Investigation of the vibration of lattice composite conical shells formed by geodesic helical ribs

Reza Nezamoleslami,Siamak E. Khadem 국제구조공학회 2017 Steel and Composite Structures, An International J Vol.24 No.2

In this paper free linear vibration of lattice composite conical shells will be investigated. Lattice composite conical shell consists of composite helical ribs and thin outer skin. A smeared method is employed to obtain the variable coefficients of stiffness of conical shell. The ribs are modeled as a beam and in addition to the axial loads, endure shear loads and bending moments. Therefore, theoretical formulations are based on first-order shear deformation theory of shell. For verification of the obtained results, comparison is made with those available in open literature. Also, using FEM software the 3D finite element model of composite lattice conical shell is built and analyzed. Comparing results of analytical and numerical analyses show a good agreement between them. Some special cases as variation of geometric parameters of lattice part, effect of the boundary conditions and influence of the circumferential wave numbers on the natural frequencies of the conical shell are studied. It is concluded, when mass and the geometrical ratio of the composite lattice conical shell do not change, increment the semi vertex angle of cone leads to increase the natural frequencies. Moreover for shell thicknesses greater than a specific value, the presence of the lattice structure has not significant effect on the natural frequencies. The obtained results have novelty and can be used for further and future researches.

Design and analysis of fiber placement for composite conical shell

Haojie Xu,Jiuru Lu,Kangmei Li,Jun Hu 대한기계학회 2022 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.36 No.3

Composite conical shells have a wide range of applications. The 3D printing technology based on FDM constrains the fibers in a plane and it is difficult to fill the fibers in the thin wall. This paper proposes a rapid prototyping method for composite materials based on curved surface fiber placement. The conical shell is divided into a series of equidistant offset surfaces. Then we designed three initial paths for fiber placement and rotated them to cover the surface of the conical shell. The resin paths are designed for filling the border layers and the gaps between the fibers. The placement process is simulated by MATLAB (R2016b) and we analyzed the parameter range, direction angle, curvature and fiber content of the three paths. When the critical parameters 0 ϕ = [0°, 42°], ξ is equal to any value and C = (0, 0.032], the corresponding initial path can reach the top of the cone shell in this study. The direction of the constant curvature curve can be designed best; when C = 0.032, the direction angle range is -90 to 90. The curvature of the geodesic path is the smallest; when 0 ϕ = 10°, the normal curvature is about 0.0001 and the geodesic curvature is equal to 0. The fiber content of the geodesic path is greatly affected by the parameter 0 ϕ , and the difference can reach 40 %. The fiber content of the linear curve is greater than 90 %. When ξ is equal to 4, the fiber content is 95 %. For the constant curvature curve, the fiber content is generally very low, about 20 %. We used a six-axis robot and a spindle to produce composite conical shell. The results show that the present design method for composite conical shell is reliable and is able to provide a useful reference for design and production of composite conical shell.

Influence of fiber paths on buckling load of tailored conical shells

Ali-Asghar Naderi,Gholam-Hossein Rahimi,Mohammad Arefi 국제구조공학회 2014 Steel and Composite Structures, An International J Vol.16 No.4

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.

Analysis of nonlinear vibration response of a functionally graded truncated conical shell with piezoelectric layers

Yuhang Zhang,Wenguang Liu,Zhipeng Lyu,Chao Liu,Lei Pang 대한기계학회 2022 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.36 No.8

The nonlinear vibration response of a functionally graded materials (FGMs) truncated conical shell with piezoelectric layers is analyzed. The vibration amplitude is suppressed by the positive and inverse piezoelectric effects. And the bifurcation phenomenon is described to reveal the motion state of the conical shell. Firstly, a truncated conical shell composed of three layers is described. And the effective material properties of the FG layer are defined by the Voigt model and the power law distribution. Next, the electric potentials of piezoelectric layers are defined as cosine distribution along the thickness direction. Meanwhile, the constant gain negative velocity feedback algorithm is used to suppress the vibration amplitude by the electric potential produced by the sensor layer. Thereafter, considering the first-order shear deformation theory and the von Karman nonlinearity, the relationship between the strain and displacement is defined. And the corresponding energy of the conical shell is calculated. After that, the motion equations of the conical shell are derived based on the Hamilton principle. Again, the nonlinear single degree of freedom equation is derived by the Galerkin method and the static condensation method. In the end, the nonlinear vibration response of FGMs truncated conical shell with piezoelectric layers under the external excitation is analyzed via using the harmonic balance method and the Runge-Kutta method. The effects of various parameters, such as ceramic volume fraction exponent, external excitation’s amplitude, control gain and geometric parameters on the nonlinear vibration response of the system are evaluated by case studies. Results indicate that the control gain plays an important role on the suppression of the vibration amplitude. The ceramic volume fraction exponents are not sensitive to the nonlinear vibration response compared with other parameters. The bifurcation behavior is observed under different parameters. The FGMs truncated conical shell with piezoelectric layers has three types of motion state, such as periodic motion, multi-periodic motion, and chaos motion.

