Showing papers on "Spherical shell published in 1991"

Human Head Dynamic Response to Side Impact by Finite Element Modeling

Abstract: The dynamic response of the human head to side impact was studied by 2-dimensional finite element modeling. Three models were formulated in this study. Model I is an axisymmetric model. It simulated closed shell impact of the human head, and consisted of a single-layered spherical shell filled wiht an inviscid fluid. The other two models (Model II and III) are plane strain models of a coronal section of the human head. Model II approximated a 50th percentile male head by an outer layer to simulate cranial bone and an inviscid interior core to simulate the intracranial contents. The configuration of Model III is the same as Model II but more detailed anatomical features of the head interior were added, such as, cerebral spinal fluid (CSF); falx cerebri, dura, and tentorium. Linear elastic material properties were assigned to all three models. All three models were loaded by a triangular pulse with a peak pressure of 40 kPa, effectively producing a peak force of 1954 N (440 lb). The purpose of this study was to determine the effects of the membranes and that of the mechanical properties of the skull, brain, and membrane on the dynamic response of the brain during side impact, and to compare the pressure distributions from the plane strain model with the axisymmetric model. A parametric study was conducted on Model II to characterize fully its response to impact under various conditions.(ABSTRACT TRUNCATED AT 250 WORDS)

Development of deuterated polystyrene shells for laser fusion by means of a density‐matched emulsion method

Abstract: High quality, microdeuterated polystyrene shells were fabricated using a density‐matched emulsion method. The diameter and wall thickness of the shell ranged from 100 to 1500 and 3 to 15 μm, respectively. The sphericity, the wall thickness uniformity, and the surface smoothness were 99.8%, 99.3% and <0.1 μm, respectively. A defect on the inner surface of the shell was smeared by replacing water in the shell with ethanol prior to the final drying process.

Linear theory of rotating fluids using spherical harmonics part II, time-periodic flows

Abstract: Expansion in spherical harmonics is used to solve linear equations of flows of homogeneous viscous fluids in a rotating frame For a truncated series, analytical solutions are obtained for the radial functions These solutions are used to investigate the modal properties of a viscous incompressible fluid in a spherical shell The results are compared to the experimental data of Aldridge The problem of identification of inertial modes in the Earth's outer core is also discussed

Sound scattering by resonantly excited, fluid-loaded, elastic spherical shells

Abstract: The scattering of sound waves by an air‐filled, elastic, spherical shell in deep waters, in the frequency domain is analyzed. This exact analysis is based on the classical formulation of three‐dimensional elastodynamics, for fluid‐loaded spherical shells of arbitrary thickness. Form functions, residual responses, and the partial‐wave expansions of both, are determined. Results are displayed in relatively wide frequency bands for various increasing shell thicknesses. The resonance features in the sonar cross sections (SCS) are isolated by means of a new hybrid modal background that substantially improves the results found with the earlier (rigid/soft) backgrounds of the resonance scattering theory (RST). The resonance features in the SCSs that correspond to each mode, and also to each of the various shell waves that propagate around its periphery are isolated. There seem to be over half‐a‐dozen shell (generalized Lamb and Stoneley) waves manifesting their influence in the SCSs within the examined band. Thr...

Effect of perturbation on the location of libration point in the robe restricted problem of three bodies

Abstract: The effect of small perturbation in the Coriolis and centrifugal forces on the location of libration point in the ‘Robe (1977) restricted problem of three bodies’ has been studied. In this problem one body,m 1, is a rigid spherical shell filled with an homogeneous incompressible fluid of densityϱ 1. The second one,m 2, is a mass point outside the shell andm 3 is a small solid sphere of densityϱ 3 supposed to be moving inside the shell subject to the attraction ofm 2 and buoyancy force due to fluidϱ 1. Here we assumem 3 to be an infinitesimal mass and the orbit of the massm 2 to be circular, and we also suppose the densitiesϱ 1, andϱ 3 to be equal. Then there exists an equilibrium point (−μ + (ɛ′μ)/(1 + 2μ), 0, 0).

Nonlinear planetary dynamos in a rotating spherical shell. I : Numerical methods

Abstract: Results are presented of an investigation of nonlinear planetary dynamo models in the rapid rotation limit for the geometry of a spherical shell. The magnetic induction equation for axisymmetric fields is solved with a prescribed differential rotation and α-effect. The nonlinearity comes from the azimuthal geostrophic flow, whose magnitude is linked to Taylor's constraint as modified by core-mantle viscous coupling in the Ekman boundary layer. The objectives of this work are to determine whether Taylor's constraint is met when the magnetic field is strong and to solve the special numerical stability problems associated with the term which describes the modified Taylor's condition. A stable numerical method based on spectral approximations is presented to solve the general α2ω-dynamo equations. Evidence of the existence of Taylor's states in the geometry of a spherical shell is demonstrated in both the α2- and the αω-limits.

