Thin Cylindrical Shell Research Articles

Parametric instability of a functionally graded cylindrical thin shell subjected to both axial disturbance and thermal environment

This paper focuses on the parametric instability of a functionally graded (FG) cylindrical thin shell under both axial disturbance and thermal environment. Based on Love's thin shell theory, and considering the temperature-dependent properties of FG cylindrical shell, the dynamic equations of the FG cylindrical shell are derived by Hamilton's principle. The multiple scales method is performed to obtain the instability boundaries of the shell with axial disturbance. The primary and combination instabilities of the shell are studied systematically. Moreover, numerical simulations are utilized to discuss the influences of axial disturbed amplitude, material heterogeneity and thermal effects on instability regions, frequency characteristics of the shell. Specially, some numerical results are given to illustrate the combined influence of axial disturbed amplitude and temperature variation on instability regions.

Artificial neural network prediction of buckling load of thin cylindrical shells under axial compression

Thin-walled circular cylindrical shells under axial compression are prone to buckling; the reduction of buckling load from the theoretical estimation is considered primarily due to imperfection sensitivity. The buckling load from carefully conducted experiments using nominally similar shells falls below the prediction by the classical theory with substantial scatter. The current design recommendations apply highly conservative knockdown factors to the theoretical buckling loads to estimate the load carrying capacity of the shell structures. In this study, a systematic analysis of experimental data from the literature has been conducted using the artificial neural network (ANN). The networks were trained using Bayesian regularisation backpropagation training function. Two network models with eight and ten neurones were used to train, test and validate 390 sets of experimental data. The buckling loads predicted by the ANN models were compared with the design recommendations by National Aeronautics and Space Administration (NASA), Eurocode 3 (EC3) and the experimental buckling loads. The ANN models predict buckling load within 10% of the experimental buckling load and can be reliably used within the parametric range used in training. The NASA design recommendations provides 10–50% conservative estimates compared to the experimental loads while EC3 predictions are conservative by more than 50%.

Functionally Graded Piezoelectric Energy Harvester Using Thin Cylindrical Shell

Presented herein is a functionally graded piezoelectric energy harvester using a thin cylindrical shell. The torsional mode for the thin cylindrical shell is studied and the effects of the functionally graded parameters on the power density are discussed. The analytical expressions for the power density are derived. From the results obtained, it can be observed that the functionally graded constant has obvious influences on the peak value of the power density. Moreover, larger values of the power density may be obtained by increasing the elastic parameter and the mass density. This work is expected to be useful in the analysis and design of energy harvester as well as new kinds of energy systems.

A new method for evaluating the natural frequency in radial breathing like mode vibration of double‐walled carbon nanotubes

AbstractThis paper investigates the radial breathing like mode (RBLM) vibration of double‐walled carbon nanotubes (DWCNTs) based on a new theory called doublet mechanics (DM) with a scale parameter. To this end, DWCNTs are considered as two concentric elastic thin cylindrical shells bounded together with van der Waals (vdW) forces between them. The vdW forces are modeled using Len‐Jones potential. Using DM, two coupled second order partial differential equations that govern the RBLM vibration of DWCNTs are derived. Subsequently, the equations of motion are solved to obtain the natural frequencies in the RBLM vibration. It is the first time that DM is used to derive the natural frequencies of the RBLM vibration for DWCNTs. The advantage of these analytical formulas is that unlike the other methods, they are explicitly dependent to scale parameter and chirality effect. It is shown that the chirality and scale parameter play significant role in the RBLM vibration response of DWCNTs. To validate the accuracy and efficiency of this work, the results obtained herein are compared with the existing theoretical and experimental results and good agreement is observed.

04.01: Buckling of very short elastic cylinders with weld imperfections under uniform bending

ABSTRACTThe length‐dependent domains of behaviour of thin elastic cylindrical shells under uniform bending have recently received significant research attention. Ovalisation is known to affect very long cylinders which undergo significant cross‐sectional flattening before failing by local buckling. This effect is restrained by the end boundary condition in shorter cylinders, which fail instead by local buckling at moments close to the classical analytical prediction. In very short cylinders, however, even this local buckling is restrained by the end boundary, and failure occurs instead through the development of a destabilising meridional fold on the compressed side. Although this is a limit point instability under bending, ovalisation does not play any role at all. This ‘very short’ length domain has only recently been explored for the first time with the aid of finite element modelling.A brief overview of the nonlinear buckling behaviour of very short elastic cylinders under uniform bending is presented in this paper. Two types of edge rotational restraint are used to illustrate the influence of a varying support condition on the stability in this short length range. It is shown that short cylinders under bending do not suffer at all from local short‐wave buckling. Additionally, when the meridional dimension of such cylinders becomes particularly short the resulting numerical models may predict indefinite stiffening without a limit point, even when the shell is modelled using more complete 3D solid continuum finite elements. Idealised weld depressions, which are realistic representations of a systemic manufacturing defect, are used to demonstrate only a very mild sensitivity to geometric imperfections at such short lengths owing to a pre‐buckling stress state dominated by local compatibility bending. The topic should be of interest to researchers studying shell problems dominated by local bending with computational tools and designers of multi‐segment shells with very close segment spacing.

