Problem In Frequency Domain Research Articles

Interaction between rigid-disc inclusion and penny-shaped crack under elastic time-harmonic wave incidence

Influence of a rigid-disc massive inclusion on a neighboring penny-shaped crack induced by the time-harmonic wave propagation in an infinite elastic matrix is investigated by the numerical solution of associated 3D elastodynamic problem. No restrictions on the mutual orientation of interacting objects and direction of wave incidence are assumed. The inclusion is perfectly bonded with a matrix and supposes the translations and rotations, the crack faces are load-free. Frequency-domain problem is reduced to a system of boundary integral equations (BIEs) relative to the interfacial stress jumps (ISJs) on the inclusion and the crack opening displacements (CODs). The subtraction technique in conjunction with mapping technique, under taking into account the structure of solution at the fronts of inclusion and crack, is applied for regularization of BIEs obtained. A discrete analogue of equations is constructed by using the collocation scheme. Numerical calculations are carried out for the grazing incidence of a plane P-wave on the crack, where the interacting inclusion is coplanar and perpendicular to the crack, and has the same radius. The shielding and amplification effects of inclusion are assessed by the analysis of mode-I stress intensity factor (SIF) in the crack vicinity depending on the wave number, incident wave direction, position of the crack front point, inclusion mass, crack-inclusion orientation and distance.

Dynamics of a torsional system with harmonically varying dry friction torque

Nonlinear dynamics of a single degree of freedom torsional system with dry friction is studied in this paper. First, the nonlinear system with a periodically varying normal load is formulated. Second, a multi-term harmonic balance method (MHBM) is re-formulated to directly solve the nonlinear time-varying problem in frequency domain. The feasibility of MHBM is demonstrated with a periodically varying friction and its accuracy is validated by numerical integration using Runge-Kutta scheme. Then, nonlinear frequency response is calculated by assuming classical Coulomb friction law under harmonically varying normal load. Effects of harmonic order and phase lag of normal load are then examined with the proposed approach. Our analysis shows that a change in the harmonic order of the normal load affects responses at both off-peak and peak frequencies while the phase lag has minimal influence on peak frequency responses.

A New Approach for Direct Solution of 2D Heat Transfer Problems in Frequency Domain with Dynamic Boundary Conditions

Article A New Approach for Direct Solution of 2D Heat Transfer Problems in Frequency Domain with Dynamic Boundary Conditions was published on September 1, 2008 in the journal International Journal of Nonlinear Sciences and Numerical Simulation (volume 9, issue 3).

Fault estimations for linear systems with polytopic uncertainties

This paper studies the fault estimations problem for linear time-invariant systems with polytopic uncertainties. Both discrete-time and continuous-time cases are considered, and the recently developed Generalized Kalman-Yakubovich-Popov (GKYP) Lemma is exploited to formulate the fault estimation filter design problem in finite frequency domain. The filter is designed to make the error between residual and fault as small as possible despite of the disturbance effects and model uncertainties. Design methods are presented in terms of solutions to a set of Linear Matrix Inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the proposed methods.

Autoregressive Modeling of Temporal Envelopes

Autoregressive (AR) models are commonly obtained from the linear autocorrelation of a discrete-time signal to obtain an all-pole estimate of the signal's power spectrum. We are concerned with the dual, frequency-domain problem. We derive the relationship between the discrete-frequency linear autocorrelation of a spectrum and the temporal envelope of a signal. In particular, we focus on the real spectrum obtained by a type-I odd-length discrete cosine transform (DCT-Io) which leads to the all-pole envelope of the corresponding symmetric squared Hilbert temporal envelope. A compact linear algebra notation for the familiar concepts of AR modeling clearly reveals the dual symmetries between modeling in time and frequency domains. By using AR models in both domains in cascade, we can jointly estimate the temporal and spectral envelopes of a signal. We model the temporal envelope of the residual of regular AR modeling to efficiently capture signal structure in the most appropriate domain.

A finite frequency approach to filter design for uncertain discrete‐time systems

AbstractThis paper studies the problem of finite frequency filter design for linear time‐invariant discrete‐time systems with polytopic uncertainties. Generalized Kalman–Yakubovich–Popov lemma is exploited to formulate the filter design problem in finite frequency domain. A design method is presented in terms of solutions to a set of linear matrix inequalities. A numerical example is given to illustrate the effectiveness of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.

Transient response of SH waves in a layered half-space with sub-surface and interface cracks

The transient scattering of SH waves by sub-surface and interface cracks parallel to the free surface in a layered elastic solid is investigated. The problem in frequency domain is solved by using a hybrid method which combines the finite element method of the near field with the boundary integral representation of the far field. The transient responses are then obtained by inverting the spectra via fast Fourier transform with the incident pulse Ricker of wavelet. Numerical results are presented for the surface displacements, dynamic stress intensity factors and wave motion in the layered half-space. Furthermore, the propagations of reflected, diffracted, and direct impact waves at any instant are clearly identified by the present method. To understand the mechanism of elastic wave interaction is very important in the field of ultrasonic non-destructive evaluation (NDE) and fracture mechanics studies.

Comparison of time domain techniques for the evaluation of the response and the stability in long span suspension bridges

During the last decades, several studies on suspension bridges under wind actions have been developed in civil engineering and many techniques have been used to approach this structural problem both in time and frequency domain. In this paper, four types of time domain techniques to evaluate the response and the stability of a long span suspension bridge are implemented: nonaeroelastic, steady, quasi steady, modified quasi steady. These techniques are compared considering both nonturbulent and turbulent flow wind modelling. The results show consistent differences both in the amplitude of the response and in the value of critical wind velocity.

