Homogeneous Cylindrical Shells Research Articles

Vibrational Power Flow Analysis for the Sandwich Cylindrical Shell Structure with a Metal–Rubber Core in the Thermal Environment

This research is designed to investigate the vibrational characteristics of a sandwich cylindrical shell structure with an elastic-porous metal–rubber core in the thermal environment by the power flow method. The finite element models of the homogeneous and sandwich cylindrical shell structures are established for harmonic response analysis completed by the mode superposition method. Further, the structural power flow is calculated and visualized based on the results of the finite element analysis. A comparison is made with the results for a plate available in the literature validating the effectiveness of the power flow visualization method. The effects of some key factors, such as the frequency, the metal–rubber core, the length-to-radius ratio, and the temperature on the power flow of the sandwich cylindrical shell structure, are analyzed using power flow cloud pictures and vector diagrams. The results reveal that the frequency affects the distribution of power flow, and the metal–rubber core can dissipate energy, whereas the length-to-radius ratio and temperature do not have a significant influence on the power flow of the sandwich cylindrical shell structure with a metal–rubber core (SCSMR). This work should be valuable for the noise and vibration control application of the SCS-MR.

A Comparison of Shell Theories for Vibration Analysis of Single-Walled Carbon Nanotubes Based on an Anisotropic Elastic Shell Model.

In the present paper, a comparison is conducted between three classical shell theories as applied to the linear vibrations of single-walled carbon nanotubes (SWCNTs); specifically, the evaluation of the natural frequencies is conducted via Donnell, Sanders, and Flügge shell theories. The actual discrete SWCNT is modelled by means of a continuous homogeneous cylindrical shell considering equivalent thickness and surface density. In order to take into account the intrinsic chirality of carbon nanotubes (CNTs), a molecular based anisotropic elastic shell model is considered. Simply supported boundary conditions are imposed and a complex method is applied to solve the equations of motion and to obtain the natural frequencies. Comparisons with the results of molecular dynamics simulations available in literature are performed to check the accuracy of the three different shell theories, where the Flügge shell theory is found to be the most accurate. Then, a parametric analysis evaluating the effect of diameter, aspect ratio, and number of waves along the longitudinal and circumferential directions on the natural frequencies of SWCNTs is performed in the framework of the three different shell theories. Assuming the results of the Flügge shell theory as reference, it is obtained that the Donnell shell theory is not accurate for relatively low longitudinal and circumferential wavenumbers, for relatively low diameters, and for relatively high aspect ratios. On the other hand, it is found that the Sanders shell theory is very accurate for all the considered geometries and wavenumbers, and therefore, it can be correctly adopted instead of the more complex Flügge shell theory for the vibration modelling of SWCNTs.

Theoretical and experimental investigation of circumferential guided waves in orthotropic annuli

The fiber composite materials fabricated by stacking the lamina structure obtain increasing attention in the industry, and at the same time, damage analysis is essential for safe operation. A proposed way to detect defects such as debonding and delamination is to induce circumferential guided waves. Accurate determination of the dispersion characteristics and wave fields is a prerequisite for using acoustic guided waves. The aim of this work is to provide such an accurate dispersion results in an arbitrarily thick cylindrically orthotropic homogeneous cylindrical shell of uniform thickness. Compared with the traditional SAFE method, the proposed method, which combines the two numerical methods, namely Floquet Boundary Condition (Floquet BC) Method and Sweeping Frequency Finite Element Modeling (SFFEM) method has obvious advantages. Through Floquet BC method, a theoretical result can be easily obtained without tedious code writing. Then SFFEM helps to verify the theoretical result in an experimental way. Besides, the slight gap between the theoretical and experimental results works as a basis for calibrating the elastic constants of composite materials provided in the manual. Simulations in COMSOL Multiphysics FE software supported by both methods and experiments by the latter have been carried out in this work. The calculated phase velocity dispersion curves demonstrated the efficiency of those two methods. The developed method can be adapted to other complex pipeline structures to extract circumferential guided wave dispersion characteristics by both simulation and experimental measurements.

