system loss factor for all families of modes of vibrations for three-, five- and seven-layered shells is evaluated and its variation with geometrical parameters is investigated.

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Chen, Meixia, Cong Zhang, Xiangfan Tao et Naiqi Deng. « Structural and Acoustic Responses of a Submerged Stiffened Conical Shell ». Shock and Vibration 2014 (2014) : 1–14. http://dx.doi.org/10.1155/2014/954253.

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This paper studies the vibrational behavior and far-field sound radiation of a submerged stiffened conical shell at low frequencies. The solution for the dynamic response of the conical shell is presented in the form of a power series. A smeared approach is used to model the ring stiffeners. Fluid loading is taken into account by dividing the conical shell into narrow strips which are considered to be local cylindrical shells. The far-field sound pressure is solved by the Element Radiation Superposition Method. Excitations in two directions are considered to simulate the loading on the surface of the conical shell. These excitations are applied along the generator and normal to the surface of the conical shell. The contributions from the individual circumferential modes on the structural responses of the conical shell are studied. The effects of the external fluid loading and stiffeners are discussed. The results from the analytical models are validated by numerical results from a fully coupled finite element/boundary element model.

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Kang, Jae-Hoon. « Vibration Analysis of Complete Conical Shells with Variable Thickness ». International Journal of Structural Stability and Dynamics 14, n^o 04 (2 avril 2014) : 1450001. http://dx.doi.org/10.1142/s0219455414500011.

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A three-dimensional (3D) method of analysis is presented for determining the free vibration frequencies of complete (not truncated) conical shells with linearly varying thickness. The complete conical shells free or clamped at the bottom edge with a free vertex are investigated. Unlike conventional shell theories, which are mathematically 2D, the present method is based upon the 3D dynamic equations of elasticity. Displacement components ur, uθ and uz in the radial, circumferential and axial directions, respectively, are taken to be periodic in θ and in time, and expressed by algebraic polynomials in the r- and z-directions. Potential (strain) and kinetic energies of the complete conical shell are formulated. The Ritz method is used to solve the eigenvalue problem, yielding the upper bound values of the frequencies by minimization. As the degree of the polynomials is increased, frequencies converge to the exact values, with four-digit exactitude demonstrated for the first five frequencies. The frequencies from the present 3D method are compared with those from other 3D approaches and 2D shell theory by previous researchers.

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Javed, Saira. « Conical-Shaped Shells of Non-Uniform Thickness Vibration Analysis Using Higher-Order Shear Deformation Theory ». Symmetry 16, n^o 5 (16 mai 2024) : 620. http://dx.doi.org/10.3390/sym16050620.

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The aim of this research is to investigate the frequency of conical-shaped shells, consisting of different materials, based on higher-order shear deformation theory (HSDT). The shells are of non-uniform thickness, consisting of two to six symmetric cross-ply layers. Simply supported boundary conditions were used to analyse the frequency of conical-shaped shells. The differential equations, consisting of displacement and rotational functions, were approximated using spline approximation. A generalised eigenvalue problem was obtained and solved numerically for an eigenfrequency parameter and associated eigenvector of spline coefficients. The frequency of shells was analysed by varying the geometric parameters such as length of shell, cone angle, node number in circumference direction and number of layers, as well as three thickness variations such as linear, sinusoidal and exponential. It was also evident that by varying geometrical parameters, the mechanical parameters such as stress, moment and shear resultants were affected. Research results concluded that for three different thickness variations, as the number of layers of conical shells increases, the frequency values decrease. Moreover, by varying length ratios and cone angles, shells with variable thickness had lower frequency values compared to shells of constant thickness. The numerical results obtained were verified through the already existing literature. It is evident that the present results are very close to the already existing literature.

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Bagheri, H., Y. Kiani et M. R. Eslami. « Free vibration of joined conical–cylindrical–conical shells ». Acta Mechanica 229, n^o 7 (8 mars 2018) : 2751–64. http://dx.doi.org/10.1007/s00707-018-2133-3.

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Krivoshapko, Sergey N. « Ruled Shells of Conical Type on Elliptical Base ». Structural Mechanics of Engineering Constructions and Buildings 20, n^o 1 (15 mars 2024) : 40–56. http://dx.doi.org/10.22363/1815-5235-2024-20-1-40-56.

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The information about main results on geometry of developable surfaces with an edge of regression which have a directrix ellipse in the base is gathered. These surfaces constitute a group called “Ruled surfaces of conical type on elliptical base”. This group includes elliptical cones, torses with two ellipses defined in the parallel planes, equal slope surfaces, and ruled surfaces with the main frame of three superellipses that are ellipses in one coordinate plane and broken straight lines in the other two coordinate planes. The paper presents a method for developing torses onto a plane, approximation of torses by folded surfaces, and parabolic ending of a thin sheet from elastic material into a torse shell. A brief review of the methods of stress-strain and buckling analysis of the considered ruled shells is given, including the displacement-based finite element method and variational energy method. It is shown that analytical methods can be used only in the case of applying the momentless shell theory for ruled thin shells of conical type. The analytical formulae for determining the normal and tangent internal forces in any momentless conic shell with a superellipse in the base are derived. References to forty four scientific articles of other authors, working or having worked on the subject of the paper are given. These references confirm the conclusions of the author and the perspectives of investigations of the considered ruled surfaces and shells.

