Conical Shells Research Articles

Dynamic analysis of sandwich conical shell with magneto/electro rheological core using a truly meshfree radial point interpolation method

Dynamic analysis of sandwich conical shell with magneto/electro rheological core using a truly meshfree radial point interpolation method

Numerical modeling and analysis of fluid-filled truncated conical shells with ring stiffeners

This study uses a hybrid finite element method to predict dynamic behavior of truncated conical shells with ring stiffeners under fluid loading. The proposed approach combines classical shell theory and the finite element method, making use of displacement functions derived from exact solutions of Sanders’ shell equilibrium equations for conical shells. The analysis of the shell-fluid interface involves leveraging the velocity potential, Bernoulli’s equation, and impermeability conditions to determine an explicit expression for fluid pressure. To the best of our knowledge, this paper is the first to compare the methods applied to ring-stiffened shells against other numerical and experimental findings. Our results on conical shells in various conditions, with and without ring stiffeners, are largely consistent with previous findings. This study also explores the influence of geometric parameters, stiffener quantity, cone angle, and applied boundary conditions on the natural frequency of fluid-loaded ring-stiffened conical shells. The paper concludes with a discussion of several useful implications for further research.

Vibration Analysis of Porous Functionally Graded Material Truncated Conical Shells in Axial Motion

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.

Nonlinear dynamic response and bifurcation of variable thickness sandwich conical shell with internal resonance

Nonlinear dynamic response and bifurcation of variable thickness sandwich conical shell with internal resonance

Числовий аналіз впливу стрічкових включень на концентрацію напружень в тонких циліндричних і конічних оболонках з прямокутними отворами

Thin-walled plate-shell structures are widely used in various branches of technology and the national economy, in particular in the aerospace industry, the oil and gas industry, power engineering, construction, etc. The continuity of such structures is often disrupted by various inhomogeneities in the form of openings, inclusions, recesses, cracks, etc., which are local stress concentrators. Reducing the concentration of the stresses that develop in the vicinity of such structural inhomogeneities is an important problem in deformable solid mechanics. In particular, a pressing problem in the design of new equipment in modern mechanical engineering is a significant reduction in material consumption and an increase in the service life of cast parts taking into account the use of new materials and technologies. Such parts are responsible for the competitiveness of new equipment for various industries. This paper presents the results of a numerical simulation and analysis of the stress and strain field of thin-walled cylindrical and truncated conical shells with rectangular openings and tape inclusions around them. The material of the inclusions has properties that differ from those of the base material of the shells. The effect of the geometrical and mechanical characteristics of the inclusions on the parameters of the stress and strain field in the vicinity of the openings was studied by varying the elastic modulus of the inclusion material and the inclusion width. For definiteness, the inclusions were assumed to be homogeneous and located in the shell plane. The stress and strain intensity distributions in the zones of local stress concentration were obtained. The numerical results for shells of both shapes were compared with the corresponding results for shells with a circular opening. The study showed that the presence of a “soft” homogeneous tape inclusion helps in reducing the stress concentration around rectangular openings by ~ (21 – 54) % depending on the width of the inclusion and its elastic modulus, both in cylindrical and in conical shells. Unlike shells with a circular opening, in this case the presence of inclusions does not cause the mechanical effect of shifting the stress concentration zone from the contour of the opening to the interface between the materials.

Vibration, Buckling and Stability Analyses of Spinning Bi-Directional Functionally Graded Conical Shells

This paper investigates the free vibration, buckling and dynamic stability of spinning bi-directional functional gradient materials (BDFGMs) conical shells. The material properties vary along the thickness and axial direction. The dynamics model is established based on the first-order shear deformation theory and the governing equations and boundary conditions of the conical shell are derived employing Hamilton’s principle. Subsequently, the differential quadrature (DQ) method is employed to discretize the governing equations into an algebraic system of equations for solving and analyzing the free vibration characteristics of the conical shell. The theoretical model’s accuracy and the solution method’s reliability are rigorously verified. The effects of temperature, functional gradient index, and rotation on the vibration characteristics, traveling wave vibration and critical speed of the conical shell in a thermal environment are systematically explored through numerical analysis. The results indicate that both the material gradient index and temperature increase lead to a decrease in the shell’s natural frequency. For the spinning BDFGMs shell, elevated temperature causes the occurrence of trailing wave vibration to advance to the critical speed. Centrifugal force emerges as the primary factor influencing the critical buckling load and unstable region variation of the spinning shell.