Analytical solution for axisymmetric buckling of joined conical shells under axial compression

Kouchakzadeh, M.A.,Shakouri, M. Techno-Press 2015 Structural Engineering and Mechanics, An Int'l Jou Vol.54 No.4

In this study, the authors present an analytical approach to find the axisymmetric buckling load of two joined isotropic conical shells under axial compression. The problem of two joined conical shells may be considered as the generalized form of joined cylindrical and conical shells with constant or stepped thicknesses. Thickness of each cone is constant; however it may be different from the thickness of the other cone. The boundary conditions are assumed to be simply supported with rigid rings. The governing equations for the conical shells are obtained and solved with an analytical approach. A simple closed-form expression is obtained for the buckling load of two joined truncated conical shells. Results are compared and validated with the numerical results of finite element method. The variation of buckling load with changes in the thickness and semi-vertex angles of the two cones is studied. Finally, application of the results in practical design and range of engineering validity are investigated.

Analytical solution for axisymmetric buckling of joined conical shells under axial compression

M.A. Kouchakzadeh,M. Shakouri 국제구조공학회 2015 Structural Engineering and Mechanics, An Int'l Jou Vol.54 No.4

In this study, the authors present an analytical approach to find the axisymmetric buckling load of two joined isotropic conical shells under axial compression. The problem of two joined conical shells may be considered as the generalized form of joined cylindrical and conical shells with constant or stepped thicknesses. Thickness of each cone is constant; however it may be different from the thickness of the other cone. The boundary conditions are assumed to be simply supported with rigid rings. The governing equations for the conical shells are obtained and solved with an analytical approach. A simple closed-form expression is obtained for the buckling load of two joined truncated conical shells. Results are compared and validated with the numerical results of finite element method. The variation of buckling load with changes in the thickness and semi-vertex angles of the two cones is studied. Finally, application of the results in practical design and range of engineering validity are investigated.

Superharmonic and subharmonic vibration resonances of rotating stiffened FGM truncated conical shells

Hamid Aris,Habib Ahmadi 국제구조공학회 2023 Structural Engineering and Mechanics, An Int'l Jou Vol.85 No.4

In this work, superharmonic and subharmonic resonance of rotating stiffened FGM truncated conical shells exposed to harmonic excitation in a thermal environment is investigated. Utilizing classical shell theory considering Coriolis acceleration and the centrifugal force, the governing equations are extracted. Non-linear model is formulated employing the von Kármán non-linear relations. In this study, to model the stiffener effects the smeared stiffened technique is utilized. The non-linear partial differential equations are discretized into non-linear ordinary differential equations by applying Galerkin’s method. The method of multiple scales is utilized to examine the non-linear superharmonic and subharmonic resonances behavior of the conical shells. In this regard, the effects of the rotating speed of the shell on the frequency response plot are investigated. Also, the effects of different semi-vertex angles, force amplitude, volume-fraction index, and temperature variations on the frequencyresponse graph are examined for different rotating speeds of the stiffened FGM truncated conical shells.

Vibrational behavior of exponentially graded joined conical-conical shells

Mohammad Rezaiee-Pajand,Emad Sobhani,Amir R. Masoodi 국제구조공학회 2022 Steel and Composite Structures, An International J Vol.43 No.5

This article is dedicated to predict the natural frequencies of joined conical shell structures made of Functionally Graded Material (FGM). The structure includes two conical segments. The equivalent material properties are found by using the rule of mixture based on Voigt model. In addition, three well-known patterns are employed for distribution of material properties throughout the thickness of the structure. The main objective of the present research is to propose a novel exponential pattern and obtain the related equivalent material properties. Furthermore, the Donnell type shell theory is used to obtain the governing equations of motion. Note that these equations are obtained by employing First-order Shear Deformation Theory (FSDT). In order to discretize the governing system of differential equations, well-known and efficient semi-analytical scheme, namely Generalized Differential Quadrature Method (GDQM), is utilized. Different boundary conditions are considered for various types of single and joined conical shell structures. Moreover, an applicable modification is considered for the continuity conditions at intersection position. In the first step, the proposed formulation is verified by solving some well-known benchmark problems. Besides, some new numerical examples are analyzed to show the accuracy and high capability of the suggested technique. Additionally, several geometric and material parameters are studied numerically.

The finite element method for dynamics of FG porous truncated conical panels reinforced with graphene platelets based on the 3-D elasticity

Lingqin Xia,Ruiquan Wang,Guang Chen,Kamran Asemi,Abdelouahed Tounsi Techno-Press 2023 Advances in nano research Vol.14 No.4

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.

Natural frequency analysis of joined conical-cylindrical-conical shells made of graphene platelet reinforced composite resting on Winkler elastic foundation

Xiangling Wang,Xiaofeng Guo,Masoud Babaei,Rasoul Fili,Hossein Farahani Techno-Press 2023 Advances in nano research Vol.15 No.4

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%.