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Tong, L. « Free Vibration of Axially Loaded Laminated Conical Shells ». Journal of Applied Mechanics 66, n^o 3 (1 septembre 1999) : 758–63. http://dx.doi.org/10.1115/1.2791722.

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Analytical solutions for the three displacements are obtained, in the form of power series, directly from the three governing equations for free vibration of laminated conical shells under axial load. Numerical results are presented for free vibration of axially loaded laminated conical shells with different geometric parameters and under two types of boundary conditions. It is found that an axial tension increases the frequencies while an axial compression decreases the frequencies. For the shells studied, the effect of axial load on the lowest frequency of the shell is found to be not sensitive to change in semivertex angle when the applied axial load is kept as a constant fraction of the critical buckling load. However, the axial load effect becomes very sensitive to variation in semivertex angle when a constant axial load is applied.

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Tani, J. « Buckling of Truncated Conical Shells Under Combined Axial Load, Pressure, and Heating ». Journal of Applied Mechanics 52, n^o 2 (1 juin 1985) : 402–8. http://dx.doi.org/10.1115/1.3169061.

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On the basis of the Donnell-type shell equations with the effect of nonlinear prebuckling deformations taken into consideration, a theoretical analysis is performed on the buckling of clamped truncated conical shells under two loads combined out of uniform pressure, axial load, and uniform heating. The problem is solved by a finite difference method. It is found that the interaction curves of buckling loads are changed remarkably by the difference in the shape of conical shells. This is due to the large nonlinear prebuckling deformation and the difference in the buckling mode between two cases of single load.

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Khatri, Kamal N. « Vibrations of Arbitrarily Laminated Fiber Reinforced Composite Material Truncated Conical Shell ». Journal of Reinforced Plastics and Composites 14, n^o 9 (septembre 1995) : 923–48. http://dx.doi.org/10.1177/073168449501400902.

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Governing equations of motion are presented for arbitrarily laminated fiber reinforced composite material truncated conical shell in which each layer is permitted an arbitrary fixed fiber orientation. Each layer has been considered to be of a specially orthotropic material with its directional elastic properties depending on the fiber orientation. Extension, bending, in-plane shear and transverse shear in all the layers have been considered and inertia effects due to transverse, meridional and rotary motions are taken into account. Convenient trigonometric series are used as solution functions in Galerkin's method to reduce the governing equations to sets of matrix equations. The correspondence principle of linear viscoelasticity has been used for evaluating the damping effectiveness of the shell. Computer programs have been developed for axisymmetric and antisymmetric vibrations of multi-layered conical shells with simply supported edges. The influence of apex angle upon the resonance frequencies and the associated system loss factors of laminated FRP conical shells is investigated.

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Ning, Wei, Dong Sheng Zhang et Ji Ling Jia. « Free Vibration Analysis of Stiffened Conical Shell with Variable Thickness Distribution ». Applied Mechanics and Materials 614 (septembre 2014) : 7–11. http://dx.doi.org/10.4028/www.scientific.net/amm.614.7.

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The free vibrations of the stiffened hollow conical shells with different variable thickness distribution modes are investigated in detail in the context of Donnel-Mushtari conical shell theory. Two sets of boundary conditions have been considered. The algebraic energy equations of the conical shell and the stiffeners are established separately. The Rayleigh-Ritz method is used to equate maximum strain energy to maximum kinetic energy which leads to a standard linear eigenvalue problem. Numerical results are presented graphically for different geometric parameters. The parametric study reveals the characteristic behavior which is usefulis inuseful in selecting the shell thickness distribution modes and the stiffener type.

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V. Naumenko, Yury, Vasyl I. Gnitko et Elena A. Strelnikova. « Liquid Induced Vibrations of Truncated Elastic Conical Shells with Elastic and Rigid Bottoms ». International Journal of Engineering & ; Technology 7, n^o 2.23 (20 avril 2018) : 335. http://dx.doi.org/10.14419/ijet.v7i2.23.15327.

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A method of estimating natural modes and frequencies of vibrations for elastic shells of revolution conveying a liquid is proposed. The vibration modes of the liquid-filled elastic shells are presented as linear combinations of their own vibration modes without liquid. The explicit expression for fluid pressure is defined using Bernoulli’s integral and potential theory suppositions. Non-penetration, kinematic, and dynamic boundary conditions are applied at the shell walls and on a free liquid surface, respectively. The solution of the hydro-elasticity problem is found out using an effective technique based on coupled finite and boundary element methods. Computational vibration analysis of elastic truncated conical shells with different fixation conditions is accomplished. Sloshing and elastic walls frequencies and modes of liquid-filled truncated conical tanks are estimated. Both rigid and elastic bottoms of shells are considered. Some examples of numerical estimations are provided to testify the efficiency of the developed method

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45

Ning, Wei, Feng Sheng Peng, Nan Wang et Dong Sheng Zhang. « A Numerical Solution for Vibration Analysis of the Stiffened Variable-Thickness Conical Shells ». Applied Mechanics and Materials 757 (avril 2015) : 121–25. http://dx.doi.org/10.4028/www.scientific.net/amm.757.121.

