Showing papers on "Spherical shell published in 2019"

Application of flügge thin shell theory to the solution of free vibration behaviors for spherical-cylindrical-spherical shell: A unified formulation

Abstract: The main purpose of this paper is to provide a semi analytical method to analyze the free vibration of spherical-cylindrical-spherical shell subject to arbitrary boundary conditions. The formulations are established based on energy method and Flugge thin shell theory. The displacement functions are expressed by unified Jacobi polynomials and Fourier series . The arbitrary boundary conditions are simulated by penalty method about spring stiffness . The final solutions of spherical-cylindrical-spherical shell are obtained by Rayleigh–Ritz method. To sufficient illustrate the effectiveness of proposed method, some numerical example about spring stiffness, Jacobi parameters etc. are carried out. In addition, to verify the accuracy of this method, the results are compared with those obtained by FEM, experiment and published literature. The results show that the proposed method has ability to solve the free vibration behaviors of spherical-cylindrical-spherical shell.

Free vibration characteristics of functionally graded porous spherical shell with general boundary conditions by using first-order shear deformation theory

Abstract: The paper analyzed the free vibration of functionally graded porous spherical shell (FGPSS) based on Ritz method. The energy method and first-order shear deformation theory (FSDT) are adopted to derive the formulas. In this paper, the displacement functions are improved on basis of domain decomposition method, in which the unified Jacobi polynomials are introduced to represent the displacement functions component along meridional direction, and the displacement functions component along circumferential direction is still Fourier series. In addition, the spring stiffness method is formed a unified format to deal with various complex boundary conditions and continuity conditions. Then the final solutions can be obtained based on Ritz method. To prove the validity of proposed method, the results of the same condition are compared with those obtained by FEM, published literatures and experiment. The results show that the proposed method has advantages of fast convergence, high calculation efficiency, high solution accuracy and simple boundary simulation.

Free vibration study of multilayer sandwich spherical shell panels with viscoelastic core and isotropic/laminated face layers

Abstract: The present work deals with the free vibration and damping characteristics study of multilayer sandwich spherical shell panels with viscoelastic material core layers and elastic face layers based on first order shear deformation theory. The displacements of the core layers are assumed to vary linearly along the thickness. Longitudinal and transverse deformations of the core layers are taken in to account with the consideration of independent transverse displacements of the elastic layers. The equation of motion is derived using Hamilton's principle in conjunction with the finite element method. Eight number of sandwich shell panels are studied mainly in two groups viz. sandwich panels with laminated base layer and isotropic base layer. Fundamental frequencies and associated system loss factors of different sandwich shell panels are deduced by solving the equation as an eigenvalue problem. The effect of thickness of the constraining layers, thickness of the core layers, viscoelastic material loss factor and aspect ratio on the natural frequencies and system loss factors of the sandwich structures are investigated.

Precessing spherical shells: Flows, dissipation, dynamo and the lunar core

Abstract: Precession of planets or moons affects internal liquid layers by driving flows, instabilities and possibly dynamos. The energy dissipated by these phenomena can influence orbital parameters such as the planet's spin rate. However, there is no systematic study of these flows in the spherical shell geometry relevant for planets, and the lack of scaling law prevents convincing extrapolation to celestial bodies. We have run more than 900 simulations of fluid spherical shells affected by precession, to systematically study basic flows, instabilities, turbulence, and magnetic field generation. We observe no significant effects of the inner core on the onset of the instabilities. We obtain an analytical estimate of the viscous dissipation, mostly due to boundary layer friction in our simulations. We propose theoretical onsets for hydrodynamic instabilities, and document the intensity of turbulent fluctuations. We extend previous precession dynamo studies towards lower viscosities, at the limits of today's computers. In the low viscosity regime, precession dynamos rely on the presence of large-scale vortices, and the surface magnetic fields are dominated by small scales. Interestingly, intermittent and self-killing dynamos are observed. Our results suggest that large-scale planetary magnetic fields are unlikely to be produced by a precession-driven dynamo in a spherical core. But this question remains open as planetary cores are not exactly spherical, and thus the coupling between the fluid and the boundary does not vanish in the relevant limit of small viscosity. Moreover, the fully turbulent dissipation regime has not yet been reached in simulations. Our results suggest that the melted lunar core has been in a turbulent state throughout its history. Furthermore, in the view of recent experimental results, we propose updated formulas predicting the fluid mean rotation vector and the associated dissipation in both the laminar and the turbulent regimes.

