Motion Of Shell Research Articles

Electromagnetic frequency prediction pattern for electrical circuited shell based on FSTT theory using electromagnetic wave prediction method

This research focuses on electromagnetic analysis of electrical circuited shell to predict possible failure using wave prediction method. The equation is established considering axial and lateral hydrostatic pressure based on first order shear deformation theory of shell motion using the wave propagation approach and classic Flügge shell equations. For validation of accuracy of this research method, a comparison carried out with experimental data. With this method the effects of circuit parameters as well as different t power-law exponent on the frequencies are investigated. The results showed fantastic agreement between the present method and experimental ones.

Free vibration and buckling behavior of porous orthotropic doubly-curved shallow shells subjected to non-uniform edge compression using higher-order shear deformation theory

Due to the continuous enhancement of manufacturing technology for porous materials, it is expected to be increasingly used in aerospace, aviation, and other engineering applications, where the necessity for lightweight structures is paramount. Also, the non-uniform edge loads caused by service conditions, complex adjacent structures, and external loads lead to localized stress concentrations within the shells. Localized stress concentrations result in a loss of load-carrying capacity in specific regions, causing step-by-step failure of the shell. This study investigates the buckling and free vibration behavior of porous orthotropic doubly-curved shallow shells with four different porosity distribution patterns subjected to non-uniform edge compressive loads. The equations of motion of doubly-curved shallow shells are established by using higher-order shear deformation theory and Hamilton’s principle. Then, the pre-buckling in-plane stress distributions of doubly-curved shallow shells are determined and appended to the equations of motion. These fundamental partial differential equations are solved by Galerkin’s method, and the critical buckling load and natural frequency formulations are achieved. By comparing with the results in published literature, the feasibility and accuracy of present formulations are validated. Finally, systematic parametric studies are carried out to discuss the effects of different non-uniform edge compression patterns, porosity distribution patterns, porosity coefficients, aspect ratios, arc length-to-thickness ratios, radius-to-arc length ratios, orthotropy ratios, and shell types on the buckling and free vibration responses of porous orthotropic doubly-curved shallow shells. Parametric studies indicate that the reduction or increment in critical buckling loads (CBLs) and fundamental natural frequencies (FNFs) of spherical shells (SSs) are more sensitive than those of hyperbolic paraboloidal shells (HPSs). The CBLs and FNFs of SSs are larger than those of HPSs. The maximum and minimum CBLs are achieved for the triangular and uniform edge compression, respectively. The porosity effect is independent of edge compression pattern types.

Structural Quality Factor of Flo-TENG under Stochastic Wave Excitation.

Triboelectric nanogenerators (TENGs) have recently emerged as a promising technology for efficient water wave energy harvesting. However, there is a paucity of clear guidance regarding the optimal designs of TENGs and their shells to achieve efficient absorption and conversion of water wave energy in real random waves. Herein, from the perspective of wave-body interaction and energy transfer, this paper proposes a structural quality factor (Qunit) for the quantitative evaluation of both the motion of floating triboelectric nanogenerator (Flo-TENG) shells and their capability to absorb and convert water wave energy efficiently. The factor is further subdivided into the amplitude structural quality factor (Qacc), which characterizes shell motion amplitude, and the frequency structural quality factor (Qf), which describes shell motion frequency. This paper systematically investigates the impact of various shell parameters such as bow shapes, curvatures, inclinations, and immersion ratios on Qacc and Qf. The findings indicate that variations in shell shape result in distinct Qunit values along different axial directions of wave propagation. These variations directly influence energy absorption efficiency in these directions. These results provide fundamental guidance for the design of high-performance Flo-TENG shells and the selection of internal energy harvesting directions to enable more efficient energy conversion.

