Showing papers on "Antisymmetric relation published in 1987"

A Composite Plate Theory for Arbitrary Laminate Configurations.

Abstract: : In order to improve the accuracy of in-plane responses of shear deformable composite plate theories, a new laminated plate theory was developed for arbitrary laminate configuration based upon Reissner's (1984) new mixed variational principle. To this end, across each individual layer, piecewise linear continuous displacements and quadratic transverse shear stress distributions were assumed. The accuracy of the present theory was examined by applying it to the cylindrical bending problem of laminated plates which had been solved exactly by Pagano (1969). A comparison with the exact solutions obtained for symmetric, antisymmetric and arbitrary laminates indicates that the present theory acurately estimates in-plane responses, even for small span-to-thickness ratios. (Author)

Thermal buckling of thick antisymmetric angle-ply laminates

Abstract: The buckling behavior of moderately thick antisymmetric angle-ply laminates that are simply supported and subject to a uniform temperature rise is analyzed. Transverse shear deformation is accounted for by employing the thermoelastic version of the Reissner-Mindlin theory. Results for the classical thin-plate theory are obtained as a special case. Numerical results are presented for fiber-reinforced laminates and show the effects of ply orientation, number of layers, plate thickness, and aspect ratio on the critical buckling temperature. Finally, an optimization procedure is proposed for the design of laminates having maximum resistance to thermal buckling.

Spin Waves in Systems with Long Period Helical Spin Density Waves Due to the Antisymmetric and Symmetric Exchange Interactions

Abstract: In order to elucidate the different behaviours of the helical spin density waves (HSDW) due to the antisymmetric and symmetric exchange interactions, spin waves in the conical spin density wave (CSDW) states and the induced ferromagnetic states (IFMS) under external magnetic fields are calculated by use of phenomenological Hamiltonians with and without the antisymmetric exchange interaction. It is found that the spin wave spectra for the two types of HSDW are strongly different from each other, especially in the magnetic field dependences, enough to be able to distinguish them. The ESR frequencies are also investigated theoretically for bothtypes. In the light of these results, the observed magnetic field dependencies of the ESR frequencies in MnSi and Fe 1- x Co x Si are discussed to prove the HSDW due to the antisymmetric exchange interaction in these compounds.

Asymmetric interactive buckling of thin-walled columns with initial imperfections

Abstract: In this paper the effect of the interaction between two or more simultaneous buckling modes on the postbuckling behaviour of uniformly compressed thin-walled members (TWM) is analysed by means of the general theory of elastic stability. The analysis is restricted to third-order terms of the energy expansion and therefore can be fruitfully applied to the investigation of structures with asymmetric postbuckling behaviour only. Initial imperfection effect is taken into account. A simplified procedure is suggested for solving the nonlinear equations relative to the evaluation of the bifurcated paths. By using the finite strip method an extensive parametric analysis is performed. It is found that when the flexural-torsional (FT) buckling interacts with a local symmetric and antisymmetric mode, sensitivity to initial inperfections is remarkable and is comparable to the one arising from the interaction between the Euler (E) and any local buckling.

Coupling between symmetric and antisymmetric modes in shells of revolution

Abstract: An analytical-numerical procedure is applied for composite laminated shells of revolu tion in investigating the coupling effect between symmetric and antisymmetric modes and its overall influence. The numerical solution is based on separating the variables in Fourier series in the circumferential direction and conical finite elements in the meridional direc tion. The contribution of the coupling effect is examined by means of parametric analysis.

A multiple scattering interaction analysis of intersecting waveguides

Abstract: A multiple scattering technique is developed for describing the physics of intersecting waveguides. In this picture the two waveguides interact by scattering the fields of each other in a self‐consistent manner. The development of such an analysis is motivated by the fact that the previous theory, which is based on the idea of symmetric and antisymmetric modes of the composite waveguide structure, has a limited validity. The analysis reveals new features of this geometry with important device applications in integrated optics.