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The free vibrations of the stiffened hollow conical shells with different variable thickness distribution modes are investigated in detail in the context of Donnel-Mushtari conical shell theory. Two sets of boundary conditions have been considered. The algebraic energy equations of the conical shell and the stiffeners are established separately. The Rayleigh-Ritz method is used to equate maximum strain energy to maximum kinetic energy which leads to a standard linear eigenvalue problem. Numerical results are presented graphically for different geometric parameters. The parametric study reveals the characteristic behavior which is useful in selecting the shell thickness distribution modes and the stiffener type. The comparison between the present results and those of finite element method shows that the present results agree well with those of finite element method.

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Xu, Jia Chu, Chao Deng et Hao Wang. « Nonlinear Stability Analysis for FGM Shallow Conical Shells Subjected to Thermal and Mechanical United Loads ». Advanced Materials Research 476-478 (février 2012) : 2515–22. http://dx.doi.org/10.4028/www.scientific.net/amr.476-478.2515.

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Based on the Von Karman large deflection theory of shallow shell, the problem of nonlinear stability of symmetrically FGM shallow conical shells under the action of mechanical and thermal loads is investigated. The nonlinear governing equation under the united action of mechanical and thermal loads of FGM shallow conical shells whose physical parameters change with the power rate is derived and solved by the modified iteration method. The nonlinear characteristic relation of load, deflection and temperature is obtained. The extremum buckling principle is employed to determine the critical buckling load. The influences of gradient constants, geometric parameters and temperature differences on buckling are discussed as well.

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Goldfeld, Yiska, Izhak Sheinman et Menahem Baruch. « Imperfection Sensitivity of Conical Shells ». AIAA Journal 41, n^o 3 (mars 2003) : 517–24. http://dx.doi.org/10.2514/2.1976.

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Shadmehri, F., S. V. Hoa et M. Hojjati. « Buckling of conical composite shells ». Composite Structures 94, n^o 2 (janvier 2012) : 787–92. http://dx.doi.org/10.1016/j.compstruct.2011.09.016.

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Tzou, H. S., et J. P. Zhong. « Electromechanics and Vibrations of Piezoelectric Shell Distributed Systems ». Journal of Dynamic Systems, Measurement, and Control 115, n^o 3 (1 septembre 1993) : 506–17. http://dx.doi.org/10.1115/1.2899129.

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Smart piezoelectric structures, conventional passive materials integrated with piezoelectric sensors, actuators, and control electronics, have great potentials in many engineering applications. This paper is devoted to a new theoretical development of generic piezoelectric shell distributed systems. System electromechanical equations and boundary conditions for a thick piezoelectric shell continuum with symmetrical hexagonal structure (Class C6v = 6 mm) are derived using Hamilton’s principle and linear piezoelectric theory. Further simplification leads to a set of new electromechanical system equations, three translated coordinates and two rotary coordinates, for piezoelectric shell continua including rotary inertias and transverse shears. For thin piezoelectric shells, the second set system equations are further simplified using Kirchhoff-Love’s assumptions. The converse effect induced electric forces/moments and boundary conditions can be used to control system dynamics via open or closed-loop control systems. Applications of the theories to a plate and shells of revolution (spherical, cylindrical, and conical shells) are demonstrated in case studies.

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Cho, Jin-Rae. « Free Vibration Responses of Functionally Graded CNT-Reinforced Composite Conical Shell Panels ». Polymers 15, n^o 9 (22 avril 2023) : 1987. http://dx.doi.org/10.3390/polym15091987.

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Functionally graded CNT (carbon nanotube)-reinforced composites (FG-CNTRCs) are intensively studied because the mechanical behaviors of conventional composites can be dramatically improved. Only a small amount of CNTs are appropriately distributed through the thickness. However, the studies on conical shell panels have been poorly reported when compared with beams, plates and cylindrical shells, even though more parameters are associated with the mechanical behaviors of conical shell panels. In this context, this study intends to profoundly investigate the free vibration of FG-CNTRC conical shell panels by developing an effective and reliable 2-D (two-dimensional) numerical method. The displacement field is expressed using the first-order shear deformation shell theory, and it is approximated by the 2-D planar natural element method (NEM). The conical shell surface is transformed into the 2-D planar NEM grid, and the approach for MITC3+shell element is employed to suppress the shear locking. The developed numerical method is validated through the benchmark experiments, and the free vibration responses of FG-CNTRC conical shell panels are investigated with respect to all the associated parameters. It is found from the numerical results that the free vibration of FG-CNTRC conical shell panels is significantly influenced by the volume fraction and distribution pattern of CNTs, the geometry parameters of the conical shell, and the boundary condition.

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