Fully localized post-buckling states of cylindrical shells under axial compression.

We compute nonlinear force equilibrium solutions for a clamped thin cylindrical shell under axial compression. The equilibrium solutions are dynamically unstable and located on the stability boundary of the unbuckled state. A fully localized single dimple deformation is identified as the edge state-the attractor for the dynamics restricted to the stability boundary. Under variation of the axial load, the single dimple undergoes homoclinic snaking in the azimuthal direction, creating states with multiple dimples arranged around the central circumference. Once the circumference is completely filled with a ring of dimples, snaking in the axial direction leads to further growth of the dimple pattern. These fully nonlinear solutions embedded in the stability boundary of the unbuckled state constitute critical shape deformations. The solutions may thus be a step towards explaining when the buckling and subsequent collapse of an axially loaded cylinder shell is triggered.

Buckling of very short elastic cylinders with weld imperfections under uniform bending

The length-dependent behaviour domains of thin elastic cylindrical shells under uniform bending have recently received significant research attention. Ovalization is known to affect very long cylinders that undergo significant cross-sectional flattening before failing by local buckling. This effect is restrained by the end boundary conditions in shorter cylinders, which instead fail by local buckling at moments close to the classical analytical prediction. In very short cylinders, however, even this local buckling is restrained by the end boundary, and failure occurs instead through the development of a destabilizing meridional fold on the compressed side. Although this is a limit point instability under bending, ovalization does not play any role at all. This ‘very short’ length domain has only recently been explored for the first time with the aid of finite element modelling. A brief overview of the non-linear buckling behaviour of very short elastic cylinders under uniform bending is presented in this paper. Two types of edge rotational restraint are used to illustrate the influence of a varying support condition on the stability in this short length range. It is shown that short cylinders under bending do not suffer at all from local short-wave buckling. Additionally, when the meridional dimension of such cylinders becomes particularly short, the resulting numerical models may predict indefinite stiffening without a limit point, even when the shell is modelled using more complete 3D solid continuum finite elements. Idealized weld depressions, which are realistic representations of a systemic manufacturing defect, are used to demonstrate only a very mild sensitivity to geometric imperfections at such short lengths owing to a pre-buckling stress state dominated by local compatibility bending. The topic should be of interest to researchers studying shell problems dominated by local bending with computational tools and designers of multi-segment shells with very close segment spacing.

Erratum to: Asymptotic approximations for pure bending of thin cylindrical shells

Erratum to: Asymptotic approximations for pure bending of thin cylindrical shells

Multi-parameter actuation of a neutrally stable shell: a flexible gear-less motor.

We have designed and tested experimentally a morphing structure consisting of a neutrally stable thin cylindrical shell driven by a multi-parameter piezoelectric actuation. The shell is obtained by plastically deforming an initially flat copper disc, so as to induce large isotropic and almost uniform inelastic curvatures. Following the plastic deformation, in a perfectly isotropic system, the shell is theoretically neutrally stable, having a continuous set of stable cylindrical shapes corresponding to the rotation of the axis of maximal curvature. Small imperfections render the actual structure bistable, giving preferred orientations. A three-parameter piezoelectric actuation, exerted through micro-fibre-composite actuators, allows us to add a small perturbation to the plastic inelastic curvature and to control the direction of maximal curvature. This actuation law is designed through a geometrical analogy based on a fully nonlinear inextensible uniform-curvature shell model. We report on the fabrication, identification and experimental testing of a prototype and demonstrate the effectiveness of the piezoelectric actuators in controlling its shape. The resulting motion is an apparent rotation of the shell, controlled by the voltages as in a 'gear-less motor', which is, in reality, a precession of the axis of principal curvature.