Acoustic Resonance in Spherically Symmetric Waves

Abstract: Resonant oscillations, produced in a gas contained in a vibrating spherical shell, are investigated. The problem is nonlinear, but the approach is different from that used in the analogous problem for plane waves, and the results differ in three major ways: (i) the amplitude of the oscillations is of a larger order of magnitude; (ii) the solutions are not unique; (iii) shock waves do not feature in the solution.

Shells of revolution

Abstract: 1. Introduction.Selected formulae of differential geometry. Selected equations from elasticity theory. Parts: I. Thin Continuous Shells. 2. Foundations of the general theory of shells.The Kirchoff-Love Theory. Vlasov's simplified theory and the theory of shallow shells. 3. Shells of Revolution of Arbitrary Meridian. Arbitrary state of loading. Rotationally symmetric and antisymmetric states of loading. 4. Statics and dynamics of spherical shells.Basic equations. Solution algorithm for displacements. Solution of the equations of Vlasov's theory. Solution for a shallow shell. A solution of Reissner's equations. 5. Statics and dynamics of conical shells. Basic equations. Solution algorithm for equations of motion expressed in terms of displacements. Solution of the governing equations of Vlasov's theory. Solution of Meissner's equations. 6. Statics and dynamics of cylindrical shells.Basic equations. Solution algorithm of equations of motion in terms of displacements. Solution of the equations of Vlasov's theory. Rotationally-symmetric bending. 7. Shells of atypical shape. Basic equations for certain shells. Rotationally-symmetric bending of shallow shells of atypical shape. 8. Membrane theory of shells.Assumptions and basic equations in curvature coordinates. Shells of revolution of arbitrary meridian. Spherical shell. Conical shell. Cylindrical shell. Hyperboloidal and toroidal shells under rotationally-symmetric loading. 9. Approximate calculations by the edge effect method.Assumptions and basic equations. Edge effects. Examples. 10. Foundations of theory of thin layered shells.Assumptions and equations of theory in curvature coordinates. Equations for shells of revolution. II. Shells of Moderate Thickness. 11. Foundations of theory of moderately-thick shells.Equations of the theory in curvature coordinates. Shells of revolution: Meissner-type equations for rotationally symmetric bending. 12. Spherical shell.Refined equations. Rotationally-symmetric bending state Reissner-type equations. A solving algorithm of the problem. Application of power series. 13. Cylindrical shell. Refined equations. Rotationally-symmetric bending state Meissner-type equations. Solution algorithm for the problem Example. III. Perforated Shells. 14. Foundations of the theory of perforated shells.Equations of the theory in curvature coordinates. Shells of revolution under rotationally-symmetric loading. 15. Spherical shells. Equations. Application of real power series. Application of complex power series. Determination of quantities independent of boundary conditions Examples. 16. Cylindrical shells. Equations. Solution algorithm. Various cases of loading example. References. Index.

Ray synthesis of the form function for backscattering from an elastic spherical shell : leaky lamb waves and longitudinal resonances

Abstract: An acoustic ray analysis is employed in synthesizing the form function for backscattering, f(θ=π,ka), from a fluid-loaded evacuated elastic spherical shell where k is the wave number of the incident plane wave and a is the outer radius of the shell The synthesis contains a component associated with a specular reflection, fsp, and contributions from leaky Lamb waves The contribution fl of the lth leaky Lamb wave is expressible in a Fabry–Perot resonator form [P L Marston, J Acoust Soc Am 83, 25–37 (1988)] A comparison of the ray synthesis for f(ka) with the exact partial-wave series representation for a 440c stainless-steel shell verifies the usefulness of the ray synthesis for the present case of a shell The present synthesis is also new in that it includes the effects of longitudinal resonances on fsp A novel ray synthesis of fsp indicates a significant resonance effect near the condition kLh=nπ (n=1,2,…) The thickness of the shell is h, and kL=ω/cL is the longitudinal wave number where cL is

The acoustic scattering by a submerged, spherical shell. II: The high-frequency region and the thickness quasiresonance

Abstract: This article presents a fundamentally oriented analysis of the complex-ka plane pole structure of the S matrix for spherical shells in the thickness range 0.02a⩽h⩽0.10a (a is the outer radius of the sphere) for the high-frequency region (100

In-beam spectroscopy of104Sn

Abstract: The very neutron deficient nucleus 104Sn has been identified in in-beam spectroscopy using the reaction50Cr(58Ni, 2p2n) and neutron and charged particle multiplicity filter detectors. Excited states up to I ≈ 10 and Ex=4 MeV were observed and the level scheme is discussed in the frame work of the spherical shell model.