Convective overshooting and penetration in a Boussinesq spherical shell

Abstract: Author(s): Korre, L; Garaud, P; Brummell, NH | Abstract: We study the dynamics associated with the extension of turbulent convective motions from a convection zone (CZ) into a stable region (RZ) that lies below the latter. For that purpose, we have run a series of three-dimensional direct numerical simulations solving the Navier-Stokes equations under the Boussinesq approximation in a spherical shell geometry. We observe that the overshooting of the turbulent motions into the stably stratified region depends on three different parameters: the relative stability of the RZ, the transition width between the two, and the intensity of the turbulence. In the cases studied, these motions manage to partially alter the thermal stratification and induce thermal mixing, but not so efficiently as to extend the nominal CZ further down into the stable region. We find that the kinetic energy below the convection zone can be modeled by a half-Gaussian profile whose amplitude and width can be predicted a priori for all of our simulations. We examine different dynamical lengthscales related to the depth of the extension of the motions into the RZ, and we find that they all scale remarkably well with a lengthscale that stems from a simple energetic argument. We discuss the implications of our findings for 1D stellar evolution calculations.

Nonlinear Vibration Behavior of Rapidly Heated Temperature-Dependent FGM Shallow Spherical Shells

Abstract: In the present research, thermally induced vibration of shallow spherical shells made of functionally graded materials is investigated. The thermomechanical properties of the FGM media are assumed ...

Structural similitude for the geometric nonlinear buckling of stiffened orthotropic shallow spherical shells by energy approach

Abstract: General similitude requirements and the scaling laws for nonlinear buckling of stiffened orthotropic shallow spherical shells are presented by applying similitude transformation to the total energy of the structural system. In the absence of the experimental data, structural similitude is completed by numerical experiments. The predicted values of the prototype, obtained by substituting the model results into the scaling laws, are compared with those values of the prototype. In practical engineering, it may be hard to fulfill the complete similarity requirements. Thus, several cases of partial similitude are mainly investigated, including models distorted in material properties of ribs, in material properties and in material properties and geometry. By using specific formulas of stiffness parameters and the displacement scale factor, distorted models can predict geometric nonlinear buckling behavior of the prototypes of the stiffened orthotropic shallow spherical shell under external pressure with good accuracy.

Charged Gravastars with Conformal Motion in f(R,T) Gravity.

Abstract: This paper studies the effects of charge on a peculiar stellar object, recognized as gravastar, under the influence of $f(R,T)$ gravity by considering the conjecture of Mazur and Mottola in general relativity. The gravastar is also known as an alternative to a black hole and is expressed by three distinct domains named as (i) the interior domain, (ii) the intermediate shell and (iii) the exterior domain. We analyze these domains for a specific $f(R,T)$ gravity model conceding the conformal Killing vectors. In the interior domain, we assume that pressure is equal to negative energy density which leads to the existence of repulsive force on the spherical shell. The intermediate shell consists of ultra-relativistic plasma and pressure which shows a direct relation with energy density and counterbalances the repulsive force applied by the interior domain. The exterior vacuum spherical domain is taken to be the de Sitter spacetime illustrated by the Reissner-Nordstrom metric. We conclude that non-singular solutions of charged gravastar with various physical properties such as length, energy, entropy and equation of state parameter are physically consistent.

Sensitivity to luminosity, centrifugal force, and boundary conditions in spherical shell convection

Abstract: We test the sensitivity of hydrodynamic and magnetohydrodynamic turbulent convection simulations with respect to Mach number, thermal and magnetic boundary conditions, and the centrifugal force. We...