Thermoelastic damping properties in hemi-ellipsoidal shells with variable thickness

Thermoelastic damping (TED) is a fundamental dissipation mechanism that inevitably exists in shell resonators with high quality factors. Based on the thermal energy method, this paper demonstrates an effective method for the TED characterization of the hemi-ellipsoidal shells with variable thickness which manifest lower TED compared with the hemispherical shells. The equation of motion of the hemi-ellipsoidal shell under clamped-free boundary conditions is established by Hamilton's principle and the assumed mode method, and the natural frequencies and mode shape functions of the hemi-ellipsoidal shell with variable thickness are obtained by solving the eigenvalue problem. The temperature field is acquired by solving the heat conduction equation along the radial direction, and an analytical model for the TED of the hemi-ellipsoidal shell with variable thickness is presented by calculating the maximum elastic potential energy and the work lost per cycle of vibration due to irreversible heat conduction. Analysis on TED at the vibration patterns of meridional wave number m = 1 and the circumferential wave number n = 2 or 3 where the shell resonators typically operate is carried out. The analytically calculated TED results are compared with those of the finite element method (FEM) to verify the feasibility and correctness of the present method. The influences of the geometrical parameters on the TED characteristics of the hemi-ellipsoidal shells with variable thickness are analyzed in detail. A meaningful discovery is that compared with the hemispherical shell, the hemi-ellipsoidal shell with variable thickness has a smaller TED when its semiminor axis is shorter than the semimajor axis, which is particularly significant for optimizing the design of the shell resonators with high quality factors.

Incipient Motion of Single Shells under Currents in Flume Experiments

Understanding the motion thresholds of shells is important, as shell motion allows the analysis of beach profiles, prevents excessive erosion of the coastline, and helps to resource the use of discarded shells, providing new ideas for the protection of beaches. In this study, the orientational motions and motion thresholds of two types of typical molluscan shells, bivalve and gastropod shells, were investigated by means of flume experiments. The final orientations with the statistically highest number of occurrences during the orientational motions of each shell were used as the initial orientations for the respective threshold flow velocity measurements. The critical Shields parameter and the incipient mean velocity of the flow were used to represent the critical threshold of the motion. The critical Shields parameters for bivalve shells in the convex upward position were overall higher on average than those for gastropod shells. The experimental data showed that the incipient mean flow velocities of bivalve shells in the convex upward position were about 1.4–2.8 times larger than those in the convex downward position. The incipient mean velocity data were regressed to obtain the motion threshold equations applicable to bivalve shells in the convex upward and convex downward positions as well as gastropod shells under different final orientations.

Analysis of quasi-periodic and chaotic motion of a dielectric elastomer shell under alternating voltage

Analysis of quasi-periodic and chaotic motion of a dielectric elastomer shell under alternating voltage

Mixed convection flows from a revolving cylindrical cavity

Efforts are made to describe the thermofluidic behavior around a spinning hot cylindrical open cavity with negligible wall thickness suspended in air within the laminar regime. Several important input parameters, such as, Rayleigh number ( 10 2 ≤ Ra ≤ 10 6 ) , aspect ratio ( 0.5 ≤ H / D ≤ 10 ) , and Reynolds number ( 0 ≤ Re D ≤ 300 ) are considered to carry out the ongoing numerical analysis. Firstly, thermal plumes are provided to describe the pattern of flow and heat transfer around the heated surfaces of shell by considering the effect of Ra , H / D , and Re D . It is predicted that the heated plume is thrown radially due to the presence of swirling motion ( Re D ≠ 0 ) of the cylindrical shell unlike the pattern of thermal plume around the stationary vessel. Furthermore, the influence of Re D on behavior of cooling rate from inner ( Q iw ) and outer ( Q ow ) surfaces has also been predicted by considering both stationary and swirling conditions. A substantial growth in Q iw is noticed with the growth of Re D for a constant H / D . This effect is substantially greater at lower H / D compared to higher H / D . Again, attempts are made to elucidate the influence of Re D on Nusselt number for cylindrical inner wall ( Nu cyl − iw ) , cylindrical outer wall ( Nu cyl − ow ) , base inner wall ( Nu base − iw ) , and base outer wall ( Nu base − ow ) . Fluid flow behavior around the stationary and revolving cylindrical open cavity is also explained by employing velocity vectors. Finally, an appropriate correlation demonstrating a reasonable agreement with numerical data is found for average Nusselt number in terms of Ra , H / D , and Re D .

