Directional radiation pattern in structural-acoustic coupled system

In this paper we demonstrate the possibility of designing a radiator using structural-acoustic interaction by predicting the pressure distribution and radiation pattern of a structural-acoustic coupling system that is composed by a wall and two spaces. If a wall separates spaces, then the wall's role in transporting the acoustic characteristics of the spaces is important. The spaces can be categorized as bounded finite space and unbounded infinite space. The wall considered in this study composes two plates and an opening, and the wall separates one space that is highly reverberant and the other that is unbounded without any reflection. This rather hypothetical circumstance is selected to study the general coupling problem between the finite and infinite acoustic domains. We developed an equation that predicts the energy distribution and energy flow in the two spaces separated by a wall, and its computational examples are presented. Three typical radiation patterns that include steered, focused, and omnidirected are presented. A designed radiation pattern is also presented by using the optimal design algorithm.     

A coupled edge-/face-based smoothed finite element method for structural-acoustic problems

The edge-based smoothed finite element method (ES-FEM) and the face-based smoothed finite element method (FS-FEM) developed recently have shown great efficiency in solving solid mechanics problems with triangular and tetrahedral meshes. In this paper, a coupled ES-/FS-FEM model is extended to solve the structural-acoustic problems consisting of a plate structure interacting with the fluid medium. Three-node triangular elements and four-node tetrahedral elements are used to discretize the two-dimensional (2D) plate and three-dimensional (3D) fluid, respectively, as they can be generated easily and even automatically for complicated geometries. The field variable in each element is approximated using the linear shape functions, which is exactly the same as that in the standard FEM. The gradient field of the problem is obtained particularly using the gradient smoothing operation over the edge-based and face-based smoothing domains in 2D and 3D, respectively. The gradient smoothing technique can provide a proper softening effect to the model, effectively solve the problems caused by the well-known “overly-stiff” phenomenon existing in the standard FEM, and hence significantly improve the accuracy of the solution for the coupled systems. Intensive numerical studies have been conducted to verify the effectiveness of the coupled ES-/FS-FEM for structural-acoustic problems.     

A hybrid finite element approach to modeling sound radiation from circular and rectangular ducts

A numerical model based on a hybrid finite element method is developed that seeks to join sound pressure fields in interior and exterior regions. The hybrid method is applied to the analysis of sound radiation from open pipes, or ducts, and uses mode matching to couple a finite element discretization of the region surrounding the open end of the duct to wave based modal expansions for adjoining interior and exterior regions. The hybrid method facilitates the analysis of ducts of arbitrary but uniform cross section as well the study of conical flanges and here a modal expansion based on spherical harmonics is applied. Predictions are benchmarked against analytic solutions for the limiting cases of flanged and unflanged circular ducts and excellent agreement between the two methods is observed. Predictions are also presented for flanged and unflanged rectangular ducts, and because the hybrid method retains the sparse banded and symmetric matrices of the traditional finite element method, it is shown that predictions can be obtained within an acceptable time frame even for a three dimensional problem.     

A new multi-objective approach to finite element model updating

The single objective function (SOF) has been employed for the optimization process in the conventional finite element (FE) model updating. The SOF balances the residual of multiple properties (e.g., modal properties) using weighting factors, but the weighting factors are hard to determine before the run of model updating. Therefore, the trial-and-error strategy is taken to find the most preferred model among alternative updated models resulted from varying weighting factors. In this study, a new approach to the FE model updating using the multi-objective function (MOF) is proposed to get the most preferred model in a single run of updating without trial-and-error. For the optimization using the MOF, non-dominated sorting genetic algorithm-II (NSGA-II) is employed to find the Pareto optimal front. The bend angle related to the trade-off relationship of objective functions is used to select the most preferred model among the solutions on the Pareto optimal front. To validate the proposed approach, a highway bridge is selected as a test-bed and the modal properties of the bridge are obtained from the ambient vibration test. The initial FE model of the bridge is built using SAP2000. The model is updated using the identified modal properties by the SOF approach with varying the weighting factors and the proposed MOF approach. The most preferred model is selected using the bend angle of the Pareto optimal front, and compared with the results from the SOF approach using varying the weighting factors. The comparison shows that the proposed MOF approach is superior to the SOF approach using varying the weighting factors in getting smaller objective function values, estimating better updated parameters, and taking less computational time.     

