Thin Cylindrical Shell Research Articles

Wave based method for vibration analysis of elastically coupled annular plate and cylindrical shell structures

Free and forced vibrations of elastically coupled thin annular plate and cylindrical shell structures under elastic boundary conditions are studied through wave based method. The method is involved in dividing the coupled structure into shell segments and annular plates. Flügge shell theory and thin plate theory are utilized to describe motion equations of segments and plates, respectively. Regardless of boundary and continuity conditions, displacements of individual members are expressed as different forms of wave functions, rather than polynomials or trigonometric functions. With the aid of artificial springs, continuity conditions between segments and plates are readily obtained and corresponding governing equation can be established by assembling these continuity conditions. To test accuracy of present method, vibration results of some coupled structures subjected to different boundary and coupling conditions are firstly examined. As expected, results of present method are in excellent agreement with the ones in literature and calculated by finite element method (FEM). Moreover, effects of annular plates, elastic coupling and boundary conditions, excitation and damping are also studied. Results show that normal displacement of annular plate mainly affects free vibrations of the coupled structures, while tangential displacement has the greatest effect on forced vibrations as meridinoal or normal excitation forced on the annular plate.

Application of a Polymer Compound to a Plane Surface by an Elastic Plate

A mathematical model of the hydroelasticity of a flow of a non-Newtonian fluid in a wedge-shaped clearance with an elastic wall has been constructed. This wall represents a thin cylindrical elastic shell inextensible along its central axis, for which the Kirchhoff–Love hypotheses are true. A fluid flow in the clearance was simulated in the approximation of the Reynolds lubrication theory with the use of an asymptotic approximation for the second invariant of the strain rate tensor. Results of numerical investigations with the mathematical model proposed are presented.

Natural Frequencies and Modes of Noncircular Cylindrical Shells with Variable Thickness

The dynamic characteristics of thin cylindrical isotropic shells with variable thickness are determined using numerical and experimental approaches. Numerical calculations are performed by the finite-element method with FEMAR software. In experimental study, stroboscopic holographic interferometry is used which makes it possible to observe interferential patterns of vibrations of the shell surface in real time. The results obtained by two different methods are compared

Calculation method of locking torque based on elastic thin shell theory for hydraulic locking sleeve

The hydraulic locking sleeve is a key component of precision instruments such as five-axis machine tools, giant astronomical telescope, and satellite antenna. This is subjected to the action of pressure load causing large elastic deformation and locking the rotational freedom of feed shaft at any angle. The maximum locking torque is an important parameter for designing the hydraulic locking sleeve. First, the hydraulic locking sleeve is simplified as elastic thin cylindrical shell structure. Neglecting the bending and twisting effects, the calculation equations describing the deformation and stress state between the hydraulic locking sleeve and rotary shaft are derived by applying the theory of elastic thin shell. Then, taking into account that one end of the hydraulic lock sleeve is fixed to the shaft sleeve seat by the end face flange; the calculating formula of the maximum locking torque of the hydraulic locking sleeve is obtained by modifying the deformation equation based on moment model. Finally, a test platform of hydraulic locking sleeve is designed, which can measure the maximum locking torque of the hydraulic locking sleeve. The error between the calculation result of locking torque theoretical calculation model and the experimental measured value is <15%. As a result, the causes of the error are analyzed, and the effects of the shaft sleeve length, wall thickness, and radius on the maximum locking torque are calculated.