Internal resonance characteristics of hyperelastic thin-walled cylindrical shells composed of Mooney–Rivlin materials

The internal resonance characteristics are investigated for a thin-walled cylindrical shell composed of incompressible Mooney–Rivlin material, where the shell is subjected to a radial harmonic excitation. Based on the Kirchhoff–Love hypothesis, Donnell’s nonlinear shallow-shell theory and variational principle of energy, the coupled nonlinear differential equations, describing the radial motion of the shell, are obtained. The existence condition of 2:1 internal resonance is given via examining the natural frequencies of different modes. Then the multiple scale method is applied to derive the amplitude–frequency relations in the presence of 2:1 internal resonance, and the stabilities of steady-state responses are determined. In addition, the accuracy of the model is verified by using a homogeneous cylindrical shell with simply supported boundary conditions, some comparisons are made with the previous published researches and good agreement is found. The effects of excitation amplitudes and the structure parameters on the resonance responses of the system are examined. Numerical results show that the range of resonance increases along with the excitation amplitude; the typical phenomenon of double-jumping appears, and the generation and vanishing of double peaks are related to the values of structure parameters.

Dynamic analysis of a multilayered piezoelectric two-dimensional quasicrystal cylindrical shell filled with compressible fluid using the state-space approach

The state-space approach is developed to analyze the dynamic behaviors of a multilayered two-dimensional piezoelectric quasicrystal circular cylinder filled with the compressible fluid. With simple support at both ends, the hollow cylindrical shell has imperfect bonding between the layers. The analytical solution of a homogeneous cylindrical shell has been derived based on the state equations. The general solution for the corresponding multilayered case is also obtained by utilizing the propagator matrix method. The numerical results present the natural frequencies in free vibration with different length-to-radius and radius-to-thickness ratios. The critical load and dynamic behaviors of the model are exactly predicted in the axial buckling problem. For the impulse case, the influences of the density of the filled fluid and coefficients of interfacial imperfections on the dynamic responses are also discussed.

Numerical Analysis of the Effect of Strain Rate on the Dynamic Strength of Cylindrical Metal-Plastic Shells under Explosive Loading

Based on the nonclassical theory of shells, an energy-consistent resolving system of dynamics equations for metal-plastic cylindrical shells is obtained by minimizing the total-energy functional of a shell as a three-dimensional body. The numerical method for solving the formulated initial-boundary-value problem is based on an explicit variational-difference scheme. The validity of the method is confirmed by the results of comparison of numerical solutions and experimental data. The ultimate deformability and strength of homogeneous fiberglass cylindrical shells and double-layer metal-plastic shells are analyzed for various reinforcement structures.

Analysis of the prediction of a bilayered cylindrical shell’s reduced cutoff frequency with data-driven approaches

Abstract The reduced cutoff frequency is one of the most important properties of elastic circumferential waves of cylindrical shells. For homogeneous thin cylindrical shells, this frequency can be calculated based on the eigen modes theory. In contrast, this theory is not practical for inhomogeneous cylindrical shells. This paper presented the methods of reduced cutoff frequency prediction using data-driven approaches. Three widely known data-driven methods, the Artificial Neural Network (ANN), the Adaptive-Network-based Fuzzy Inference System (ANFIS), the Support Vector Machine (SVM), are employed to develop the prediction models. The training and testing datasets for these models are determined from the plane of modal identification. In this study, the considered bilayered cylindrical shells are made of stainless steel/polymer. Three prediction scenarios are assessed. The difference between these scenarios is the physical and geometrical parameters which considered as relevant entries of data-driven approaches. In the first and second scenarios, a comparative analysis indicates that the ANN models performed better than other models with highest prediction accuracy value of 0.9761 and the lowest mean relative error (MRE) of 0.4017%. In the third scenario the SVM model was the best model with highest accuracy of 0.9895 and lowest root mean square error (RMSE) of 0.0227.

