Elliptical Cylindrical Shells Research Articles

Собственные колебания композитных эллиптических цилиндрических оболочек с жидкостью

Собственные колебания композитных эллиптических цилиндрических оболочек с жидкостью

Dynamic Analysis of Functionally Graded Porous (FGP) Elliptic Cylindrical Shell Based on Jacobi Polynomials Ritz Method

The lightweight of structure is widely applied in industrial applications, and the conflict between both dynamic stability and structural lightweight is still prominent. In this paper, functionally graded porous (FGP) elliptic cylindrical shells and panels with general boundary conditions are analyzed to explore the effect of the FGP on dynamic performance. First, the FGP elliptic cylindrical shell and panel models are established. Therein, three kinds of porosity distribution are considered, including nonsymmetric, symmetric, and uniform distributions. The energy expressions of the FGP elliptic cylindrical shell and panel are established by the first-order shear deformation theory (FSDT). To simulate various boundary conditions, the artificial spring boundary technique is employed in this study. Then, the Jacobi orthogonal polynomials and Fourier series are adopted to express the admissible displacements. Finally, the accuracy of this model is verified by comparing it with open literature and ABAQUS software. Results show that the variations of the boundary conditions, linear springs, thickness ratio, and porosity have close relation with the dynamic performance of the structure by affecting the stiffness of the structure.

Stress State of Non-Thin Elliptical Cylindrical Shells Under a Local Longitudinal Load

Stress State of Non-Thin Elliptical Cylindrical Shells Under a Local Longitudinal Load

Solution of Dynamic Problems for Elliptical Cylindrical Shells Under Distributed Impulsive Loads*

Solution of Dynamic Problems for Elliptical Cylindrical Shells Under Distributed Impulsive Loads*

1D-Hierarchical Ritz and 2D-GDQ Formulations for the free vibration analysis of circular/elliptical cylindrical shells and beam structures

The present paper proposes a comparison between two different computational techniques to evaluate the natural frequencies of some selected structural components. More specifically, three case studies are investigated: i) Isotropic circular and elliptical cylindrical shells; ii) Non-homogeneous circular cylindrical shell sectors; iii) Homogeneous and non-homogeneous rectangular beams. The 1D-Hierarchical Ritz Formulation (HRF) with 3D capabilities and the 2D-Generalized Differential Quadrature (GDQ) formulation (both in a weak- and a strong-form) are assessed by using a Finite Element Method (FEM) software. For both computational methodologies the Method of Power Series Expansion of the Displacement Components (MPSEDCs) has been employed. A parametric investigation is performed to study the sensitivity of the natural frequencies to some significant parameters, namely, the boundary conditions, the length-to-thickness ratio, as well as some material and geometrical properties. The main advantages of the proposed solution techniques are discussed in terms of convergence and accuracy, for each selected case study.

Calculation of an Elliptic Cylindrical Shell Outside Elastic Limits Based on the FEM with Various Forms of Defining Equations

At the loading step when the shell is deformed outside the elastic limits, the relations between strain increments and stress increments are used in three forms. In the first two forms, the dependences of the strain increments were obtained by differentiating the relations of the deformation theory of plasticity both with the use of the hypothesis of the material incompressibility during plastic deformation and without it. In the third form, to obtain the governing equations, we proposed an algorithm based on the hypothesis that the deviator components of the strain increments are proportional to the deviator components of the stress increments without taking into account the hypothesis of the material incompressibility during elastoplastic deformation and without dividing the stress increments into elastic and plastic parts.

Free Vibrations of an Open Elliptical Cylindrical Shell*

The dynamic characteristics of an open elliptical cylindrical shell clamped at one and two ends are numerically determined usingFEMAPcomputer-aided design and engineering analysis software system with NX NASTRAN solver. The dependences of the natural frequencies on the opening angle relative to the major and minor semi-axes are compared. The behavior of the first natural modes is analyzed.

Stress-strain state of elliptic cross-section cylindrical shells with beveled cuts

Stress-strain state of elliptic cross-section cylindrical shells with beveled cuts

Free vibration analysis of infinitely long thick-walled hollow elliptical cylinder

Various shell theories have been used in the past to study the free vibration of the elliptic cylindrical shells. However, as the thickness ratio of the shell increases, the accuracy of the results for shear deformation theories declines. In this article, the classical theory of elasticity is employed to study the free vibration of a thick cylinder with an elliptic cross-section. The milestone of the analytically established model is based on Navier’s equation, Helmholtz decomposition and Mathieu equations. The new model would specifically be applicable to the high thickness ratios where the structure response becomes highly complex and the high-order shell theories fail to obtain accurate results. Numerical example have been conducted in order to show the key effect of the cylinder’s aspect ratio on the dispersion curve and deformed mode shape of the elliptical cylinder. Finally, the validity of the proposed analytical solution was compared to a finite element simulation in Comsol Multiphysics.