Vibroacoustic analysis of submerged fluid-filled cylindrical shell

This study presents a comprehensive Chebyshev-Fourier spectral method for analyzing the free and forced vibroacoustic characteristics of submerged fluid-filled cylindrical shells in heavy fluids. The vibroacoustic interaction system of submerged cylindrical shells consists of three discrete regions: The Sanders shell theory is applied for the shell structure, whereas the wave equation is used to determine the fluid inside. The external fluid pressure on the shell is described using the Helmholtz boundary integral equation. The governing equations for the shell's motion, the formulation of the external fluid pressure on the fluid-structure-interaction (FSI) surface using first-class Chebyshev polynomial and Fourier series expansions, and the internal sound pressure employing two-dimensional Chebyshev polynomial and Fourier series expansions, are seamlessly integrated with Gauss-Chebyshev-Lobatto sampling techniques. Artificial springs are implemented to replicate the boundary conditions of the cylindrical shell. The precision of the proposed methodology is corroborated by comparisons with existing literature and finite element method (FEM) results. Furthermore, the research examines how the properties of the acoustical medium on the vibroacoustic responses of the cylindrical shell. Results indicate that the presence of air inside the shell slightly influence on its acoustic radiation. However, replacing the internal medium with water significantly alters the shell's original radiation characteristics.

Nonlinear vibrations of porous-hyperelastic cylindrical shell under harmonic force using harmonic balance and pseudo-arc length continuation methods

The resonant responses are investigated for the porous-hyperelastic Mooney–Rivlin cylindrical shell subjected to a radial harmonic excitation. Considering the higher-order shear deformation theory (HSDT), fourth-order strain-displacement relations are derived, which include the radial geometric imperfections varying along the thickness direction. Using the porous-hyperelastic Mooney–Rivlin constitution relation and Lagrange equation, the differential governing equations of motion are obtained for the porous-hyperelastic cylindrical shells. The resonant conditions are presented and the accuracy of the mathematical models is verified. The harmonic balance and pseudo-arc length continuation methods are used to obtain the amplitude-frequency and forced-amplitude curves. The stability of the solutions is analyzed by Floquet theory. The effects of the external excitation amplitudes, structure parameters and porosity infill parameters on the linear frequencies, amplitude-frequency responses and force-amplitude responses are discussed for the imperfect porous-hyperelastic cylindrical shells. The results show that the linear frequencies of the porous-hyperelastic cylindrical shells increase obviously as the uniform and sigmoid function porosity parameters reach the certain values. The increase of the structure parameters enhances the response amplitudes of the first-order mode and minified response amplitudes of the second-order mode. The decreasing porosity ratios weaken the softening nonlinear behaviors of the porous-hyperelastic cylindrical shells. With the changes of the external excitation amplitudes and structure parameters, the motion of the porous-hyperelastic cylindrical shell indicates that the synchronous vibrations occur with the period and chaotic vibrations alternately.

EQUATIONS OF MOTION OF AN ISOTROPIC SPHERICAL MOMENT ELASTIC SHELL*2

Using the previously obtained equations of motion of thin moment elastic shells of constant thickness with an arbitrary middle surface, the equations of motion of an isotropic moment spherical shell in terms of forces and “displacements” (kinematic parameters) are constructed. In this case, the metric of the middle spherical surface is taken into account, as the curvilinear coordinates of which two angular coordinates of the standard spherical coordinate system with the origin at the center of the middle surface are used. First, a closed system is written down, which includes the equations of motion in the physical components of the tensors of internal forces and moments, as well as additional similar characteristics corresponding to the moment properties of the model, and physical relationships. Then, by excluding physical relations, it is reduced to twelve equations of motion in kinematic parameters, written in operator form. In this case, the coefficients of partial derivative operators are simplified by neglecting terms that have a higher order of smallness relative to the thickness of the shell. Despite the bulkiness of the system, it is written in a compact form. Boundary conditions are not written, since the shell is considered closed. By introducing additional hypotheses similar to those used in the classical theory of shells (neglecting the compression of a normal fiber, the Kirchhoff – Love hypothesis about the connection between the tangential components of the rotation angle vector of a normal fiber and normal displacement, as well as the hypothesis about the connection between the normal to the middle surface part of the coordinate of the rotation angle vector and its tangential components) the number of equations and unknowns decreases. To carry out this procedure, a variational Hamilton equation is constructed, which takes into account the connections between kinematic parameters imposed by the hypotheses, and then the corresponding one is transformed using the generalized Ostrogradsky – Gauss theorem.