Nonlinear TE waves in a dielectric slab waveguide with two optically nonlinear layers

Abstract: Properties of TE waves in a slab waveguide composed of five layers, including two Kerr-like nonlinear layers, are analyzed and examined. We find in particular the occurrence of an asymmetric mode, in addition to the expected symmetric and antisymmetric modes, though the waveguide geometry is symmetric. For the TE 0 symmetric mode, TE 1 antisymmetric and asymmetric modes, the dispersion curves, the relations between the effective index and the optical power density, and the variations of the transverse electric field patterns are illustrated and discussed in detail. As a result of this analysis, the regions in which the respective modes mainly reside are elucidated. We find that the effective index value of the symmetric mode at which the guide power vanishes is larger than that of the antisymmetric mode. For the case in which the effective indexes of the asymmetric and antisymmetric modes are identical, the power in the former mode is found to be larger than that in the latter.

Initial Postbuckling Behavior of Imperfect, Antisymmetric Cross-Ply Cylindrical Shells Under Torsion

Abstract: This paper deals with the initial postbuckling of antisymmetric cross-ply closed cylindrical shells under torsion. Under the assumptions employed in Koiter’s theory of elastic stability, the structure is imperfection-sensitive in certain intermediate ranges of the reduced-Batdorf parameter (approx. 4 ≤ ZH ≤ 20.0). Due to different material bending-stretching coupling behavior, the (0 deg inside, 90 deg outside) two-layer clamped cylinder is less imperfection sensitive than the (90 deg inside, 0 deg outside) configuration. The increase in torsional buckling load due to a higher value of Young’s moduli ratio is not necessarily accompanied by a higher degree of imperfection-sensitivity. The paper is the first to consider imperfection shape to be identical to the torsional buckling mode and presents concise parameter variations involving the reduced-Batdorf paramter and Young’s moduli ratio.

The first two moments of energy level distributions in N-electron spin-adapted model spaces

Abstract: Formulae are derived for the average value and for the dispersion of the spectrum of an electronic Hamiltonian in a finite-dimensional, antisymmetric and spin-adapted space. Both the moments are expressed in terms of the corresponding two-electron quantities. The derivation is based on the theory of spin-adapted reduced Hamiltonians.

Heisenberg-Weyl algebras of symmetric and antisymmetric bosons

Abstract: All the polynomials in symmetric ((2)) and antisymmetric ((11)) u(n) bosons are constructed in u(n) bases and u(n)-reduced matrix elements for the bosons between polynomial basis states are computed. Applications to representation theory of Lie groups, paired-fermion and boson physics are briefly discussed.

Clarification of the electronic asymmetry of Λ doublets in 3Π electronic states of diatomic molecules

Abstract: The reflection symmetry of the spatial part of the electronic wave function for 3Π diatomic molecular states is examined carefully for the individual Λ doublet levels by means of an approach presented earlier [M. H. Alexander and P. J. Dagdigian, J. Chem. Phys. 80, 4325 (1984)]. The results are: For a 3Π molecule in Hund’s case (a) the electronic wave function in the Ω=1 (F2) e levels will be antisymmetric and, in the the f levels, symmetric with respect to reflection of the spatial coordinates of the electrons in the plane of rotation of the molecule. The electronic wave functions in the F1 and F3 levels will not have a defined plane of symmetry. By contrast, in the Hund’s case (b) high J limit, the electronic wave function in the F1e, F2 f, and F3e levels will be antisymmetric and, in the F1 f, F2e, and F3 f levels, symmetric with respect to reflection. Thus, the symmetry of the wave functions in the F2Λ‐doublet levels reverses with the passage from case (a) to case (b). In the case (b) limit, the main ...