Effect of radial loads on the natural frequencies of thin-walled circular cylindrical shells

In this paper, we study the variation of natural frequencies for thin walled circular cylindrical shells subject to external radial load (uniform and hydrostatic pressure). The study has been performed for four different types of boundary conditions viz. pinned-pinned, pinned-free, clamped-free and one end is pinned and other end axially constrained. Towards this, we have used approximate shape functions and Galerkin projections of the PDEs governing the shell motion, linearized about a steady state solution due to the applied mean radial pressure. Our results have very good agreement with the experimental and theoretical results available in literature. They have also been verified against finite element analysis (FEA) using ABAQUS. We have found that with increasing magnitude of inward radial load, the natural frequency decreases, however, the circumferential wavenumber corresponding to the lowest natural frequency increases. For outward radial load the opposite happens. Furthermore, the circumferential wavenumbers corresponding to lowest natural frequency and first buckling mode are different for short cylinders with the difference decreasing with increasing length of the cylinder. We have also found an interesting result for the beam mode vibration of cylindrical shells. For short cylinders, the natural frequency of the beam mode increases (decreases) with internal (external) pressure, which is consistent with other circumferential modes. Subsequently, we obtain a critical length at which the applied radial pressure has no effect on the natural frequency. For cylinders longer than the critical length, the effect of the radial load is opposite of that observed for the short cylinders, and this is contrary to the behavior of the other circumferential modes. As a result, buckling of the beam mode happens for an outward radial (internal) pressure.

Nonlinear analysis of dynamic stability for the thin cylindrical shells of supercavitating vehicles

The dynamic stability of supercavitating vehicles under periodic axial loading is investigated in this article. The supercavitating vehicle is simulated as a long and thin cylindrical shell subjected to periodic axial loading and simply supported boundary conditions. The nonlinear transverse vibration differential equation is obtained in terms of nonlinear geometric equations, physical equations, and balance equations of cylindrical shells. Mathieu equation with periodic coefficients and nonlinear term is derived by employing Galerkin variational method and Bolotin method. The analytical expressions of the steady-state amplitudes of vibrations in the first- and second-order instable regions are obtained by solving nonlinear Mathieu equation derived in this article. Numerical results are presented to analyze the influence of the sailing speed, ratio of loads, the frequency of axial loads, and the mode of vibration on parametric resonance curves and to show the nonlinear parametric resonance curves incline toward the side where it is greater than the excitation frequency, which significantly extends the range of the exciting region. The presented results indicate the enlargement of the exciting region will cause shrinkage of the safe frequency range of external loads and decrease in dynamic stability of supercavitating vehicle.

The Relationship between Structural Intensity and Sound Field Characteristics of Cylindrical Shells

It is an important subject in many engineering areas to recognize the vibro-acoustic behaviors of vibrational structures. Many researches have been done to study this characteristics of plane structure with structural intensity (SI) analysis. This paper extends the subject to study this subject by structural intensity approach in cylindrical shell structure and present a method of controlling the sound energy transmission. Structural intensity, a powerful method, can not only quantitatively reflect power flow strength, but also can provide the energy flow directions and distributions. The structural intensity patterns vary under different load and damping conditions, and thus affects the energy level of radiation sound field in cylindrical shell. In this paper, Numerical simulation system was built to represent the simply supported thin cylindrical shell coupled vibration and acoustical radiation structure which excited by harmonic normal point force. We get the corresponding results of structural intensity distribution, sound pressure and acoustic intensity of internal radiation sound field by adjusting damper positions, and calculating the sound field energy. The characteristics of SI of thin cylindrical shell are investigated, and the relationships between SI and sound field are established. We hope that our works could provide researchers new ideas for noise reduction of similar shell structures in potential applications.

Experimental Study on the Influence on Vibration Characteristics of Thin Cylindrical Shell with Hard Coating under Cantilever Boundary Condition

This research has experimentally investigated the influence on vibration characteristics of thin cantilever cylindrical shell (TCS) with hard coating under cantilever boundary condition. Firstly, the theoretical model of TCS with hard coating is established to calculate its natural frequencies and modal shapes so as to roughly understand vibration characteristic of TCS when it is coated with hard coating material. Then, by considering its nonlinear stiffness and damping influences, an experiment system is established to accurately measure vibration parameters of the shell, and the corresponding test methods and identification techniques are also proposed. Finally, based on the measured data, the influences on natural frequencies, modal shapes, damping ratios, and vibration responses of TCS with hard coating are analyzed and discussed in detail. It can be found that hard coating can play an important role in vibration reduction of TCS, and for the most modes of TCS, hard coating will result in the decrease of natural frequencies, but the decreased level is not very big, and its damping effects on the higher frequency range of the shell are weak and ineffective. Therefore, in order to make better use of this coating material, we must carefully choose the concerned antivibration frequency range of the shell; otherwise it may lead to some negative effects.