Charged gravastars with conformal motion in f (R,T ) gravity

Abstract: This paper studies the effects of charge on a peculiar stellar object, recognized as gravastar, under the influence of $f(R,T)$ gravity by considering the conjecture of Mazur and Mottola in general relativity. The gravastar is also known as an alternative to a black hole and is expressed by three distinct domains named as (i) the interior domain, (ii) the intermediate shell and (iii) the exterior domain. We analyze these domains for a specific $f(R,T)$ gravity model conceding the conformal Killing vectors. In the interior domain, we assume that pressure is equal to negative energy density which leads to the existence of repulsive force on the spherical shell. The intermediate shell consists of ultra-relativistic plasma and pressure which shows a direct relation with energy density and counterbalances the repulsive force applied by the interior domain. The exterior vacuum spherical domain is taken to be the de Sitter spacetime illustrated by the Reissner-Nordstrom metric. We conclude that non-singular solutions of charged gravastar with various physical properties such as length, energy, entropy and equation of state parameter are physically consistent.

Physics of even-even superheavy nuclei with $96 < Z < 110$ in the quark-meson-coupling model

Abstract: The quark-meson-coupling (QMC) model has been applied to the study of the properties of even-even superheavy nuclei with 96≤Z≤110, over a wide range of neutron numbers. The aim is to identify the deformed shell gaps at N=152 and N=162, predicted in macroscopic-microscopic (macro-micro) models, in a model based on the mean-field Hartree-Fock+BCS approximation. The predictive power of the model has been tested on proton and neutron spherical shell gaps in light doubly closed (sub)shell nuclei Ca40, Ca48, Ni56, Ni56, Ni78, Zr90, Sn100, Sn132, Gd146, and Pb208, with results in a full agreement with experiment. In the superheavy region, the ground-state binding energies of 98≤Z≤110 and 146≤N≤160 differ, in the majority of cases, from the measured values by less than ±2.5MeV, with the deviation decreasing with increasing Z and N. The axial quadrupole deformation parameter, β2, calculated over the range of neutron numbers 138≤N≤184, revealed a prolate-oblate coexistence and shape transition around N=168, followed by an oblate-spherical transition towards the expected N=184 shell closure in Cm, Cf, Fm, and No. The closure is not predicted in Rf, Sg, Hs, and Ds as another shape transition to a highly deformed (β2≈0.4) shape in Sg, Hs, and Ds for N>178 appears, while Rf288 (N=184) remains oblate. The bulk properties predicted by QMC, such as ground-state binding energy, two-neutron separation energy, the empirical shell-gap parameter δ2n and Qα values, are found to have a limited sensitivity to the deformed shell gaps at N=152 and 162. However, the evolution of the neutron single-particle spectra with 0≤β2≤0.55 of Cm244, Cf248, Fm252, No256, Rf260, Sg264, Hs268, and Ds272, as representative examples, gives a (model-dependent) evidence for the location and size of the N=152 and 162 gaps as a function of Z and N. In addition, the neutron number dependence of neutron pairing energies provides supporting indication for existence of the energy gaps. Based on these results, the mean-field QMC and macro-micro models and their predictions of deformed shell structure of superheavy nuclei are compared. Clearly the QMC model does not give results as close to the experiment as the macro-micro models. However, considering that it has only four global variable parameters (plus two parameters of the pairing potential), with no local adjustments, the results are promising.

Likely equilibria of stochastic hyperelastic spherical shells and tubes

Abstract: In large deformations, internally pressurised elastic spherical shells and tubes may undergo a limit-point, or inflation, instability manifested by a rapid transition in which their radii suddenly increase. The possible existence of such an instability depends on the material constitutive model. Here, we revisit this problem in the context of stochastic incompressible hyperelastic materials, and ask the question: what is the probability distribution of stable radially symmetric inflation, such that the internal pressure always increases as the radial stretch increases? For the classic elastic problem, involving isotropic incompressible materials, there is a critical parameter value that strictly separates the cases where inflation instability can occur or not. By contrast, for the stochastic problem, we show that the inherent variability of the probabilistic parameters implies that there is always competition between the two cases. To illustrate this, we draw on published experimental data for rubber, and derive the probability distribution of the corresponding random shear modulus to predict the inflation responses for a spherical shell and a cylindrical tube made of a material characterised by this parameter.

Studies a star made of anisotropic fluid packed in a spherical shell

Abstract: We provide a general framework of global behavior of static solutions of spherically symmetric objects for the modeling of compact objects, making it an ideal fluid to study, analytically and numer...