A state space solution for onset of surface instability of elastic cylinders with radially graded Young's modulus

A state space solution is developed to analyze surface instability of cylindrical structures with Young's modulus varying arbitrarily in the radial direction. By using the incremental theory for surface instability of elastic materials, the equilibrium equations for the incremental stress field from a fundamental state are derived for radially graded elastic cylinders subjected to an axial compression, which together with the boundary conditions constitute an eigenvalue problem. In the present work, a state space method is established to solve the eigenvalue problem and predict the critical condition for onset of surface instability. The state space solutions for three typical examples are presented and shown to be in good agreement with the numerical results by the finite element method, including the analytical solution for a thin cylindrical shell. In particular, a transition of the critical buckling mode for a soft cylinder covered by a bilayer is illustrated clearly by the present method. In contrast to the finite element method, the state space method is a semi-analytical approach with higher computational efficiency for arbitrarily graded elastic cylinders, including layered structures.

Investigation on inconsistency of theoretical solution of thermal buckling critical temperature rise for cylindrical shell

In order to solve the inconsistency problem of the theoretical solutions of critical buckling temperature rise for thin cylindrical shells reported in the existing literatures, a first attempt was made in the present study to perform a derivation process on the critical internal force, thermal stress and critical buckling temperature rise for the rectangular thin plate and thin cylindrical shell based on small deformation theory and the Donnell form of the nonlinear equilibrium equations, respectively. Thereafter, the theoretical solutions of the thermal stresses under different boundary conditions and temperature rise variations were determined. The results show that the theoretical solutions of the internal force, thermal stress and critical buckling temperature rise are in good agreement with the numerical results. Finally, the reason leading to the inconsistency of the theoretical solution of the critical buckling temperature rise was elucidated 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.

Asymptotic approximations for pure bending of thin cylindrical shells

A simplified partial wrinkling scenario for in-plane bending of thin cylindrical shells is explored by using several asymptotic strategies. The eighth-order boundary eigenvalue problem investigated here originates in the Donnel–Mushtari–Vlasov shallow shell theory coupled with a linear membrane pre-bifurcation state. It is shown that the corresponding neutral stability curve is amenable to a detailed asymptotic analysis based on the method of multiple scales. This is further complemented by an alternative WKB approximation that provides comparable information with significantly less effort.

수압을 받는 원통형 실린더의 초기부정을 고려한 좌굴해석

Pressure hulls of submerged structures are generally designed as circular cylinders, spheres or cones with form of axisymmetric shell of revolution to withstand the high external pressure of deep ocean. The compressive buckling (implosion) due to hydrostatic pressure is the main concern of structural design of pressure hull and many design codes are provided for it. It is well-known that the buckling behavior of thin shell of revolution is very sensitive to the initial geometric imperfections introduced during the construction process of cutting and welding. Hence, the theoretical solutions for thin shells with perfect geometry often provide much higher buckling pressures than the measured data in tests or real structures and more precise structural analysis techniques are prerequisite for the safe design of pressure hulls. So this paper dealt with various buckling pressure estimation techniques for unstiffened circular cylinder under hydrostatic pressure conditions. The empirical design equations, eigenvalue analysis technique for critical pressure and collapse behaviors of thin cylindrical shells by the incremental nonlinear FE analysis were applied. Finally all the obtained results were compared with those of the pressure chamber test for the aluminium models. The pros and cons of each techniques were discussed and the most rational approach for the implosion of circular cylinder was recommended.

PHYSICAL FIELDS OF CIRCULAR CYLINDRICAL PIEZOCERAMIC RECEIVER IN PRESENCE OF A FLAT ACOUSTIC SOFT SCREEN

System in the form of a circular cylindrical piezoceramic transducer near a flat acoustic screen was analyzed. The aim of the work was to solve the problem of receiving plane sound waves by «cylindrical piezoceramic transducer – flat acoustically soft screen» system.Considered system was characterized by a violation of the radial symmetry of the radiation load of the transducer while maintaining the radial symmetry of the electric load. At the same time, the energy perceived by the system under consideration is distributed between all modes of oscillation of the transducer, while the conversion of mechanical energy into electric is realized only at zero mole of oscillations.Special attention was paid to the method of coupled fields in multiply connected domains using the imaging method. The design model of the «transducer–creen» system was formulated taking into account the interaction of acoustic, mechanical and electric fields in the process of energy conversion, the interaction of a cylindrical transducer with a flat screen and the interaction of a converter with elastic media outside and inside it. The physical fields of the system under consideration were determined by following solutions: the wave equation; equations of motion of thin piezoceramic cylindrical shells in displacements; equations of stimulated electrostatics for piezoceramics for given boundary conditions, conditions for coupling fields at interfaces and electrical conditions.A general conclusion was made concerning solving of an infinite system of linear algebraic equations with respect to the unknown coefficients of the expansion of the fields. As an example of the application of the obtained relations, a calculation was made and an analysis of the dependences of the electric fields of the system under consideration for various parameters of its construction on the direction of arrival on the plane wave system was conducted.