A tensor artificial viscosity using a finite element approach

We derive a tensor artificial viscosity suitable for use in a 2D or 3D unstructured arbitrary Lagrangian–Eulerian (ALE) hydrodynamics code. This work is similar in nature to that of Campbell and Shashkov [1]; however, our approach is based on a finite element discretization that is fundamentally different from the mimetic finite difference framework. The finite element point of view leads to novel insights as well as improved numerical results. We begin with a generalized tensor version of the Von Neumann–Richtmyer artificial viscosity, then convert it to a variational formulation and apply a Galerkin discretization process using high order Gaussian quadrature to obtain a generalized nodal force term and corresponding zonal heating (or shock entropy) term. This technique is modular and is therefore suitable for coupling to a traditional staggered grid discretization of the momentum and energy conservation laws; however, we motivate the use of such finite element approaches for discretizing each term in the Euler equations. We review the key properties that any artificial viscosity must possess and use these to formulate specific constraints on the total artificial viscosity force term as well as the artificial viscosity coefficient. We also show, that under certain simplifying assumptions, the two-dimensional scheme from [1] can be viewed as an under-integrated version of our finite element method. This equivalence holds on general distorted quadrilateral grids. Finally, we present computational results on some standard shock hydro test problems, as well as some more challenging problems, indicating the advantages of the new approach with respect to symmetry preservation for shock wave propagation over general grids.     

A finite element approach for scattering from inhomogeneous media with a rough interface

Electromagnetic scattering from an inhomogeneous medium with a one-dimensional rough interface is analysed. The proposed procedure combines the finite element method (FEM), to model the electromagnetic field in the inhomogeneous region, with a perturbative technique to account for the contributions due to the rough interface. Backscattering and bistatic scattering coefficients are computed and plotted for both plane wave and Gaussian beam incident fields in the case of TM_z polarization.     

Non-linear coupled slosh dynamics of liquid-filled laminated composite containers: a two dimensional finite element approach

This paper brings into focus some of the interesting effects arising from the non-linear motion of the liquid free surface, due to sloshing, in a partially filled laminated composite container along with the associated coupling due to fluid-structure interaction effects. The finite element method based on two-dimensional fluid and structural elements is used for the numerical simulation of the problem. A numerical scheme is developed on the basis of a mixed Eulerian-Lagrangian approach, with velocity potential as the unknown nodal variable in the fluid domain and displacements as the unknowns in the structure domain. The FE formulation based on Galerkin weighted residual method along with an iterative solution procedure are explained in detail followed by a few numerical examples. Numerical results obtained by the present investigation for the rigid containers are first compared with the existing solutions to validate the code for non-linear sloshing without fluid-structure coupling. Thereafter the computational procedures are advanced to obtain the coupled interaction effect of non-linear sloshing in laminated composite containers.     

A finite element approach for predicting nozzle admittances

A finite element method is used to predict the admittances of axisymmetric nozzles. It is assumed that the flow in the nozzle is isentropic and irrotational, and the disturbances are small so that linear analyses apply. An approximate, two dimensional compressible model is used to describe the steady flow in the nozzle. The propagation of acoustic disturbances is governed by the complete linear wave equation. The differential form of the acoustic equation is transformed to an integral equation by using Galerkin's method, and Green's theorem is applied so that the acoustic boundary conditions can be introduced through the boundary residuals. The boundary conditions are described for both straight and curved sonic lines. A two dimensional FEM with linear elements is used to solve the acoustic equation. A one dimensional FEM is also used to solve the reduced equation of Crocco, and the solution verifies the sufficiency of the boundary residual formulation. Comparison between computed admittances and experimental data is shown to be quite good.     

A bandstructure approach to the calculation of density correlation functions with application to Vanadium

We discuss how to use KKR bandstructure to evaluate the density-density correlation function in DFA (density functional) — RPA approximation without introducing adjustable parameters. We stress the importance to determine the dielectric function to a high degree of accuracy in the high frequency range to guarantee the fulfillment of the f-sum rule. Results for Vanadium as a typical example of a transition metal are presented and compared to experiment.     

A finite element for the study of coupled bending-prevented torsion of a straight beam

Prevented torsion has been the subject of numerous works, yet curiously in classical finite element programs there appears to be an absence of elements enabling one to take into account the stiffness in warping or the fact that shear centre and surface centre of a section do not always coincide. The object of this article is to present an element which has been experimentally tested and which could enable one to fill the present gap and thus improve accuracy in calculations of structures formed of straight cylindrical beams of any section.     