Free vibration analysis of moderately thick isotropic homogeneous open cylindrical shells using improved Fourier series method

In this paper an Improved Fourier series method has been employed to study the free vibrations of isotropic homogeneous moderately thick open cylindrical shells with arbitrary subtended angle and general elastic restraints. In this method, regardless of the boundary conditions, each of the displacement components of open shell is invariably expressed as a simple trigonometric series with accelerated and uniform convergence over the solution domain. Distributed elastic restraints are used to specify the elastic boundary conditions along the shell edges and therefore, arbitrary boundary restraints can be achieved by varying the values of spring’s stiffness. All the unknown expansion coefficients are treated as the generalized coordinates and solved using the Rayleigh-Ritz technique. A considerable number of new vibration results for isotropic open cylindrical shells with various geometric parameters and boundary conditions are presented. The effects of boundary stiffness, thickness to radius ratio and subtended angle on the vibration characteristics are also discussed in detail.

Free vibration of conical shells with intermediate ring support

Free vibration behaviour of a shear deformable conical shell with intermediate ring support is analysed in this research. It is assumed that the conical shell is made from a linearly elastic isotropic homogeneous material. To capture the through-the-thickness shear deformations and rotary inertia effects, first order shear deformation theory of shells accompanied with the Donnell type of kinematic assumptions are adopted to establish the general equations of motion and the associated boundary conditions with the aid of Hamilton's principle. The resulting system of equations are discreted using the semi-analytical generalised differential quadratures (GDQ) method. The shell is divided into two sections, where the continuity conditions are satisfied at the ring position. Considering various types of boundary conditions for the shell ends and continuity conditions at the ring position, an eigenvalue problem is established to examine the natural frequencies of the shell reinforced with an intermediate ring support. After proving the efficiency and validity of the present method for the case of thin isotropic homogeneous cylindrical shell with intermediate ring support, parametric studies are carried out for the case of shear deformable conical shells with intermediate ring support.

Crack Tip Fields for Interfacial Crack of FGMs Cylindrical Shell with Reissner’s Effect

The higher order crack-tip fields for the interfacial crack between functionally graded material(FGM) and homogeneous material cylindrical shells are presented. The crack is oriented in circumferential direction. The material properties of FGMs are assumed to be exponential functions with their gradient direction perpendicular to the interface. Base on Reissner theory, the governing equations are derived for weak-discontinuous problems of cylindrical shells. By using the eigen-expansion method, the high order crack tip fields are obtained.

Post-buckling of cylindrical shells with spiral stiffeners under elastic foundation

In this paper, an analytical method for the Post-buckling response of cylindrical shells with spiral stiffeners surrounded by an elastic medium subjected to external pressure is presented. The proposed model is based on two parameters elastic foundation Winkler and Pasternak. The material properties of the shell and stiffeners are assumed to be continuously graded in the thickness direction. According to the Von Karman nonlinear equations and the classical plate theory of shells, strain-displacement relations are obtained. The smeared stiffeners technique and Galerkin method is used to solve the nonlinear problem. To valid the formulations, comparisons are made with the available solutions for nonlinear static buckling of stiffened homogeneous and un-stiffened FGM cylindrical shells. The obtained results show the elastic foundation Winkler on the response of buckling is more effective than the elastic foundation Pasternak. Also the ceramic shells buckling strength higher than the metal shells and minimum critical buckling load is occurred, when both of the stiffeners have angle of thirty degrees.

Influences of shear stresses and rotary inertia on the vibration of functionally graded coated sandwich cylindrical shells resting on the Pasternak elastic foundation

In this study, the behavior of vibration of sandwich cylindrical shells covered by functionally graded coatings and resting on the Pasternak elastic foundation considering combined influences of shear stresses and rotary inertia are examined. It is assumed that the effective material properties of functionally graded coatings changes exponentially in thickness direction. The modified Donnell type equations of motion of functionally graded and homogeneous sandwich cylindrical shells on the Pasternak elastic foundation are deduced using the first-order shear deformation theory. Basic equations are reduced to an algebraic equation of the sixth order and numerically solving this algebraic equation gives the dimensionless fundamental frequency. The expressions for the dimensionless fundamental frequencies of functionally graded and ceramic coated sandwich cylindrical shells with and without taking into account the effects of Pasternak elastic foundation and shear stresses obtained in a special case. Calculations, the influences of an elastic foundation, compositional profiles of coatings, shear stresses, rotary inertia, and sandwich shell geometry parameters on the nondimensional fundamental frequency are described. The results are verified by comparing the obtained values with those in the existing literature.