Качественные эффекты при колебаниях кольцевых подкрепляющих элементов с присоединенной массой, как частный случай тонкой бесконечно длинной круговой цилиндрической оболочки

Качественные эффекты при колебаниях кольцевых подкрепляющих элементов с присоединенной массой, как частный случай тонкой бесконечно длинной круговой цилиндрической оболочки

Influence of Attached Body on the Frequency and Modes Free Vibrations Cylindrical Shells

The paper uses the method of final element in linear function in MSC «Nastran» software complex to study the influence of the inertial properties of the added rigid body-locking rod, which is directed towards mid-surface in normal, by changing its length and the relative mass value on its own dynamic performance of thin circular cylindrical shell. The findings are compared with the case vibration of the shell, carrying the added mass and with the well-known analytic solutions. The mode state (MS) of the construction made the shells with added rod has been studied. The MS of the construction depends on geometrical and physical parameters and on the kind of vibrational forms of the body connected to it have been identified. The rod connected to the shell expands the range frequency of vibration in relation to the shell, carrying the added mass. The influence of its inertial properties with increase of length of the body connected to shell (distancing center of mass connected rod from the shell) had become increasingly important. However, the influence of inertial properties connected with increase in the size of the body accession to shell is decreasing. The ranges, when inertia of jointed body may be disregarded, were presented.

Energy analysis of waves with negative group velocity in cylindrical shell

The problem of joint oscillations of a thin infinite cylindrical Kirchoff-Love shell is considered. The free vibrations of the system are found. The propagating waves and energy flux are analyzed. Much attention is given to the exploration of waves with negative group velocity in the neighborhood of the bifurcation point of dispersion curves. The asymptotics of dispersion curves are used in the neighborhood of the bifurcation point for this case. The interval of system parameters (the relation of lengths of circle waves and lengths of waves along cylinder to the relative thickness of the cylinder) is estimated when the negative group velocity arises. The range of frequencies and wavenumbers where this effect is observed is also estimated. The difference in the kinds of asymptotics for the regular case and the case of bifurcation is discussed. The analysis of arising effects is carried out in terms of kinematic and dynamic variables and in terms of energy flux. Relative advantages and disadvantages of these approaches are discussed. Comparison of the contributions of various mechanisms of energy transmission in the shell to the integral energy flux is performed. A special role of the rotational component in the occurrence of a subzero integrated energy flux is analyzed. The dependence of subzero energy flux and dynamic and kinematic variables on the relative thickness of the shell, the mode number and other parameters of the system is considered. The proportionality of the energy flux and its components for various modes is analyzed. The possible fields of application of the obtained effects are established.

Rock Uniaxial Compression Test and Axial Splitting

Axial splitting is an important failure mechanism in rock engineering. This failure mechanism is particularly observed in the vicinity of free surfaces of rock structures. Different possibilities such as existence of defects, pores and micro-cracks in the rock specimen have been attributed as the cause of axial splitting in the literature. Based on some physical uniaxial compression tests on Pennsylvania blue sandstone, an alternative theory for axial splitting is proposed. In this theory, axial shear cracks are considered that are induced because of non-uniform deformation of the specimen ends. Dislocation along these axial shear cracks is the cause of rock lateral dilation which results in radial stresses. The radial stresses push out the cylindrical thin shells of the specimen. Consequently, radial cracks are developed which subsequently cause rock spalling in mode-I fracture. The proposed failure mechanism is discussed within the framework of a simplified theoretical model. The prediction of the model is then compared with the physical observations. In addition, a discrete element bonded particle system is utilized for rock simulation in uniaxial compression testing. The prediction of the numerical model is consistent with the physical observations.