Vibration analysis of laminated anisotropic shells of revolution

Abstract: An efficient computational procedure is presented for the free vibration analysis of laminated anisotropic shells of revolution, and for assessing the sensitivity of their response to anisotropic (nonorthotropic) material coefficients. The analytical formulation is based on a form of the Sanders-Budiansky shell theory including the effects of both the transverse shear deformation and the laminated anisotropic material response. The fundamental unknowns consist of the eight stress resultants, the eight strain components, and the five generalized displacements of the shell. Each of the shell variables is expressed in terms of trigonometric functions in the circumferential coordinate and a three-field mixed finite element model is used for the discretization in the meridional direction. The three key elements of the procedure are: (a) use of three-field mixed finite element models in the meridional direction with discontinuous stress resultants and strain components at the element interfaces, thereby allowing the elimination of the stress resultants and strain components on the element level; (b) operator splitting, or decomposition of the material stiffness matrix of the shell into the sum of an orthotropic and nonorthotropic (anisotropic) parts, thereby uncoupling the governing finite element equations corresponding to the symmetric and antisymmetric vibrations for each Fourier harmonic; and (c) application of a reduction method through the successive use of the finite element method and the classical Bubnov-Galerkin technique. The potential of the proposed procedure is discussed and numerical results are presented to demonstrate its effectiveness.

Eigenmode analysis of symmetric parallel waveguide couplers

Abstract: An analysis of a laterally symmetric parallel waveguide structure has been carried out by using symmetric and antisymmetric eigenmodes in the coupled mode equations. As opposed to modes of each individual guide, eigenmodes are orthogonal and therefore comply with coupled mode formalism. Of particular interest has been the popular configuration Z -cut LiNbO 3 with Wave propagation along the crystal Y -axis. The theory shows that output versus voltage characteristics are nonperiodic in voltage, and furthermore, they are asymmetric if the eigenmodes are not equally excited. The uniform electrode coupler can easily be explained in terms of eigenmode coupling and interference.

Heat kernal expansion coefficient. I. An extension

Abstract: The author argues that it is possible to obtain the asymptotic expansion coefficients for an operator with torsion from the expansion coefficients for an operator without torsion. This is possible when both operators act on the same set of eigenfunctions in the same way, and therefore have the same spectrum. The author calculates in four dimensions (a2(- Square Operator +Bk Del k+X)) using the Schwinger-DeWitt ansatz. Then following the argument above he obtains (a2(- Square Operator -Bk Del k+X)) where tildes denote torsion. He compares results with a modest direct calculation using 'toy torsion' (totally antisymmetric and covariantly constant) and obtains agreement. He discusses the results and reviews the literature. He finds no other algorithms for (a2(- Square Operator +Bk Del k+X)) consistent with the limiting case (a2(- Square Operator +Bk Del k+X)). There are three appendices with useful coincidence limits and curvature tensor relations.

Transverse-magnetic-polarized nonlinear modes guided by a symmetric five-layer dielectric structure.

Abstract: TM-polarized nonlinear modes supported by a symmetric five-layer dielectric structure consisting of a nonlinear medium of thickness θ (characterized by the diagonal dielectric tensor ∊11 = ∊22 ≡ ∊0, ∊33 = ∊0 + α|E3|2, where E3 is the TE-field component) sandwiched between two linear films of thickness β (with dielectric constant ∊1), which are bounded from the free ends by the same nonlinear medium, are analyzed. Dispersion relations and the expressions for the power flow, derived for the symmetric and antisymmetric modes, show that for a sufficiently large value of β/λ, where λ is the wavelength, these modes should show bistable behavior, provided that power flow is the control parameter.

The hyperspherical expansion method

Abstract: This lecture is divided in four main sections. In the first one we study the general properties of harmonic polynomials, we derive various hyperspherical harmonic basis and we explain how to construct antisymmetric harmonic polynomials.

Model‐size reduction for the non‐linear dynamic analysis of quasi‐symmetric structures