Liquid induced vibrations of partially liquid-filled elastic cylindrical-conical shells

The main objective of this study to develop efficient numerical techniques based on coupled finite and boundary element methods to estimate natural vibration frequencies in compound reservoirs with liquid. Elastic structures composed of cylindrical and conical shells connected by rings have been examined. The space between the shells is filled with an ideal, incompressible fluid. The advantage of the proposed approach lies in the ability to investigate both free and forced vibrations of empty and liquid-filled shells structures within the framework of the single computer technology. The benchmark test calculations demonstrated the high accuracy and efficiency of the proposed approach. The novelty and practical value of the obtained results lie in the ability to investigate fuel tanks of complex shapes under various conditions.

Adjusting dynamic and damping performance in fiber-reinforced magnetorheological elastomer composite conical shells subjected to compressive loads

This study explores the dynamic behavior of axially loaded conical shells composed of magnetorheological elastomer composites (MRECs). The investigation focuses on analyzing the impact of compressive loads on the frequencies and loss factors of these composites. The MRECs consist of laminates reinforced with fibers, enabling tunable viscoelastic properties through the utilization of magnetic fields. The equivalent mechanical characteristics of the MREC are calculated using the modified Voigt and Halpin–Tsai micromechanical rules. By employing the first-order shear deformation theory and Sanders-based strains, the kinematics of the conical shell are accurately modeled. A semi-analytical analysis, combining trigonometric expansion and the generalized differential quadrature (GDQ) methods, is employed to solve the system's highly coupled partial differential equations. Two consecutive analyses are performed. Firstly, the critical buckling load of the MREC conical shell is obtained through a stability analysis. Subsequently, the frequencies and loss factors of the shell in the pre-buckling zone are computed. Parametric analyses are conducted to study the impact of key factors, including magnetic field strength, compressive load magnitude, composite properties, geometric parameters, and boundary conditions. The proposed methodology is rigorously validated through meticulous accuracy and convergence analysis. The outcomes provide valuable insights into the dynamic response of axially loaded magnetorheological elastomer composite conical shells, highlighting their potential in adjustable dynamic and damping systems.

The rigid-flexible coupling vibration of assembled disk-composite conical shell structure of electric aircraft in hygrothermal circumstance

A novel theoretical formulation for addressing the coupling vibration of the rigid disc and flexible composite conical shell structure (RDFCCSs) in hygrothermal circumstances is established to investigate the vibration evolution of the rigid-flexible composite thin-walled coupled structure of new energy electric aircraft. According to Donnell's thin shell theory, the potential energy of the composite conical shell under hygrothermal load is calculated. A uniform mass model and a set of artificial springs distributed on the interface of the shell and disk are imported to simulate the RDFCCSs. The governing equation of the RDFCCSs with arbitrary foundations in hygrothermal circumstances is deduced according to the Rayleigh-Ritz variational procedure. Systematic experiments and finite element simulations have been demonstrated to confirm the accuracy of the proposed method. Three new rigid-flexible coupling vibration modes of the RDFCCSs that differ from the traditional single thin-walled conical shell element due to the influence of the disk have been revealed. After that, the unique vibration characteristics of RDFCCSs under various masses, axial loads, hygrothermal environments and interface connection stiffnesses are discussed in detail.

Nonlinear Free Vibration Analysis of Functionally Graded Porous Conical Shells Reinforced with Graphene Nanoplatelets

The nonlinear vibration analysis of functionally graded reinforced with graphene platelet (FG-GRC) porous truncated conical shells surrounded by the Winkler-Pasternak elastic foundation is presented in this paper. An improved model for evaluating the material properties of porous composites is proposed. Three types of porous distribution and three patterns of graphene nanoplatelets (GPLs) dispersion are estimated. Coupled with the effect of the Winkler-Pasternak elastic foundation, the nonlinear governing equations are developed by using the Hamilton principle. The Galerkin integrated technique is employed to obtain the linear and nonlinear frequencies of the shells. After the present method is validated, the effects of the pores, GPLs, the Winkler-Pasternak foundation, and the semi-vertex are investigated in detail. The results show that the linear frequency can be raised by increasing the values of the mass volume of the GPL and foundation parameters. In contrast, the ratio of nonlinear to linear frequency declines as the mass volume of the GPLs and foundation parameters rises. Furthermore, it is found that the minimum ratio of nonlinear to linear frequency can be obtained as the semi-vertex angle is about 55º, and the effect of porosity distribution on the linear and linear frequencies might be neglected.