Rescuing the nonjet (NJ) azimuth quadrupole from the flow narrative

According to the flow narrative commonly applied to high-energy nuclear collisions a cylindrical-quadrupole component of 1D azimuth angular correlations is conventionally denoted by quantity $v_2$ and interpreted to represent elliptic flow. Jet angular correlations may also contribute to $v_2$ data as "nonflow" depending on the method used to calculate $v_2$, but 2D graphical methods are available to insure accurate separation. The nonjet (NJ) quadrupole has various properties inconsistent with a flow interpretation, including the observation that NJ quadrupole centrality variation in A-A collisions has no relation to strongly-varying jet modification ("jet quenching") in those collisions commonly attributed to jet interaction with a flowing dense medium. In this presentation I describe isolation of quadrupole spectra from pt-differential $v_2(p_t)$ data from the RHIC and LHC. I demonstrate that quadrupole spectra have characteristics very different from the single-particle spectra for most hadrons, that quadrupole spectra indicate a common boosted hadron source for a small minority of hadrons that "carry" the NJ quadrupole structure, that the narrow source-boost distribution is characteristic of an expanding thin cylindrical shell (strongly contradicting hydro descriptions), and that in the boost frame a single universal quadrupole spectrum (L\'evy distribution) on transverse mass $m_t$ accurately describes data for several hadron species scaled according to their statistical-model abundances. The quadrupole spectrum shape changes very little from RHIC to LHC energies. Taken in combination those characteristics strongly suggest a unique {\em nonflow} (and nonjet) QCD mechanism for the NJ quadrupole conventionally represented by $v_2$.

Vibration control of a cylindrical shell with concurrent active piezoelectric patches and passive cardboard liner

This article extends a recent publication [MSSP (2016), 176−196] by developing a Rayleigh-Ritz model of a thin cylindrical shell to predict its response subject to concurrent active and passive damping treatments. These take the form of piezoelectric patches and a distributed cardboard liner, since the effects of such combined treatments are yet to be investigated. Furthermore, prior literature typically considers only the “bimorph” active patch configuration (with patches on the inner and outer shell surfaces), which is not feasible with an interior passive liner treatment. Therefore, a novel configuration—termed as “unimorph”—is proposed and included in the model. Experiments are performed on a shell with active patches (under harmonic excitation from 200 to 2000Hz) in both the bimorph and unimorph configurations to provide evidence for the analytical model predictions. The proposed model is then employed to assess competing control system designs by examining local vs. global control schemes as well as considering several alternate active patch locations, both with and without the passive damping. Non-dimensional performance metrics are devised to facilitate comparisons of vibration attenuation among different designs. Finally, insertion loss values are measured under single-frequency excitation to evaluate several vibration control designs, and to compare the effects of alternate damping treatments.

Exact solution of thermoelectroelastic behavior of a fluid-filled FGPM cylindrical thin-shell

This study deals with the thermoelectroelastic behaviors of a fluid-filled functionally graded piezoelectric material (FGPM) cylindrical thin-shell under the combination of mechanical, thermal and electrical loads. The FGPM is composed of piezo ceramic and metal components and the holistic material properties are assumed to vary continuously through the thickness of the shell with power law. Based on the classical cylindrical shell theory, the governing differential equations are derived. Applying the analytical method, exact solution of the problem is obtained. Finally, through numerical examples, the influences of various factors on the thermoelectroelastic behaviors of the fluid-filled FGPM cylindrical thin-shell have been analyzed and discussed.