Free vibration analysis of FGM spherical and elliptical shells under nonlinear thermal environments

The thermo-mechanical effects of the free vibration of functionally graded (FG) spherical and elliptical shells under nonlinear temperature distributions (NTD) are investigated. The geometries of the FG spherical and elliptical shells are expressed in terms of the surface fundamental form, and the displacement function is derived based on higher-order shear deformation theory (HSDT). Temperature-dependent (TD) material and heat conduction are investigated based on Voigt's micromechanical model. The equation of motion of the thermo-elastic FG shells is formulated using the classical Hamilton's principle. Numerical results are obtained using the finite element method with quadrilateral Lagrangian isoparametric elements. A comparison of the results for the free vibration of FG shells based on the FSDT and HSDT approaches is presented. The first fundamental mode is the axisymmetric mode for the circular plate and oblate shell, but the results are otherwise for spherical and prolate shells. The torsional mode occurs in the seventh mode within the first ten vibrational modes for the prolate shell. In addition, the frequency parameter in the torsional mode is independent of the different support conditions. Parametric studies show that the non-dimensional frequency parameters of the FG shells decrease quickly, then slowly, as the volume fraction index increases. Finally, the frequency parameters decrease when the temperature at the top of the FG shell surface increases.

Study of Gap Flow Effects on Sound Transmission Through a Micro-Perforated Sandwich Cylindrical Shell Excited by a Plane Wave

This paper presents a theoretical model to study sound transmission through a micro-perforated double-walled sandwich cylindrical shell with emphasis on the potential of internal gap flow to improve the sound insulation performance. This model adopts Donnell’s thin shell theory to govern the shell motions and a simplified model based on Biot’s theory to describe sound propagation in the porous lining. The mean acoustic particle velocity model with the grazing flow effect is applied to define the coupling condition between the fluid medium and the perforated shell. Transmission loss (TL) through the configuration with one gap flow is numerically calculated using the mode superposition method when subjected to an oblique plane wave in the presence of an external mean flow. Results reveal that the gap flow in the opposite direction to the external flow would elevate the mid-frequency TL. Gap depth has a complicated effect on TL since it influences the aerodynamic damping of the gap flow and sound dissipation in the porous layer. The average TL in 20–20[Formula: see text]000[Formula: see text]Hz is then optimized with a genetic algorithm, and an increase of 17.82 dB is finally achieved. The possibility of tuning the structural sound insulation performance by the gap flow has been verified.

Creep of Concrete in Shell Structures: Nonlinear Theory.

The creep of concrete is one of the main problems threatening concrete structural development and the stability and safety of structures. However, the nonlinear theory is the key to solving the problem of taking into account the physical and mechanical properties of concrete creep in shell structures. To create such a theory, the original shell is replaced by a continuous equivalent elastic shell. To determine the stress-strain state of the structure, the equations of nonlinear creep and crack growth are derived, and a deformation model of the section is created. The behavior of the structure at all stages of the life cycle is investigated by solving the solving systems of differential equations of equilibrium, motion, and perturbation of the equivalent shell. The values of the ratios of dependence of long-term and short-term critical loads on deformations, forces, cracks, etc., are given. The accuracy of the solution of the developed nonlinear theory is compared with the linear theory of concrete creep as well as experimental data. The results show that, according to the linear theory, for the values for the short term and long term, up to 56% and up to 39% of critical loads are overestimated, respectively. The creep process in practical engineering can be effectively controlled by the results of the proposed theory.