Traveling wave vibration and critical rotating speed of rotating porous metal conical shell with elastic boundary conditions

This article examines the traveling wave vibration modes of rotating porous metal conical shell (PMCS) by exploiting the differential quadrature method (DQM). A series of artificial springs are introduced to the system to simulate arbitrary elastic support boundary conditions. Making use of the generalization virtual displacements principle and the first-order shear deformation theory (FSDT) of laminate plate, the theoretical formula is derived, in which both the Coriolis force and the initial circumferential tension brought on by the rotation of the conical shell are included. The trigonometric function is used to indicate the circumferential mode shapes, while the DQM is adopted in generatrix direction to acquire the unified solution. By comparing the present research results and those of the previous researches, the reliability and convergence of the present formulation and numerical simulation are confirmed. Considering three different porosity distributions of the PMCS, the effects of porosity distribution, geometrics, spinning speed, boundary constraint types and the circumferential wave number on frequencies and mode shapes of traveling wave vibration of the PMCS are investigated in detail. Furthermore, the critical rotating speed (CRS) and resonance angular speed are discussed for the rotating PMCS.

Thermoelastic free vibration of rotating pretwisted porous p-FGM, e-FGM, and s-FGM conical shells in nonlinear temperature distribution

The free vibration response of rotating pretwisted functionally graded (FG) conical shells in nonlinear thermal conditions is investigated using a finite element approach with the purpose of application in turbomachinery blades. With the aid of power, exponential, and sigmoid laws, the pretwisted conical shell is functionally graded in its transverse direction. The distribution of both even and uneven porosity is considered. The one-dimensional Fourier heat conduction equation is used to assess the nonlinear temperature distribution across the thickness of the FG conical shell. Lagrange’s equation is used to obtain the dynamic equation of motion of the rotating pretwisted FG conical shell. The proposed finite element model employs an eight-noded isoparametric shell element with five degrees of freedom per node. The effect of several factors, including porosity, temperature, twist angle, and rotational speed on the free vibration response of the FG porous conical shell has been investigated. The findings reveal that the porosity volume fraction has a significant influence on the natural frequency. The nonlinear temperature difference and pretwist angle both cause stiffness reduction to the FG conical shell upon increasing, whereas the presence of rotational speed inducts geometrical stiffness resulting in centrifugal stiffening.

Free vibrational behavior of a conical sandwich shell with a functionally graded auxetic honeycomb core

In the presented paper, the free vibration of a conical sandwich shell with a re-entrant auxetic honeycomb (AH) core made of ceramic-metal functionally graded material (FGM) is analyzed. The percentage (volume fraction) of ceramic in the functionally graded auxetic honeycomb (FGAH) core changes from zero at the inner surface of the core to one at the outer surface according to a power-law function. The FGAH core is enfolded with a homogenous outer face layer made of ceramic and a homogenous inner one made of metal. The shell is modeled based on the first-order shear deformation theory (FSDT), and Hamilton’s principle is utilized to attain the governing equations and boundary conditions. A trigonometric-based analytical solution is carried out in the circumferential direction, and an approximate solution is presented in the meridional direction via the differential quadrature method (DQM). The impacts of various factors on the natural frequencies are inspected like the thickness of the core-to-thickness of the shell ratio, geometric factors of the cells in the FGAH core, and material gradation in the FGAH core.

Ruled Shells of Conical Type on Elliptical Base

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.

Numerical investigation of melting process enhancement in shell and coil latent heat storage tanks by the simultaneous use of conical coil and conical shell

Efficient energy storage rates are crucial for latent heat energy storage units. Building on previous studies highlighting the benefits of shell and helical tube configurations, which enhance energy storage rates through increased heat exchange areas, this research introduces a novel configuration featuring a combination of conical shell and conical coil. Various geometric variations, including conical/cylindrical shells and conical coils, are explored to assess their impact on charging performance using numerical simulations based on the enthalpy-porosity method. The study investigates three different numbers of coil turns (4, 6, and 8) for each configuration. Results demonstrate that the proposed conical shell and conical coil configuration significantly accelerates the melting rate, achieving a liquid fraction of 0.897 within 160 min—an improvement of 7.6 % compared to the conventional shell and helical tube configuration with the same phase change material quantity. Additionally, increasing coil turns from 6 to 8 yields an 8.8 % rise in the liquid fraction for the simple cylindrical case, comparable to the 7.6 % increase achieved by the proposed conical configuration. The findings underscore the preference for geometry modifications over increasing coil turns, as the latter leads to greater space occupation within the tank, resulting in reduced energy storage capacity and a concomitant 30 % undesirable increase in heat transfer fluid pressure drop.