An analytical solution for nonlinear dynamic response and vibration of FG‐CNT reinforced nanocomposite elliptical cylindrical shells resting on elastic foundations

AbstractThe present study deals with the nonlinear dynamic response and vibration of functionally graded carbon nanotubes (FG‐CNT) reinforced composite elliptical cylindrical shells resting on elastic foundations in thermal environments using an analytical solution. The nanocomposite elliptical cylindrical shells are reinforced by single‐walled carbon nanotubes. Based on the classical shell theory with the geometrical nonlinearity in von Kármán and the nonlinear dynamic response and vibration results are obtained by using the Airy stress function, Galerkin method, and Runge‐Kutta method. In numerical results, the effect of geometrical parameters, initial geometric imperfection, Winkler and Pasternak elastic foundations and volume fractions and types of distribution of CNTs on the nonlinear dynamic response and vibration of FG‐CNT reinforced composite elliptical cylindrical shells are investigated.

Shell-type acoustic metasurface and arc-shape carpet cloak

We systematically propose a thin shell-type acoustic metasurface, which could be used to design a carpet cloak that closely covers an arc-shaped object, therefore providing the necessary support for hiding an object with any arbitrary shape. To facilitate the experimental measurement, however, the work here starts with some rotary spherical shell-type and ellipsoidal shell-type cell structures. The measured and calculated sound transmission loss (STL) results of these structures suggest that the sound insulation performances of the shell-type structure are quite different from those of the plate-type structure, indicating a possible break in the shape of the classical sound insulation curve. Considering also that cylindrical shell structures are more widely used in practice than the rotary shell structures, a number of two-dimensional bilayer cylindrical and elliptic cylindrical shell structures were, therefore, designed in this assay. Due to the asymmetry of the structure, the shell-type cells could exhibit bianisotropic sound absorption, reflection and effective parameters. Furthermore, the stiffness of the thin shell structure changed nonlinearly with the changing of the radius of curvature, with a wing shape tendency. In addition, a bilayer cylindrical shell-type acoustic metasurface and an arc-shaped carpet acoustic cloak were successively designed, wherein the phased compensation of differently shaped cell structures could be adjusted by means of a new engineering iso-phase design method. This work could provide the necessary guidance to extend existing results in the field of membrane- and plate-type acoustic metamaterials for shell-type structures, and the realization of the arc-shaped cloak could provide support for the design of a carpet acoustical cloak for use with arbitrary shapes.

Nonlinear thermal vibration of carbon nanotube polymer composite elliptical cylindrical shells

This paper investigated the nonlinear vibration and dynamic response of the carbon nanotube polymer composite elliptical cylindrical shells on elastic foundations in thermal environment. The material properties of the nanocomposite elliptical cylindrical shells are assumed to depend on temperature and graded in the thickness direction according to various linear functions. The shell is subjected to the combination of the uniformly distributed transverse load in harmonic form and the uniform temperature rise. The motion and geometrical compatibility equations are derived based on the Reddy’s higher order shear deformation shell theory. The natural frequencies and the deflection amplitude–time curves of the shell are determined by using the Galerkin method and fourth-order Runge–Kutta method. The numerical results show not only the positive influences of carbon nanotube volume fraction and elastic foundations but also the negative influences of initial imperfection and temperature increment on the nonlinear vibration and dynamic response of the carbon nanotube polymer composite elliptical cylindrical shells. The reliability of the present results is verified by comparing with other publications.

Stress–Strain State Near a Hole in a Shear-Compliant Composite Cylindrical Shell with Elliptical Cross-Section

Static problems for a composite elliptical cylindrical shell with a curved hole are formulated and solved numerically using a developed method. The system of governing equations based on Timoshenko’s refined theory of non-shallow shells and Hooke’s law for orthotropic materials is derived. The method is based on the finite-element method. The influence of the mechanical and geometrical parameters of the shell acted upon by a tensile axial force on the stress, strain, and displacement distributions near a circular hole is studied.