Spin–orbit coupling of Europa’s ice shell and interior

Europa is an icy ocean world, differentiated into a floating ice shell and solid interior, separated by a global ocean. The classical spin–orbit coupling problem considers a satellite as a single rigid body, but in the case of Europa, the existence of the subsurface ocean enables independent motion of the ice shell and solid interior. This paper explores the spin–orbit coupling problem for Europa from a dynamical perspective, yielding illuminating analytical and numerical results. We determine that the spin behavior of Europa is influenced by processes not captured by the classical single rigid body spin–orbit coupling analysis. The tidal locking process for Europa is governed by the strength of gravity-gradient coupling between the ice shell and solid interior, with qualitatively different behavior depending on the scale of this effect. In this coupled rigid model, the shell can potentially undergo large angular displacements from the solid interior, and the coupling plays an outsize role in the dynamical evolution of the moon, even without incorporating the dissipative effects of shell non-rigidity. We additionally discuss the effects of a realistic viscoelastic shell, and catalogue other torques that we expect to be sub-dominant in Europa’s spin dynamics, or whose importance is unknown. Finally, we explore how the choice of tidal model affects the resulting equilibrium spin state.

Nuclear spin relaxation in aqueous paramagnetic ion solutions.

A Brownian shell model describing the random rotational motion of a spherical shell of uniform particle density is presented and validated by molecular dynamics simulations. The model is applied to proton spin rotation in aqueous paramagnetic ion complexes to yield an expression for the Larmor-frequency-dependent nuclear magnetic resonance spin-lattice relaxation rate T_{1}^{-1}(ω) describing the dipolar coupling of the nuclear spin of the proton with the electronic spin of the ion. The Brownian shell model provides a significant enhancement to existing particle-particle dipolar models without added complexity, allowing fits to experimental T_{1}^{-1}(ω) dispersion curves without arbitrary scaling parameters. The model is successfully applied to measurements of T_{1}^{-1}(ω) from aqueous manganese(II), iron(III), and copper(II) systems where the scalar coupling contribution is known to be small. Appropriate combinations of Brownian shell and translational diffusion models, representing the inner and outer sphere relaxation contributions, respectively, are shown to provide excellent fits. Quantitative fits are obtained to the full dispersion curve of each aquoion with just five fit parameters, with the distance and time parameters each taking a physically justifiable numerical value.

Ключевые вопросы создания надувных тормозных устройств для увода вышедших из строя спутников в плотные слои атмосферы. Часть 1. Проектный облик. Движение в разреженной атмосфере

Development of the near-Earth space is accompanied by space debris appearing in the near-Earth orbits and consisting of artificial satellites, elements of other spacecraft, launch vehicles and upper stages with the exhausted resource. High activity of enthusiasts creating nanosatellites of the CubeSat class forces to make gloomy forecasts of space pollution. To clean the near-Earth space from debris, a variety of projects is proposed that provide for collection of the already accumulated debris and equipping the new generation of rocket and space systems with means for transferring to the burial orbits or into the atmosphere dense layers. Promising means of eliminating space debris include inflatable braking devices designed to transfer the fastened objects into the atmosphere dense layers. The braking device temperature state is formed under the influence of thermal radiation flows from the Sun and the Earth and kinetic heating caused by motion in the rarefied atmosphere. The paper considers options of the conceptual design of an inflatable braking device for nanosatellites of the CubeSat class positioned in the low Earth orbits. Results are provided of simulating motion of the thin-walled spherical shell of the inflatable braking device. Duration of reaching the atmosphere dense layers was estimated.

Can radial motions in the stellar halo constrain the rate of change of mass in the Galaxy?

