• Steel and Composite Structures
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• v.38 no.1
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• pp.47-66
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• 2021

This work addresses the free vibration analysis of Functionally Graded Porous (FGP) nanocomposite truncated conical shells with Graphene PLatelet (GPL) reinforcement. In this study, three different distributions for porosity and three different dispersions for graphene platelets have been considered in the direction of the shell thickness. The Halpin-Tsai equations are used to find the effective material properties of the graphene platelet reinforced materials. The equations of motion are derived based on the higher-order shear deformation theory and Sanders's theory. The Fourier Differential Quadrature (FDQ) technique is implemented to solve the governing equations of the problem and to obtain the natural frequencies of the truncated conical shell. The combination of FDQ with higher-order shear deformation theory allows a very accurate prediction of the natural frequencies. The precision and reliability of the proposed method are verified by the results of literature. Moreover, a wide parametric study concerning the effect of some influential parameters, such as the geometrical parameters, porosity distribution, circumferential wave numbers, GPLs dispersion as well as boundary restraint conditions on free vibration response of FGP-GPL truncated conical shell is also carried out and investigated in detail.

• Advances in nano research
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• v.15 no.4
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• pp.367-384
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• 2023

Natural frequency behavior of graphene platelets reinforced composite (GPL-RC) joined truncated conical-cylindrical- conical shells resting on Winkler-type elastic foundation is presented in this paper for the first time. The rule of mixture and the modified Halpin-Tsai approach are applied to achieve the mechanical properties of the structure. Four different graphene platelets patterns are considered along the thickness of the structure such as GPLA, GPLO, GPLX, GPLUD. Finite element procedure according to Rayleigh-Ritz formulation has been used to solve 2D-axisymmetric elasticity equations. Application of 2D axisymmetric elasticity theory allows thickness stretching unlike simple shell theories, and this gives more accurate results, especially for thick shells. An efficient parametric investigation is also presented to show the effects of various geometric variables, three different boundary conditions, stiffness of elastic foundation, dispersion pattern and weight fraction of GPLs nanofillers on the natural frequencies of the joined shell. Results show that GPLO and BC3 provide the most rigidity that cause the most natural frequencies among different BCs and GPL patterns. Also, by increasing the weigh fraction of nanofillers, the natural frequencies will increase up to 200%.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1993.10a
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• pp.106-112
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• 1993

This paper presents the optimum design of reinforced concrete conical shell which is fixed at the base and free at the top. The calculation of stresses is done using the SMAP(Segmented Matrix Analysis Package)program which uses the simple finite element method of analysis. The objective function contains the ratios of the unit cost of reinforcements and formwork to that of concrete. To Simplify the optimization procedure, the final optimum design of conical shell is obtained by combining the result of each element. The results are presented and discussed.

• Structural Engineering and Mechanics
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• v.45 no.2
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• pp.259-275
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• 2013

Free vibration of symmetric angle-ply layered conical shell frusta of variable thickness is analyzed under shear deformation theory with different boundary conditions by applying collocation with spline approximation. Linear and exponential variation in thickness of layers are assumed in axial direction. Displacements and rotational functions are approximated by Bickley-type splines of order three and obtained a generalized eigenvalue problem. This problem is solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. The vibration of three and five-layered conical shells, made up of two different type of materials are considered. Parametric studies are made for analysing the frequencies of the shell with respect to the coefficients of thickness variations, length-to-radius ratio, length-to-thickness ratio and ply angles with different combination of the materials. The results are compared with the available data and new results are presented in terms of tables and graphs.

• Steel and Composite Structures
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• v.35 no.6
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• pp.765-777
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• 2020

In the context of classic conical shell formulation, nonlinear forced vibration analysis of truncated conical shells and annular plates made of multi-scale epoxy/CNT/fiberglass composites has been presented. The composite material is reinforced by carbon nanotube (CNT) and also fiberglass for which the material properties are defined according to a 3D Mori-Tanaka micromechanical scheme. By utilizing the Jacobi elliptic functions, the frequency-deflection curves of truncated conical shells and annular plates related to their forced vibrations have been derived. The main focus is to study the influences of CNT amount, fiberglass volume, open angle, fiber angle, truncated distance and force magnitude on forced vibrational behaviors of multi-scale truncated conical shells and annular plates.