Free vibration analysis of coupled functionally graded (FG) doubly-curved revolution shell structures with general boundary conditions

In this paper, free vibration behavior of coupled functionally graded (FG) doubly-curved revolution shell structures with general boundary conditions is studied by the using unified Jacobi-Ritz method. The first-order shear deformation theory in conjunction with a multilevel partition technique is adopted to establish the theoretical model. The substructure of the theoretical model mainly includes the FG elliptical, hyperbolical, paraboloidal and cylindrical shells and three kinds of coupled FG shell structures containing paraboloidal-cylindrical shells, elliptical-cylindrical shells and hyperbolical-cylindrical shells are also considered in actual calculation. To obtain the continuous conditions at the interface and satisfy the arbitrary boundary conditions, the boundary and coupling spring techniques are adopted in this paper. In despite of the shell components and the boundary conditions, a mix function which is with the Jacobi polynomials along the meridional direction and the standard Fourier series along the circumferential direction is used as the admissible displacements of each shell segment. The convergence and comparison studies for the FG doubly-curved revolution shell structures with different boundary conditions, coupling parameters and Jacobi parameters are carried out to verify the reliability and accuracy of the present solutions. To enhance the understanding of the titled problem, some mode shapes of coupled FG shell structure are provided. Through comparative analysis, including the experimental and numerical comparison, it is obvious that the current method has good stability and rapid convergence properties and the present results agree closely with those reference results no matter what the frequency parameters or mode shapes are. The influence of the geometric dimensions and material constants on the vibration behavior of coupled FG shell structure is also reported.

Nonlinear Deformation and Stability of Discrete-Reinforced Elliptical Cylindrical Composite Shells under Torsion and Internal Pressure

The problem of strength and stability of shells under torsion and internal pressure was solved. It was found out the influence of the internal pressure, ellipticity and nonlinearity of deformation on the critical buckling load of the shell.

Analysis of Influence of the Geometrical Parameters of Elliptic Cylindrical Shells with Variable Thickness on their Stress-Strain State

The stress–strain state of open and closed variable-thickness elliptic cylindrical shells is studied. To solve the problem, the Mushtari–Donell–Vlasov shell model and numerical-analytical approach based on the spline-collocation and discrete-orthogonalization methods are used. Various types of boundary conditions and variable loadings are considered. The influence of the type of variable loading and thickness on the distribution of displacements and stresses in the shells is analyzed.

Dynamics of a Three-Layer Elliptic Cylindrical Shell Reinforced with Discrete Rings

The equations of non-axisymmetric vibrations of three-layer elliptical cylindrical shells with reinforcement rings under non-stationary loading are derived. The elements of this elastic structure are described using the refined Timoshenko-type model of shells and rods. The numerical method of solving the dynamic equations is based on the integro-interpolation method of constructing the finite-difference schemes for equations with discontinuous coefficients. The problem of the dynamic behavior of a three-layer elliptical cylindrical shell with discrete ribs under distributed non-stationary loading is solved. The numerical results are given in the form of plots and analyzed.

Elastoplastic State of an Elliptical Cylindrical Shell with a Circular Hole

Static problems for an elastoplastic elliptical cylindrical shell with a circular hole are formulated and a numerical method for solving it is developed. The basic equations are derived using the Kirchhoff–Love theory of deep shells and the theory of small elastoplastic strains. The method employs the method of additional stresses and the finite-element method. The influence of plastic strains and geometrical parameters of the shell subject to internal pressure on the distributions of stresses, strains, and displacements in the zone of their concentration is studied.

Free Vibrations of Nonthin Elliptic Cylindrical Shells of Variable Thickness

The problem of the free vibrations of nonthin elliptic cylindrical shells of variable thickness under various boundary conditions is solved using the refined Timoshenko–Mindlin theory. To solve the problem, an effective numerical approach based on the spline-approximation and discrete-orthogonalization methods is used. The effect of the cross-sectional shape, thickness variation law, material properties, and boundary conditions on the natural frequency spectrum of the shells is analyzed.

Nonlinear dynamic response of elliptical cylindrical shell underHarmonic excitation

The nonlinear dynamic response of elliptical cylindrical shell under transverse harmonic excitation is experimentally investigated. The elliptical cylindrical shell depicts softening nonlinearity for the excitation range considered. The circumferential variation of acceleration at different time instants of a cycle depicts standing, travelling waves over part of the circumference and travelling waves along the full circumference with/without variable amplitude depending upon the forcing frequency. For symmetric excitation, the travelling wave response is observed for the forcing frequency ωF=81, 85–89, 97.5–99.6, 112, 123.2, 149–155, 178–200 Hz. The participation of different modes involving 1:1, 1:2, 1:3 external, 1:1, 1:2, 2:3 internal resonances and the presence of harmonics including multiples of 1/2, 1/3 are reported.