The vibration and buckling of sandwich cylindrical shells covered by different coatings subjected to the hydrostatic pressure

The vibration and buckling of sandwich cylindrical shells covered by different types of coatings, such as functionally graded (FG), metal and ceramic coatings and subjected to a uniform hydrostatic pressure using first order shear deformation theory (FOSDT) is discussed. Four types of sandwich cylindrical shells are considered. The volume fraction of FG coatings varies according to a simple power law function of thickness coordinate, while that of the core equals unity. The effective material properties of FG coatings are assumed to be graded in the thickness direction according to an exponential law distribution. The equations of motion of FG sandwich cylindrical shells are deduced using the FOSDT. The closed-form solutions for non-dimensional frequencies and critical hydrostatic pressures are obtained. The influences of compositional profiles of coatings, shear stresses and sandwich shell characteristics on the non-dimensional frequencies and critical hydrostatic pressures for FG and homogeneous sandwich cylindrical shells are discussed.

Natural frequency characteristics of thin-walled homogeneous and manifold layered cylindrical shells under pressure using energy method

Energy method for the vibration of two types of cylindrical shells, namely thin-walled homogeneous isotropic and manifold layered isotropic cylindrical shells under uniform external lateral pressure is presented. The study is carried out based on strain-displacement relationship from Love’s shell theory with beam functions as axial modal function. A manifold layered cylindrical shell configuration is formed by three layers of isotropic material where the inner and outer layers are stainless steel and the middle layer is aluminum. The homogeneous cylindrical shell is made-up of isotropic one layer with stainless steel. The governing equations with uniform external lateral pressure for homogeneous isotropic and manifold layered isotropic cylindrical shells are obtained using energy functional by the Lagrangian function with Rayleigh-Ritz method. The boundary conditions that are presented at the end conditions of the cylindrical shell are simply supported-simply supported, clamped-clamped and free-free. The influences of uniform external lateral pressure and symmetrical boundary conditions on the natural frequency characteristics for both homogeneous and manifold layered isotropic cylindrical shells are examined. For all boundary conditions considered, the natural frequency of both cylindrical shells with symmetric uniform lateral pressure increases as h/R ratio increases and those considering natural frequency of the both cylindrical shells with symmetric uniform lateral pressure decrease as L/R ratio increases.

Fonksiyonel Değişimli Malzemelerle Kaplı Seramik Silindirik Panelin Titreşim Analizi

In this study, the vibration of ceramic cylindrical panel covered by FGM coatings composed of zirconium oxide (ZrO2) and titanium-aloy (Ti6Al4V) is investigated. First, a sandwich cylindrical panel covered by FGM coatings is designed. After the derivation of basic equations are found expression for the frequency of ceramic cylindrical panels covered by FGM coatings. Discusses the influence of coatings profiles, sandwich shell characteristics, the radius-tothickness ratio and the core-to-coating thickness ratio on the dimensionless frequencies for FG and homogeneous sandwich cylindrical shells

Infinitesimal Stability of the Equilibrium States of an Incompressible, Isotropic Elastic Tube Under Pressure

The infinitesimal stability of the equilibrium states of an arbitrary incompressible, isotropic and homogeneous elastic cylindrical shell in a pure radial expansion under a constant inflation pressure is studied for both thick- and thin-walled shells. The classical criterion of infinitesimal stability yields a general stability theorem relating the frequency and pressure response and reveals that points at which the pressure is stationary define the domain of unstable or neutrally stable states. All results are expressed in terms of a general shear response function, and specific results are provided for the Mooney-Rivlin, Gent and Ogden models, the second having limited extensibility, the last including experimental data. Every static state of a Mooney-Rivlin tube is stable so long as the pressure is less than an asymptotic limit that increases with the thickness. Otherwise, only the Ogden model exhibits static states of instability for all long cylindrical tubes of thickness less than a transitional value above which all static states are infinitesimally stable. A long cylindrical cavity in all three unbounded models is stable for all pressures. All results are illustrated graphically.