Thermoelastic analysis of axisymmetric conical shells: Investigating stress–strain response under uniform heat flow with semi-coupled approach

ABSTRACT This study addresses the issue of thermal stresses and strains in a thin-walled conical shell subjected to uniform heat flow along its side surfaces and at both ends of the thermal insulation shell. The governing equations are derived using a semi-coupled static thermoelastic equation and an energy equation. The energy equation ignores strain rate effects, but static behavior equations consider temperature variations in axisymmetric thin-walled conical shells. Semicoupled methods, due to their simpler analysis, are suitable for thermal stress analysis when structural and thermal disturbances differ significantly. To obtain solutions, the Galerkin finite element method is employed, yielding valuable insights. Using the Galerkin reduced weight residual method, the sum of the weight residuals on the shell thickness is set to zero. Through a comprehensive problem-solving approach, the effects of increasing the angle of the cone apex in different thermal boundary conditions are investigated in two one-ended and two-ended cases.

Free Vibration Analysis of Polymer/Graphene Nanoplatelet/Fiber Truncated Conical Shells Embedded in an Elastic Foundation

Free Vibration Analysis of Polymer/Graphene Nanoplatelet/Fiber Truncated Conical Shells Embedded in an Elastic Foundation

Study on the Fundamental Frequency and Dynamic Mode of Traveling Wave Vibration of Rotating PJCS

The vibrations of rotating joined conical–conical shells with classical supported conditions have been studied extensively. As a matter of fact, in some cases, these classical boundary conditions cannot exactly model actual situations. Moreover, theoretical frameworks on them are still limited. This research aims to investigate the fundamental frequencies and dynamic mode shapes of the traveling wave of the rotating porous metal material joined conical–conical thin shells (PJCS) with elastic supports. By utilizing artificial spring technology, arbitrary elastic supported boundary conditions and classical boundary conditions are achieved efficiently. A new dynamic model has been formulated with the help of the first-order shear deformation theory (FSDT) and Hamilton’s principle. By employing the generalized differential quadrature (GDQ) method along with stress boundary conditions and generalized eigenvalues, various factors such as porosity, semi-vertex angles and stiffness are analyzed for their impact on the fundamental frequencies of forward wave (FW), backward wave (BW) and mode shapes. The presented results are validated through the convergence and comparison studies from literatures. The interesting and novel results indicate that the in-plane displacement constraints have the most significant impact on the critical speed, while the lateral displacement constraint has the least effect. The vibrations are more easily excited for the part with a larger half vertex angle. Rotating PJCS with Type 1 has the biggest critical rotating speed.

Effects of non-uniformity in thickness and volume fraction of agglomerated CNTs on the dynamics of a spinning CNT-reinforced nanocomposite truncated conical shell

In the presented work, the free vibration analysis of a rotating truncated conical shell whose thickness varies in the meridional direction is examined. The material that the shell is made of is a polymeric matrix (epoxy) enriched with carbon nanotubes (CNTs) whose volume fraction varies in the meridional direction. CNTs agglomeration is considered and the density and elastic constants of such a two-phase nanocomposite are calculated sequentially based on the Eshelby–Mori–Tanaka approach alongside the rule of mixture. The conical shell is modeled using the first-order shear deformation theory (FSDT) including the relative acceleration, Coriolis acceleration, and centrifugal acceleration along with the initial hoop tension, and the governing equations are obtained utilizing Hamilton’s principle. The solution of governing equations is performed via the combination of an analytical solution in the circumferential direction and a numerical one in the meridional direction via the differential quadrature method (DQM). The impacts of several parameters on the forward and backward natural frequencies of such a rotating shell are studied such as chirality, mass fraction and dispersion pattern of the CNTs, thickness variation parameters, and boundary conditions. It is observed that higher natural frequencies and critical rotational speeds can be achieved for CNT-reinforced conical shells when the volume fraction of the CNTs and the thickness of the shell increase from its small radius to the large one.

Thermoelastic analysis of variable thickness truncated conical shell subjected to thermomechanical load with internal heat generation using perturbation technique

In this article, the behavior of the truncated conical shell subjected to thermomechanical loading in their inner and outer layers with internal heat generation source is investigated. The displacement field obeys kinematic of the first order shear deformation theory and the first-order temperature theory is used. Two-dimensional temperature analysis has been performed along the thickness and axis of the shell, which can be defined under various loading and thermomechanical boundary conditions. The set of governing equations is a system of differential equations with variable coefficients which are solved by using the analytical matched asymptotic expansion of the perturbations technique. The mentioned solution has little computational cost, therefore can be used well in parametric studies for optimization. It was shown, axial displacement is somehow independent of the radial axis and its maximum value occurs near the upper boundary. The conical shell has expanded in the radial direction. Also the maximum temperature happens approximately in the middle of the length of the conical shell. The parametric study showed, with the increase heat flux in the outer layer thereby expanding the area of heat application which would let more heat in than out. Also it was found, controlling the lifetime of the structure is the result of directing the cone angle. The results obtained from the analytical solution were compared with the Finite Element Method (FEM) analysis and the results of similar related articles, only to show a good agreement.