Analytical Model of Corneal Surgery

Abstract: We present a model of the human cornea in order to study the changes in its shape resulting from surgical operations (e.g., radial keratotomy). A simple closed-form solution is given for a thin linearly elastic spherical shell model of the cornea. We assume axisymmetry and isotropy in the shell surface. The surgery is modeled by permitting Young's modulus and shell thickness to depend on position. The analytical nature of the solution permits principal shell curvatures to be explicitly calculated. The model is used to investigate the effect of surgery on corneal flattening and the associated sensitivity to intraocular pressure changes.

Non-linear buckling of squarely-latticed shallow spherical shells

Abstract: In this paper, a theory for the analysis of large deflection of squarely-latticed shallow spherical shells is constructed by adopting the equivalent continuum method. The von Karman type non-linear differential equations of such latticed shells under actions ofaxisymmetrically distributed loads are derived. An approximate boundary value problem for a uniformly-loaded latticed shallow spherical shell is formulated with variational principles. A practical case of a latticed cap of a petroleum vessel subject to external uniform loads is investigated with this theory, and corresponding buckling loads are numerically presented.

Buckling Design of Imperfect Welded Hemispherical Shells Subjected to External Pressure

Abstract: Welded hemispherical or spherical shells in practice have initial geometric imperfections in them that are random in nature. These imperfections determine the buckling resistance of a shell to external pressure but their magnitudes will not be known until after the shell has been built. If suitable simplified, but realistic, imperfection shapes can be found, then a reasonably accurate theoretical prediction of a spherical shell's buckling/collapse pressure should be possible at the design stage.The main aim of the present paper is to show that the test results obtained at the David Taylor Model Basin (DTMB) on 28 welded hemispherical shells (having diameters of 0.75 and 1.68 m) can be predicted quite well using such simplified shape imperfections. This was done in two ways. In the first, equations for determining the theoretical collapse pressures of externally pressurized imperfect spherical shells were utilized. The only imperfection parameter used in these equations is δ0, the amplitude of the inward r...

Lamb and creeping waves around submerged spherical shells resonantly excited by sound scattering. II: Further applications

Abstract: The scattering of plane sound waves from an air-filled steel spherical shell submerged in water in the frequency band 0⩽k1a⩽500 is studied. This analysis is based on a methodology [Ayres et al., Int. J. Solids Struct. 23, 937–946 (1987) and G. Gaunaurd and M. F. Werby, J. Acoust. Soc. Am. 82, 2021–2033 (1987)] proposed that uses the exact three-dimensional equations of dynamic elasticity to describe the shell motions and to predict its sonar scattering cross section. This approach is valid at all frequencies, for shells of any thickness, of any (constant) curvature, and it accounts for their fluid-loaded condition. The methodology is used to predict the cross sections, which are later interpreted on the basis of the various resonance features that manifest themselves in the frequency response. The spectral locations of these resonances depend on the various types of elastic waves propagating along the shell, or in the surrounding fluid. The exact plots are generated for the phase (cp) velocities of these (Lamb) waves always accounting for the curvature and fluid-loading effects present on the shell, without appeals to plate waves or theories. Some of the dispersion plots were generated using the Donnell shell-theory approximation, which seems to yield accurate results up to the coincidence frequency. Aside from the broad resonance lobe present at the coincidence frequency, there is another high-frequency resonance lobe, due to a thickness-resonance effect, which was also predicted and displayed. A partial-wave analysis of the resonance response curve for a thin shell, around its coincidence frequency, serves to identify the origins of the various types of observed resonance features and to relate them to the elastic and acoustic waves that propagate along the shell or the outer fluid. Many computer-generated graphs are displayed to illustrate the above points.

Similarities between various Lamb waves in submerged spherical shells, and Rayleigh waves in elastic spheres and flat half-spaces

Abstract: A variety of resonance features are studied in the back-scattering cross sections (BSCS) of an air-filled metal spherical shell submerged in water and insonified by a plane cw sound wave. Rayleigh (R) and whispering gallery (WG) waves were originally investigated for vibrational purposes for (flat) half-spaces in contact with vacuum. Lamb waves were originally studied in flat plates also in contact with vacuum. These old findings are generalized to the cases of an elastic spherical shell (o.d./i.d.=2a/2b) fluid-loaded on both surfaces, and excited by an incident plane wave. The various (leaky-type) Lamb waves present in the shell are shown to reduce to the earlier R/WG waves as a≫1≫b and ρf→0. The manner in which each one of these various shell waves manifests itself in the various frequency bands of the shell’s BSCS as perceived by a remote sensor is also studied. Dispersion plots for the various phase velocities of the various waves are displayed in very wide (i.e., 0

Implosion of a two‐layer shell driven by a shaped pressure pulse

Abstract: An analytical model for the implosion of a two‐layer spherical shell target driven by a two‐step pressure pulse is developed. The process of formation of the central spark is approximately described and the effect of the prepulse on the final stage of fuel and pusher is studied. The size of the central spark is determined by the thermal conduction, and scaling laws relating the temperature and density of the spark with the parameters of the fuel and the pulse are found. These scaling laws can be useful in the design of high‐gain targets for inertial confinement fusion.