Research on nonlinear postbuckling of functionally graded cylindrical shells under radial loads

The nonlinear postbuckling behaviors of functionally graded cylindrical shells (FGCSs) under uniform radial pressure are investigated by using the nonlinear large deflection theory of cylindrical shells. According to an inhomogeneous parameter, the material properties of functionally graded materials vary smoothly through the thickness. With the temperature-dependent material properties taken into account, various effects of thermal environment are compared. In addition, the effects of the inhomogeneous parameter and the dimensional parameters are also investigated. The present theoretical results are verified by the experimental results of homogeneous cylindrical shells.

On the solution of eigenvalue problems of laminated non-homogeneous orthotropic circular shells with clamped edges subjected to hydrostatic pressure

This article presents a method to study the free vibration and stability of laminated homogeneous and non-homogeneous orthotropic cylindrical, truncated and complete conical shells of general staking with clamped edges under a hydrostatic pressure. Based on the Love first approximation theory, the basic relations, the modified Donnell-type stability and compatibility equations have been obtained for laminated orthotropic truncated conical shells, the material properties of which vary piecewise continuously in the thickness direction. To solve this problem an unknown parameter λ was included in the approximation functions. Applying Galerkin methods, the buckling pressures and fundamental natural frequencies of laminated homogeneous and non-homogeneous orthotropic conical shells are obtained. The parameter λ which is included in the obtained formulas is obtained from the minimum conditions of critical stresses and frequencies. The different generalized values are obtained for the parameter λ for buckling pressures and frequencies of cylindrical shells, truncated and complete conical shells. The appropriate formulas for single-layer and laminated cylindrical shells made of homogeneous and non-homogeneous, orthotropic and isotropic materials are found as a special case. Finally, the influences of the degree of non-homogeneity, the number and ordering of layers and the variations of conical shell characteristics on the critical hydrostatic pressure and natural frequencies are investigated. The results obtained for homogeneous cases are compared with their counterparts in the literature.

Buckling of Imperfect, Axisymmetric, Homogeneous Shells of Variable Thickness: Perturbation Solution

This paper presents the first of a series of solutions to the buckling of imperfect cylindrical shells subjected to an axial compressive load. The initial problem is the case of a homogeneous cylindrical shell of variable thickness that is of an axisymmetric nature. The equilibrium equations as first introduced by Donnell over 70 years ago are thoroughly presented as basis for a solution employing perturbation methods. The ultimate objective of these calculations is to achieve a quantitative assessment of the critical buckling load considering the small axisymmetric deviations from the nominal shell wall thickness. Clearly in practice, large diameter thin wall shells of revolution that form stacks (as found in flue gas desulphurization absorber assemblies) are never fabricated with constant diameters and thicknesses over the entire length of the assembly. As such, ASME Boiler and Pressure Vessel Code Section VIII shell thickness tolerances as supplemented by ASME Code Case 2286-1 are reviewed and addressed in comparison to the resulting solutions with respect to the critical buckling loads. The method and results described herein are in stark contrast to the “knockdown factor” approach currently utilized in ASME Code Case 2286-1. Recommendations for further study of the imperfect cylindrical shell are also outlined in an effort to improve on the current rules regarding column buckling of large diameter shells designed in accordance with ASME Section VIII, Divisions 1 and 2 and ASME STS-1 in combination with the suggestions contained within Code Case 2286-1.

Acoustic modes of finite length homogeneous and layered cylindrical shells: Single and multiwall carbon nanotubes

We present a numerical study of the normal modes of vibration of both homogeneous and heterogeneous finite length cylindrical shells of arbitrary wall thickness with applications toward single and multiwall carbon nanotubes in the continuum limit. The method is checked by comparison of computed and measured resonance spectra for a machined aluminum cylindrical shell. The dependence of the natural frequencies of various radial modes with the length and radius of single wall tubes is investigated and compared to atomistic models and Raman spectroscopy data. The radial dependence for the radial breathing mode and four harmonics of the squash mode are found to be well fitted by power laws and agree with analytical solutions in the thin wall limit. A general model for an elastically heterogeneous layered cylindrical shell is applied to multiwall tubes with graphene sheets and gaps between the sheets represented by two different materials. The frequency dependence on length and diameter is investigated for tubes composed of two to four concentric shells.