Nonlinear buckling analysis of pre-stressed ring-stiffened circular cylindrical shells under external pressure

This paper is concerned with the nonlinear buckling behavior of pre-stressed ring-stiffened thin circular cylindrical shells under external pressure. According to the geometrical nonlinearity, governing equations are derived by incorporating initial stresses based on Donnell-type shell theory. The “smeared stiffeners” approach is used for ring stiffeners. The numerical analyses are conducted by Gelerkin’s method to obtain critical buckling loads of shells. This study shows effects of initial stresses on stability of shells. Moreover, effects of initial stresses on buckling modes of shells are discussed.

A novel ‘boundary layer’ finite element for the efficient analysis of thin cylindrical shells

Classical shell finite elements usually employ low-order polynomial shape functions to interpolate between nodal displacement and rotational degrees of freedom. Consequently, carefully-designed fine meshes are often required to accurately capture regions of high local curvature, such as at the ‘boundary layer’ of bending that occurs in cylindrical shells near a boundary or discontinuity. This significantly increases the computational cost of any analysis.This paper is a ‘proof of concept’ illustration of a novel cylindrical axisymmetric shell element that is enriched with rigorously-derived transcendental shape functions to exactly capture the bending boundary layer. When complemented with simple polynomials to express the membrane displacements, a single boundary layer shell element is able to support very complex displacement and stress fields that are exact for distributed element loads of up to second order. A single element is usually sufficient per shell segment in a multi-strake shell.The predictions of the novel element are compared against analytical solutions, a classical axisymmetric shell element with polynomial shape functions and the ABAQUS S4R shell element in three problems of increasing complexity and practical relevance. The element displays excellent numerical results with only a fraction of the total degrees of freedom and involves virtually no mesh design. The shell theory employed at present is kept deliberately simple for illustration purposes, though the formulation will be extended in future work.

Magnetic field created by a conducting cylindrical shell of finite length

A conceptually simple result, which was recently derived for the circulation of the magnetic field created by a finite portion of wire carrying a slowly varying current, is used with the superposition principle and symmetry considerations to obtain an expression for the magnetic field of a thin cylindrical shell of finite length. This expression is combined with a new formula for an oblique solid angle, to obtain closed form solutions for the magnetic field created by the thin cylindrical shell segment in all regions of space. The solutions derived herein are applied in the limiting situations where the cylindrical shell’s length or radius is very large and compared to the known results for the magnetic field of a long conducting tube, and of an infinite plane, respectively. In addition, the use of physical principles of superposition and symmetry in this study is instructive from an educational perspective.

Investigation and a Technique for Calculating the Mode of Deformation of the Bayonet Catch of the Steam Chamber of a Bpm-100 Automatic Line

A computational procedure and technique for computing the strength and tension of a bayonet catch (represented as a thin short cylindrical shell, with a ring on one edge of the shell and teeth along the other edge) loaded on the side of the teeth with a regular load are proposed. It is shown that with this type of loading, the stresses and displacements differ significantly from the computed values obtained in axisymmetric loading.

Vibro-acoustics of cylindrical shells with distributed damping liners

Distributed passive damping treatments (such as cardboard liners, and foam or visco-elastic materials) are routinely placed inside the automotive drive shafts to reduce the airborne and structureborne noise over the applicable mid-frequency range. To better understand the underlying mechanism(s), experimental and analytical studies are undertaken. First, a laboratory experiment is designed to measure vibro-acoustic response functions of a thin cylindrical shell with different cardboard liner thicknesses. Second, the properties of a cardboard liner material are determined by conducting an experiment on an elastic plate treated with a cardboard liner. Third, an analytical framework for shell vibration is developed and the relative sliding motion between substructure and liner is explicitly described. The proposed model agrees well with the experiment in terms of natural frequency shifts, modal loss factors, and modal insertion losses. Several damping mechanisms such as material damping, dry friction, and interfacial viscous friction are examined. Finally, various aspects of the problem including unresolved issues will be briefly discussed.