• Steel and Composite Structures
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• v.16 no.4
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• pp.375-387
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• 2014

The purpose of this paper is to propose a method for evaluation of varying stiffness coefficients of tailored conical shells (TCS). Furthermore, a comparison between buckling loads of these shells under axial load with the different fiber path is performed. A circular truncated conical shell subjected to axial compression is taken into account. Three different theoretical path containing geodesic path, constant curvature path and constant angle path has been considered to describe the angle variation along the cone length, along cone generator of a conical shell are offered. In the TCS with the arbitrary fiber path, the thickness and the ply orientation are assumed to be functions of the shell coordinates and influencing stiffness coefficients of the structure. The stiffness coefficients and the buckling loads of shells are calculated basing on classical shells theory (CST) and using finite-element analysis (FEA) software. The obtained results for TCS with arbitrary fiber path, thickness and ply orientation are derived as functions of shell longitudinal coordinate and influencing stiffness coefficients of structures. Furthermore, the buckling loads based on fiber path and ply orientation at the start of tailored fiber get to be different. The extent of difference for tailored fiber with start angle lower than 20 degrees is not significant. The results in this paper show that using tailored fiber placement could be applied for producing conical shells in order to have greater buckling strengths and lower weight. This work demonstrates the use of fiber path definitions for calculated stiffness coefficients and buckling loads of conical shells.

• Advances in nano research
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• v.14 no.4
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• pp.375-389
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• 2023

In this study, free vibration analysis of functionally graded (FG) porous truncated conical shell panels reinforced by graphene platelets (GPLs) has been investigated for the first time. Additionally, the effect of three different types of porosity distribution and five different types of GPLs patterns on dynamic response of the shell are also studied. Halpin-Tsai micromechanical model and Voigt's rule are used to determine Young modulus, shear modulus and Poisson's ratio with mass densities of the shell, respectively. The main novelties of present study are: applying 3D elasticity theory and the finite element method in conjunction with Rayleigh-Ritz method to give more accurate results unlike other simplified shell theories, and also presenting a general 3D solution in cylindrical coordinate system that can be used for analyses of different structures such as circular, annular and annular sector plates, cylindrical shells and panels, and conical shells and panels. A convergence study is performed to justify the correctness of the obtained solution and numerical results. The impact of porosity and GPLs patterns, the volume of voids, the weight fraction of graphene nanofillers, semi vertex and span angles of the cone, and various boundary conditions on natural frequencies of the functionally graded panel have been comprehensively studied and discussed. The results show that the most important parameter on dynamic response of FG porous truncated conical panel is the weight fraction of nanofiller and adding 1% weight fraction of nanofiller could increase 57% approximately the amounts of natural frequencies of the shell. Moreover, the porosity distribution has great effect on the value of natural frequency of structure rather than the porosity coefficient.

• Structural Engineering and Mechanics
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• v.55 no.4
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• pp.719-742
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• 2015

This paper dealt the free vibration analysis of thick truncated conical composite sandwich shells with transversely flexible cores and simply supported boundary conditions based on a new improved and enhanced higher order sandwich shell theory. Geometries were used in the present work for the consideration of different radii curvatures of the face sheets and the core was unique. The coupled governing partial differential equations were derived by the Hamilton's principle. The in-plane circumferential and axial stresses of the core were considered in the new enhanced model. The first order shear deformation theory was used for the inner and outer composite face sheets and for the core, a polynomial description of the displacement fields was assumed based on the second Frostig's model. The effects of types of boundary conditions, conical angles, length to radius ratio, core to shell thickness ratio and core radius to shell thickness ratio on the free vibration analysis of truncated conical composite sandwich shells were also studied. Numerical results are presented and compared with the latest results found in literature. Also, the results were validated with those derived by ABAQUS FE code.

• Structural Engineering and Mechanics
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• v.58 no.6
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• pp.1001-1020
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• 2016

The study is to investigate the free vibration of antisymmetric angle-ply conical shells having non-uniform sinusoidal thickness variation. The arbitrarily varying thickness is considered in the axial direction of the shell. The vibrational behavior of shear deformable conical shells is analyzed for three different support conditions. The coupled differential equations in terms displacement and rotational functions are obtained. These displacement and rotational functions are invariantly approximated using cubic spline. A generalized eigenvalue problem is obtained and solved numerically for an eigenfrequency parameter and an associated eigenvector of spline coefficients. The vibration characteristic of the shells is examined for cone angle, aspect ratio, sinusoidal thickness variation, layer number, stacking sequence, and boundary conditions.

• Steel and Composite Structures
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• v.25 no.5
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• pp.581-591
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• 2017

The dynamic instability of truncated conical shells subjected to dynamic axial load within first order shear deformation theory (FSDT) is examined. The conical shell is made from functionally graded (FG) orthotropic material. In the formulation of problem a dynamic version of Donnell's shell theory is used. The equations are converted to a Mathieu-Hill type differential equation employing Galerkin's method. The boundaries of main instability zones are found applying the method proposed by Bolotin. To verify these results, the results of other studies in the literature were compared. The influences of material gradient, orthotropy, as well as changing the geometric dimensions on the borders of the main areas of the instability are investigated.