Different Models of Rolling for a Robot Ball on a Plane as a Generalization of the Chaplygin Ball Problem

Abstract: This paper addresses the problem of the rolling of a spherical shell with a frame rotating inside, on which rotors are fastened. It is assumed that the center of mass of the entire system is at the geometric center of the shell. For the rubber rolling model and the classical rolling model it is shown that, if the angular velocities of rotation of the frame and the rotors are constant, then there exists a noninertial coordinate system (attached to the frame) in which the equations of motion do not depend explicitly on time. The resulting equations of motion preserve an analog of the angular momentum vector and are similar in form to the equations for the Chaplygin ball. Thus, the problem reduces to investigating a two-dimensional Poincare map. The case of the rubber rolling model is analyzed in detail. Numerical investigation of its Poincare map shows the existence of chaotic trajectories, including those associated with a strange attractor. In addition, an analysis is made of the case of motion from rest, in which the problem reduces to investigating the vector field on the sphere S2.

Dual Optical Signal-based Intraocular Pressure-sensing Principle Using Pressure-sensitive Mechanoluminescent ZnS:Cu/PDMS Soft Composite

Abstract: This paper presents a novel principle for intraocular pressure (IOP)-sensing (monitoring) based on a pressure-sensitive soft composite in which a dual optical signal is produced in response to impulsive pressure input. For the initial assessment of the new IOP sensing principle, a human eye is modeled as the spherically shaped shell structure filled with the pressurized fluid, including cornea, sclera, lens and zonular fiber, and a fluid-structure interaction (FSI) analysis was performed to determine the correlation between the internal pressure and deformation (i.e., strain) rate of the spherical shell structure filled with fluid by formulating the finite element model. The FSI analysis results for human eye model are experimentally validated using a proof-of-conceptual experimental model consisting of a pressurized spherical shell structure filled with fluid and a simple air-puff actuation system. In this study, a mechanoluminescent ZnS:Cu- polydimethylsiloxane (PDMS)-based soft composite is fabricated and used to generate the dual optical signal because mechanically driven ZnS:Cu/PDMS soft composite can emit strong luminescence, suitable for soft sensor applications. Similar to the corneal behavior of the human eye, inward and outward deformations occur on the soft composite attached to the spherical shell structure in response to air puffing, resulting in a dual optical signal in the mechnoluminescence (ML) soft composite.

Buckling load prediction of an externally pressurized thin spherical shell with localized imperfections

Abstract: A simple formula for buckling load was derived from the asymptotic analysis of nonlinear behavior of a thin spherical shell. Firstly, two asymptotic cases were studied: the initial post-buckling re...

Shallow shell theory of the buckling energy barrier: From the Pogorelov state to softening and imperfection sensitivity close to the buckling pressure.

Abstract: We study the axisymmetric response of a complete spherical shell under homogeneous compressive pressure p to an additional point force For a pressure p below the classical critical buckling pressure p_{c}, indentation by a point force does not lead to spontaneous buckling but an energy barrier has to be overcome The states at the maximum of the energy barrier represent a subcritical branch of unstable stationary points, which are the transition states to a snap-through buckled state Starting from nonlinear shallow shell theory, we obtain a closed analytical expression for the energy barrier height, which facilitates its effective numerical evaluation as a function of pressure by continuation techniques We find a clear crossover between two regimes: For p/p_{c}≪1 the postbuckling barrier state is a mirror-inverted Pogorelov dimple, and for (1-p/p_{c})≪1 the barrier state is a shallow dimple with indentations smaller than shell thickness and exhibits extended oscillations, which are well described by linear response We find systematic expansions of the nonlinear shallow shell equations about the Pogorelov mirror-inverted dimple for p/p_{c}≪1 and the linear response state for (1-p/p_{c})≪1, which enable us to derive asymptotic analytical results for the energy barrier landscape in both regimes Upon approaching the buckling bifurcation at p_{c} from below, we find a softening of an ideal spherical shell The stiffness for the linear response to point forces vanishes ∝(1-p/p_{c})^{1/2}; the buckling energy barrier vanishes ∝(1-p/p_{c})^{3/2}; and the shell indentation in the barrier state vanishes ∝(1-p/p_{c})^{1/2} This makes shells sensitive to imperfections which can strongly reduce p_{c} in an avoided buckling bifurcation We find the same softening scaling in the vicinity of the reduced critical buckling pressure also in the presence of imperfections We can also show that the effect of axisymmetric imperfections on the buckling instability is identical to the effect of a point force that is preindenting the shell In the Pogorelov limit, the energy barrier maximum diverges ∝(p/p_{c})^{-3} and the corresponding indentation diverges ∝(p/p_{c})^{-2} Numerical prefactors for proportionalities both in the softening and the Pogorelov regime are calculated analytically This also enables us to obtain results for the critical unbuckling pressure and the Maxwell pressure