Free vibration analysis of rotating fiber–metal laminate circular cylindrical shells

In this article, free vibration of rotating fiber–metal laminate thin circular cylindrical shells has been analyzed. Strain–displacement relations have been obtained based on Love’s first approximation shell theory. The variations of frequencies of the fiber–metal laminate cylindrical shell with rotational speeds for different axial and circumferential wave numbers, L/R ratios, metal thicknesses and volume fractions of metal have been presented. Also, free vibrations of the rotating fiber–metal laminate shell have been studied for carbon/epoxy, glass/epoxy and aramid/epoxy composite materials combining thin aluminum layers. The results showed that with increasing rotating speed, the gap between backward and forward waves frequencies increased.

Redirection and splitting of sound waves by a periodic chain of thin perforated cylindrical shells

A line of perforated cylindrical shells in air is practically transparent for sound since each individual unit is a weak scatterer. However, strong scattering occurs due to the coupling to the acoustic eigenmodes of the chain. Here we develop an analytical theory of sound transmission and scattering at a linear chain of perforated shells and predict strong anomalous effect for oblique incidence. The chain eigenmodes are weakly decaying, with symmetric profile and anomalous dispersion, or with antisymmetric profile and normal dispersion, and their excitation leads to deep minima in the transmission and 90̊-redirection of the external sound. At normal incidence, only the symmetric eigenmode can be excited, otherwise both modes are excited at close frequencies. Moreover, the wave which resonates with the normal-dispersion mode is redirected along the “right” direction, whereas the wave resonating with the anomalous-dispersion mode is redirected in the “wrong” direction. Thus, a periodic chain of perforated shells may serve not only as a 90̊-redirecting antenna but also as a splitter of sound waves with close frequencies. For example, an acoustic signal containing two frequencies around 3 kHz can be split into monochromatic components propagating in opposite directions along the chain, if the beat frequency is ≈500 Hz.

A robust approach for analysing dispersion of elastic waves in an orthotropic cylindrical shell

Dispersion of elastic waves in a thin orthotropic cylindrical shell is considered, within the framework of classical 2D Kirchhoff-Love theory. In contrast to direct multi-parametric analysis of the lowest propagating modes, an alternative robust approach is proposed that simply requires evaluation of the evanescent modes (quasi-static edge effect), which, at leading order, do not depend on vibration frequency. A shortened dispersion relation for the propagating modes is then derived by polynomial division and its accuracy is numerically tested against the full Kirchhoff-Love dispersion relation. It is shown that the same shortened relation may be also obtained from a refined dynamic version of the semi-membrane theory for cylindrical shells. The presented results may be relevant for modelling various types of nanotubes which, according to the latest experimental findings, possess strong material anisotropy.

Development of beam modal function for free vibration analysis of FML circular cylindrical shells

The free vibration of fiber–metal laminate (FML) thin circular cylindrical shells with different boundary conditions has been studied in this research. Strain–displacement relations have been obtained according to Love’s first approximation shell theory. To satisfy the governing equations of motion, a beam modal function model has been used. The effects of different FML parameters such as material properties lay-up, volume fraction of metal, fiber orientation, and axial and circumferential wavenumbers on the vibration of the shell have been studied. The frequencies of shells have been calculated for carbon/epoxy and glass/epoxy as composites and for aluminum as metal. The results demonstrate that the influences of FML lay-up and volume fraction of composite on the frequencies of the shell are remarkable.

Thermomechanical buckling and post-buckling of cylindrical shell with functionally graded coatings and reinforced by stringers

The cylindrical shells reinforced by stringers have been widely used in modern engineering structures such as storage tanks, missile, submarine hull, oil-transmitting pipeline, etc. In this present article, the thermomechanical buckling and post-buckling behaviors of a cylindrical shell with functionally graded (FG) coatings are investigated by an analytical approach. The cylindrical shell is reinforced by outside stringers under torsional load in the thermal environment. The layers of FG coatings are assumed to be made by functionally graded materials (FGMS) combining of ceramic and metal phases and the core of the shell is made from homogeneous material. The classical shell theory based on the von-Karman assumptions is used to model the thin cylindrical shell. Using Galerkin's procedure and Airy stress function, the governing equations can be solved to obtain the closed-form solution for the critical buckling load and postbuckling load-deflection curves of simply supported shells. Moreover, many important parametric studies of stringers, temperature field, material volume fraction index, the thickness of metal layer, etc. are taken into investigation. According to numerical examples, it is revealed that the outside strings have considerably impact on thermomechanical buckling and postbuckling behaviors of the shells.