Blast gauge wherein four pressure sensors are positioned in a tetrahedral configuration on the surface of a sphere

Abstract: The blast gauge has a spherical fairing containing four pressure sensors whose positions on the surface of the sphere form the apices of a tetrahedron. The fairing may have a solid metal sphere with cavities adapted to house the pressure sensors in which the metal is aluminum or an alloy thereof or a foam filled spherical shell containing cavities adapted to house the pressure sensors. The spherical fairing is carried by a tubular support adapted to contain the signal leads from the sensors. In a preferred form the blast gauge includes computing means adapted to receive the signals from the pressure sensors and provide data showing the velocity and direction of any shock wave impinging upon the spherical fairing.

The acoustic scattering by a submerged, spherical shell. III : Pole trajectories in the complex-ka plane

Abstract: Previously, a fundamentally oriented analysis was presented of the complex‐ka plane pole structure of the S matrix for a thin spherical shell for 0

Target identification by means of impulse radar

Abstract: The scattering interaction of short electromagnetic pulses with a spherical target is studied. The target is assumed penetrable and is modeled as an air-filled dielectric shell. The radar cross-section (RCS) of such a target is obtained and its resonance features are analyzed. A dielectric composition makes the resonance features become very prominent compared with the case of an ideally conducting sphere. When the interrogating waveform is a pulse of short duration, the resonance features of the backscattering cross-section can be extracted within the frequency band of the incident pulse. To verify theoretical predictions, spherical targets were illuminated with short broad-band pulses using an impulse radar system. The actual shape of the pulse that is incident on the target is theoretically modeled using a digital filter design techniques, and the predicted backscattered returns of spherical targets are compared with selected echoes of the pulses transmitted by the impulse radar. The authors verify that the shape of the predicted backscattered pulse that results from the design method agrees well with the experimental findings using metal spheres of three different sizes. By means of an incident pulse of designed shape, the form-function in the backscattering radar cross-section of a dielectric target is predicted using a discrete Fourier transform (DFT) technique. It is shown that many of the resonance features of a dielectric spherical shell can be extracted from the frequency band of the incident pulse employing this method. The methodology that is developed can handle broadband pulses of any sufficiently smooth spectrum, interacting with (lossy or lossless) dielectric scatterers, and can extract the resonance features within the frequency band of the transmitted pulse. Accordingly, this methodology could also be used for assessing the performance of high-power impulse radar systems.

Symmetric elements in geometrical analysis of large deformations of spherical shells

Abstract: The paper is devoted to the study of two axisymmetric elements in the geometrical analysis of spherical shells. The application of the elements makes it possible to correctly describe the behaviour of the shell in the range from small to very large deformations. Simple, closed-form analytic expressions for the strain energy of the elements are obtained. The analysis of a spherical shell loaded by a concentrated force and external pressure is presented as an example for result verification. The results are in good agreement with experimental data. The two elements can be used to solve linear, non-linear and stability problems of spherical shells. It is therefore possible to easily implement the results for further elasto-plastic analysis or use them when the shell is a part of a larger structure.

Thermal convection in a spherical shell with a variable radius ratio

Abstract: We consider, as a model for the Earth's core, an electrically conducting fluid sphere with a solid concentric inner core. We impose an azimuthal magnetic field B0(r,θ)1o, azimuthal shear flow U0(r,θ)1 o and temperature distribution T0 (r), where (r,θ,o) are spherical polar coordinates, and consider the linear stability of this basic state. We investigate the effect of the growth of an inner core on convection due to a uniform distribution of heat sources, and find that increasing the inner boundary radius is initially beneficial to convection. Further, increasing the magnetic field strength increases the range of this effect. The introduction of differential rotation provides us with results for a sphere corresponding to those in other geometries (Fearn and Proctor, 1983b; Fearn, 1989). For values of the Roberts number, q = K/n, considered here (q = 10−6 and q = 1) convection becomes inhibited when the magnetic Reynolds number Rm (which measures the strength of the shear) is O(q). When Rm>q conve...