Optically thin outbursts of rotating neutron stars cannot be spherical

Abstract: We investigate three-dimensional relativistic trajectories of test particles in the spacetime of a slowly rotating compact star, under the combined influence of gravity and a strong, near-Eddington radiation field. While in the static case a spherically symmetric shell of matter suspended above the stellar surface can be formed at the location of radial equilibrium of effective forces, the same is not true for a rotating star. In the latter case the symmetry is broken by the interplay between motion in the non-static spacetime and the influence of strong radiation drag forces, pushing particles towards the equatorial plane. As a result an expanding spherical shell of matter ejected from the neutron star surface collapses on a short timescale into a single stable equatorial ring supported by radiation. These findings have implications for the geometry of optically thin outflows during luminous neutron star bursts.

Analytical study of transient thermo-mechanical responses in a fractional order generalized thermoelastic diffusion spherical shell with variable thermal conductivity and diffusivity

Abstract: With the great development of micro-electromechanical devices and wide application of subpicosecond/femtosecond ultrafast laser technology in micro-machining of micro-electromechanical devi...

Onset of fully compressible convection in a rapidly rotating spherical shell

Abstract: The onset of thermal convection in a rapidly rotating spherical shell is studied by linear stability analysis based on the fully compressible Navier–Stokes equations. Compressibility is quantified by the number of density scale heights regime.

Transient dynamic analysis of laminated shallow spherical shell under low-velocity impact

Abstract: The impact of transient response laminated shallow shells due to transverse foreign object was investigated analytically and experimentally. The analytical analysis is presented by using the new higher order shear deformation shell theory. The contact force ishassumedhtohbe a known inputhtohthehanalysis. Contact force and transverse deflection of laminated shell have been measured with a piezoelectric force transducer (load cell) and a piezoelectric bending transducer respectively. Laminates made from E-glass polyester and E-glass/carbon/polyester having different thickness and stacking sequences have been used. The analysis can be used to calculate the difference between the transient stresses, displacements, velocities, accelerations and energy observation at the center of laminated shell are plotted as function of time during impact between E-glass/polyester and E-glass/carbon/polyester by MATLAB code at different impact heights to determine whether they have a good resistant ability to impact. Finally, it was compared with the results of an experimental test to verify the accuracy and reliability of the theoretical analysis.

Dilute suspension of neutrally buoyant particles in viscoelastic turbulent channel flow

Abstract: Direct numerical simulations of viscoelastic turbulent channel flow laden with neutrally buoyant spherical particles are performed. Two FENE-P viscoelastic and one Newtonian fluid are examined, and for each the particle-laden configuration is contrasted to a reference condition without seeding. The size of the particles is larger than the dissipation length scale, and their presence enhances drag in a manner that is intrinsically different in the viscoelastic and Newtonian flows. While the particles effectively suppress the turbulence activity, they significantly enhance the polymer stresses. The polymer chains are markedly stretched in the vicinity of the particles, altering the correlation between the turbulence and polymer work that is commonly observed in single-phase viscoelastic turbulence. At the lower elasticity, the particles enhance the cycle of hibernating and active turbulence and, in turn, their migration and volume-fraction profiles are qualitatively altered by the intermittency of the turbulence. Particle–fluid momentum transfer is investigated by estimating the local fluid field on a trimmed spherical shell around the individual particles. And by comparing the particle microstructures, a lower probability of particle alignment in the streamwise direction is observed in the viscoelastic configuration. This effect is attributed to a qualitative difference in the conditionally averaged velocity fields in the vicinity of the particles in the Newtonian and viscoelastic flows.