ABSTRACT A change in the mass of the Galaxy with time will leave its imprint on the motions of the stars, with stars having radially outward (mass-loss) or inward (mass accretion) bulk motions. Here, we test the feasibility of using the mean radial motion of stars in the stellar halo to constrain the rate of change of mass in the Galaxy, e.g. due to decay of dark matter. In the lambda cold dark matter (ΛCDM) paradigm, the stellar halo is formed by accretion of satellites on to the host galaxy and its mean radial motion 〈VR〉 is eventually expected to be close to zero. But due to incomplete mixing most haloes have substructures and this can lead to non-zero 〈VR〉 in them. Using simulations, we measure the mean radial motion of stars in 13 ΛCDM stellar haloes lying in a spherical shell of radius 30 kpc. For most haloes, the shell motion is quite small, with 75 per cent of haloes having $\langle V_\text{R}\rangle \lesssim 1.2 \:{\rm km}\, {\rm s}^{-1}$. When substructures are removed by using a clustering algorithm, 〈VR〉 is reduced even further, with 75 per cent of haloes having $\langle V_\text{R}\rangle \lesssim 0.6 \:{\rm km}\, {\rm s}^{-1}$. A value of $\langle V_\text{R}\rangle \approx 0.6 \:{\rm km}\, {\rm s}^{-1}$ can be attained corresponding to a galactic mass-loss rate of 2 per cent per Gyr. We show that this can place constraints on dark matter decay parameters such as the decay lifetime and the kick velocity that is imparted to the daughter particle. The advent of all-sky stellar surveys involving millions to billions of stars is encouraging for detecting signatures of dark matter decay.

Forced vibroacoustic response of a cylindrical shell in an underwater acoustic waveguide

An analytical approach is proposed to analyze vibroacoustics of an infinitely long thin cylindrical shell under line-distributed harmonic excitation immersed in an underwater waveguide formed by a free surface and a rigid floor. Equations of motion of the thin shell are modeled using Flügge’s shell theory, the fluid–structure coupling is implemented with the image source method to account for the infinite reflections of acoustic waves off the waveguide boundaries and Graf’s addition theorem is used to reconcile the coordinate systems of the image sources in the analytical expressions. The vibroacoustic response from the proposed analytical model is verified by numerical results obtained from a finite element model, showing excellent agreement. The analytical approach provides a computationally efficient tool for parametric investigation into the relative effects of the proximity of the free surface and/or rigid floor on the vibroacoustic behavior of the shell.

Thermoelastic damping in cylindrical shells with arbitrary boundaries

An effective method is proposed for the dynamic modelling and thermoelastic damping (TED) evaluation of the cylindrical shells with arbitrary boundaries. The arbitrary boundary conditions of the cylindrical shell are simulated by a set of springs, and the degree of the boundary condition is achieved by adjusting the spring stiffnesses. Hamilton's principle with the Rayleigh-Ritz method is employed to establish the equation of motion of the cylindrical shell, and the natural frequencies of the cylindrical shell with arbitrary boundaries are obtained by solving the eigenvalue problem of the equation of motion. An analytical model for the TED in the cylindrical shell is obtained by computing the dissipated energy and the maximum elastic potential energy in the cylindrical shell. The correctness and feasibility of the present theoretical model are verified by comparing the natural frequencies and TED obtained by this analytical method with those from the published literature and the finite element method (FEM). The convergence analysis of the analytical expression of TED is carried out. The influences of geometrical parameters and different types of spring stiffnesses on the TED are studied. In addition, the effects of the boundary conditions and the vibration modes of the structure on the TED characteristics of the cylindrical shells with arbitrary boundaries are analyzed. The present model provides theoretical reference for optimizing the cylindrical shell resonators with high quality factors.

Behaviour of a non-linear mesh cylindrical shell as an element of mems and nems

A new mathematical model of a non-linear mesh cylindrical shell behaviour in the temperature field under normal distributed load is constructed. The construction of the mathematical model takes into account the Kirchhoff-Love kinematic model and the Duhamel-Neumann hypothesis. The scaling effect is taken into account by the modified moment theory of elasticity. It is assumed that the displacement and rotation fields are not independent. Geometric nonlinearity is taken into account according to T. von Karman's theory. The equations of motion of the smooth shell, boundary and initial conditions are derived from the variational Ostrogradsky-Hamiltonian principle. The lattice structure of the shell was modelled by the continuum theory of G. I. Pshenichny. This allowed us to replace the regular rib system by a continuous layer. The equilibrium conditions of a rectangular element were used to write down the relations connecting stresses occurring in an equivalent smooth shell with stresses in the ribs. The Lagrange multiplier method has been used to determine the physical relationships for the mesh shell. By means of the method of establishment the study of features of the shell's plasticity has been carried out and the frequencies of natural linear vibrations depending on the mesh geometry have been obtained.