Abstract: A computational procedure is presented for the efficient non‐linear dynamic analysis of quasi‐symmetric structures. The procedure is based on approximating the unsymmetric response vectors, at each time step, by a linear combination of symmetric and antisymmetric vectors, each obtained using approximately half the degrees of freedom of the original model. A mixed formulation is used with the fundamental unknowns consisting of the internal forces (stress resultants), generalized displacements and velocity components. The spatial discretization is done by using the finite element method, and the governing semi‐discrete finite element equations are cast in the form of first‐order non‐linear ordinary differential equations. The temporal integration is performed by using implicit multistep integration operators. The resulting non‐linear algebraic equations, at each time step, are solved by using iterative techniques. The three key elements of the proposed procedure are: (a) use of mixed finite element models with independent shape functions for the stress resultants, generalized displacements, and velocity components and with the stress resultants allowed to be discontinuous at interelement boundaries; (b) operator splitting, or restructuring of the governing discrete equations of the structure to delineate the contributions to the symmetric and antisymmetric vectors constituting the response; and (c) use of a two‐level iterative process (with nested iteration loops) to generate the symmetric and antisymmetric components of the response vectors at each time step. The top‐ and bottom‐level iterations (outer and inner iterative loops) are performed by using the Newton—Raphson and the preconditioned conjugate gradient (PCG) techniques, respectively. The effectiveness of the proposed strategy is demonstrated by means of a numerical example and the potential of the strategy for solving more complex non‐linear problems is discussed.

Model‐size reduction for the analysis of symmetric structures with asymmetric boundary conditions

Abstract: A simple computational procedure is presented for reducing the size of the analysis model for a symmetric structure with asymmetric boundary conditions to that of the corresponding structure with symmetric boundary conditions. The procedure is based on approximating the asymmetric response of the structure by a linear combination of symmetric and antisymmetric global approximation vectors (or modes). The key elements of the procedure are (1) restructuring the governing finite-element equations to delineate the contributions to the symmetric and antisymmetric components of the asymmetric response, (2) successive application of the finite element method and the classical Rayleigh-Ritz technique. The finite-element method is first used to generate a few global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the Rayleigh-Ritz technique. The effectiveness of the computational procedure is demonstrated by means of numerical examples of linear static problems of shells, and its potential for solving nonlinear problems is discussed.

Transient response of fluid-loaded elastic plates via an impulse response method

Abstract: A general time domain approach to evaluate the transient velocity and pressure fields of fluid‐loaded plates, which are excited by one‐dimensional broadband excitations, is presented. A mechanical pressure, which is independent of the acoustic field, is used to excite the plate. The approach is based on the use of a time‐dependent in vacuo modal expansion of the velocity of the plate. As a result of the fluid coupling, the time‐dependent velocity coefficients of the modes are described by a set of coupled, linear, convolution integral equations which can be solved by marching forward in time. If both symmetric and antisymmetric modes are excited, they are not coupled and the equations are separated into two sets which are solved independently. Typical numerical results are presented showing the impulse responses of the modal admittance of the plate, the coupling coefficients, the modal velocities of the plate when coupling effects are included and are neglected, and the pressure in the farfield.

On the uniqueness of solitary Rossby waves

Abstract: (Received 18 December 1985; revise d 17 March 1986 and 10 June 1986)AbstractThe explicit solitary Rossby wave solutions found by Larichev, Reznik and Berestov areshown to be unique for the model equations considered, in the sense that there are noother antisymmetric wave solutions which are not of these forms. This is done byadapting arguments used by Amick and Fraenkel to show the uniqueness of the Hill'svortex solution. It is based on the maximum principle and the domain folding method ofGidas, Ni and Nirenberg, and involves showing that the function >|//y is radiallysymmetric, where ^ is the streamfunction of a solitary wave and y the horizontalcartesian coordinate perpendicular to the x-axis, along which the waves move at steadypositive speed. This argument is also used to show the uniqueness of the well-knownexplicit solutions for cylindrical vortices. The result does not apply directly to ridersolutions of Flierl et al., which are not antisymmetric, but it does restrict the possiblerider solutions that can form because of their association with particular antisymmetricsolutions.

Collective 2+ states in the U(5) classical limit of the proton-neutron interacting boson model

Abstract: The U(5) classical limit of the proton-neutron interacting boson model Hamiltonian, appropriate for the collective 2/sup +/ states, is investigated. The symmetric and mixed-symmetry 2/sup +/ states are identified as arising from the boson-number-weighted symmetric and antisymmetric vibrations in the beta degree of freedom, respectively. Also approximate formulas for the energies away from the U(5) limit and for the reduced matrix elements of the E2 and M1 transition operators are given.