A non-conforming monolithic finite element method for problems of coupled mechanics

In this study, a Lagrange multiplier technique is developed to solve problems of coupled mechanics and is applied to the case of a Newtonian fluid coupled to a quasi-static hyperelastic solid. Based on theoretical developments in [57], an additional Lagrange multiplier is used to weakly impose displacement/velocity continuity as well as equal, but opposite, force. Through this approach, both mesh conformity and kinematic variable interpolation may be selected independently within each mechanical body, allowing for the selection of grid size and interpolation most appropriate for the underlying physics. In addition, the transfer of mechanical energy in the coupled system is proven to be conserved. The fidelity of the technique for coupled fluid–solid mechanics is demonstrated through a series of numerical experiments which examine the construction of the Lagrange multiplier space, stability of the scheme, and show optimal convergence rates. The benefits of non-conformity in multi-physics problems is also highlighted. Finally, the method is applied to a simplified elliptical model of the cardiac left ventricle.     

Statistical approach to calculation of lifetime with respect to annihilation of a positron-anion system

The lifetimes with respect to annihilation of bound positron-anion systems are calculated in the framework of a statistical model of an atom with consideration of anion electrons. To find the positron wave function, a variational procedure with allowance for the explicit form of the potential that acts on the positron in the anion is used. Calculated lifetimes are compared with Hartree-Fock calculations for some halogen ions. Ways of comparing the results of the theory with experiment are noted.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 49–53, February, 1991.     

A fully coupled 3-D mixed finite element model of Biot consolidation

The numerical solution to the Biot equations of 3-D consolidation is still a challenging task because of the ill-conditioning of the resulting algebraic system and the instabilities that may affect the pore pressure solution. Recently new approaches have been advanced based on mixed formulations. In the present paper a fully coupled 3-D mixed finite element model is developed with the aim at alleviating the pore pressure numerical oscillations at the interface between materials with different permeabilities. A solution algorithm is implemented that takes advantage of the block structure of the discretized problem. The proposed model is verified against well-known analytical solutions and successfully experimented with in realistic applications of soil consolidation.     

A systematic approach to the calculation of tricritical temperature with application to the nematic-smecticA phase transition

Using the Landau expansion equations have been found that allow for systematic calculations of tricritical temperature for a given molecular model. The theory has been applied to nematic-smecticA (NA) phase transition of liquid crystals. It has been shown exactly that the NA tricritical temperature depends only on the couplings between the two lowest order translational order parameters and the orientational degrees of freedom. Numerical results of Mayer and Lubensky for the NA tricritical point have been derived exactly. Also a stability condition of the obtained solution has been discussed.Alexander von Humboldt Foundation Fellow, 1985–1986     

A dipole loudspeaker with a balanced directivity pattern

Analytical equations describing radiation characteristics of an oscillating ring in a circular finite baffle are derived, including the limiting case of a dipole point source at the center. An oscillating sphere would represent the ideal dipole source, having a constant directivity pattern at all frequencies, but would be inconvenient to realize especially in portable devices. It is found that a planar piston with uniform surface velocity but variable phase arranged to emulate the sphere does not have such a smooth on-axis response as the sphere. Instead a planar piston with the same phase distribution but uniform pressure represents an ideal planar source with a smooth on-axis response and near constant directivity. The surface velocity is plotted and it is then shown that a similar response can be achieved using a finite number of concentric rings based on this velocity distribution.     

矩形折射率分布长周期光纤光栅特性中耦合精度的分析

采用耦合模理论,针对光纤芯层为矩形折射率分布的长周期光纤光栅,分析不同模式间耦合对计算精度的影响。结果表明:对于一阶低次包层模式,偶次包层模式与光纤芯层基模的耦合常数要远远小于奇次包层模式与光纤芯层基模的耦合常数。因此,在不影响计算精度的情况下,可以采用忽略偶次包层模式的方法来提高计算速度。同时,根据不同的计算波长范围和计算精度的要求,可以选择合适的正弦折射率调制阶数范围来减小计算工作量。     

Maximum entropy approach to the coupled quadrupole system

The spectral functions of the spin pair correlation functions in a coupled quadrupole system are evaluated using the maximum entropy formalism starting from the exact derivation of the frequency moments to fourth order at the high temperature limit. The numerical computations are carried out for different wave vectors and ratios of the anisotropic field to the quadrupolar interaction. The effects of these parameters on the spectral function are discussed.     

Approximation of the thermally coupled MHD problem using a stabilized finite element method

A numerical formulation to solve the MHD problem with thermal coupling is presented in full detail. The distinctive feature of the method is the design of the stabilization terms, which serve several purposes. First, convective dominated flows in the Navier–Stokes and the heat equation can be dealt with. Second, there is no restriction in the choice of the interpolation spaces of all the variables and, finally, flows highly coupled with the magnetic field can be accounted for. Different aspects related to the design of the final fully discrete and linearized algorithm are also discussed.