Problem of Low-frequency Localized Oscillations in a Thin Film with Growing Islands

Influence of localization waves to islands growing on a thin film is investigated. The film is modelled as a fluid layer covered by an inertial surface with the variable density of mass and surface tension. Mathematically, the problem is reduces to analysis of a system of non-linear equations describing the growth of island nuclei and wave propagation in the films. The existence of trapped modes for the corresponding frequency-domain problem is established. We show that for large time wave localization near islands gives some contribution in the increase of the velocity of island growth.

Shape and material optimization using gradient methods and the adjoint problem in time and frequency domain

PurposeShape and material parameters have major influence on the performance of electromagnetic components. Optimization of these parameters is therefore vital in electromagnetic design. Reduction of the radar cross section (RCS) for aircraft and frequency selective surfaces are two well known examples. Shape and materials optimization is performed for different scatterers in 2D.Design/methodology/approachContinuum design sensitivities for microwave problems are applied for the gradient‐based optimization of scatterers' shape and material parameters. The goal function is chosen to be an average of the monostatic RCS for a sector of incident angles over a frequency band. Numerical tests are presented for 2D scatterers and, specifically, a perfectly electrically conducting scatterer and an absorber on the front edge of an airplane wing are considered. The results are compared with theoretical findings and results in the open literature.FindingsIt is demonstrated that a dense frequency sampling of the goal function over a wide frequency band relaxes the requirements on the angular resolution. The broad band requirements on the RCS also avoids corrugations without the resorting to regularization methods and penalty terms added to the goal function. The optimization algorithm refines, in a small number of iterations, the initial geometry of the scatterer to an optimized design with strongly reduced RCS.Originality/valueShape and material parameters have major influence on the performance of electromagnetic components. Optimization of these parameters for scatterers demonstrates that a densely evaluated goal function over a broad frequency band has the advantages of: lowering the requirements on angular resolution; avoiding corrugations; and regularizing the problem by the broad frequency band requirements which often are naturally included in the performance specification of electromagnetic devices.

Use of Barycentric Dual Grids for the Solution of Frequency Domain Problems by FIT

In this paper, the finite integration technique for the approximation of three-dimensional electromagnetic boundary value problems in the frequency domain is formulated for primal grids composed of either oblique parallelepipeds or oblique triangular prisms or tetrahedra, adopting as dual grid the barycentric subdivision of the primal one. Novel constitutive relations are in particular derived assuring solution matrices of symmetric and positive definite type.

Dynamical Calculation of Plane Frameworks using Boundary Integral Equations

AbstractThe beam bending problem according to Timoshenkos theory can be solved using the Finite Element method. Here, the Boundary Integral Method is applied to the bending problem in frequency domain, providing an analytical solution for beams and systems of beams like trusses. An example is presented to demonstrate the method.

Théorème d'unicité pour un problème d'ondes élastiques

In this Note we prove a uniqueness theorem for the an elastic waves problem (in frequency domain). The propagation domain is a stratified half-space with a vertical borehole. We impose radiation conditions at infinity which ensure uniqueness of the solution. To cite this article: L. Alem, L. Chorfi, C. R. Acad. Sci. Paris, Ser. I 336 (2003).

Photon migration in turbid media: a finite-element solution for the most favorable path

A better understanding of the fundamental principles of photon migration in highly scattering media is of great importance for developing new methods for disease diagnosis, imaging, and tomography. In this paper we present a most-favorable-path approach to the problem of light propagation in turbid media, based on the diffusion equation. The most favorable path, on which photons will be found, can be obtained from the path of the net flux propagation. The diffusion intensity and the direction of the net flux can be calculated with the finite-element method, which can deal with heterogeneous problems and frequency-domain problems within complex geometry, and can introduce boundary effects as well. Simulations were conducted for phantoms with different optical parameters and source-detector separations. Experiments have been performed to verify this new method. The most favorable path is found to be more sensitive to the source-detector separation and the absorption coefficient of the medium than to the scattering coefficient. The feasibility of using the theory in optical tomography for the recognition of objects hidden in turbid media is discussed.

A wavelet-balance approach for steady-state analysis of nonlinear circuits

In this paper, a novel wavelet-balance method is proposed for steady-state analysis of nonlinear circuits. Taking advantage of the superior computational properties of wavelets, the proposed method presents several merits compared with those conventional frequency-domain techniques. First, it has a high convergence rate O(h/sup 4/), where h is the step length. Second, it works in time domain so that many critical problems in frequency domain, such as nonlinearity and high order harmonics, can be handled efficiently. Third, an adaptive scheme exists to automatically select proper wavelet basis functions needed at a given accuracy. Numerical experiments further prove the promising features of the proposed method in solving steady-state problems.

Worst-case asymptotic properties of ℋ/sub ∞/ identification

This paper studies asymptotic properties of /spl Hscr//sub /spl infin// identification problems and algorithms. The sample complexity of time- and frequency-domain /spl Hscr//sub /spl infin// identification problems is estimated, which exhibits a polynomial growth requirement on the input observation duration for the time-domain /spl Hscr//sub /spl infin// identification problem, and a linear growth rate of frequency response samples required for the frequency-domain /spl Hscr//sub /spl infin// identification problem. The divergence behavior is also established for linear algorithms for the time- and frequency-domain problems. The results extend previous work to more restricted sets of linear time-invariant systems with more refined a priori information, specifically imposed on the stability degree and the steady-state gain of the systems, thus demonstrating that no robustly convergent linear algorithms can exist even for a small set of exponentially stable systems.

A Fourier approach to the natural pixel discretization of brain single‐photon emission computed tomography

AbstractWe apply the natural pixel (NP) approach to the single‐photon emission computed tomography (SPECT) problem. The NP approach allows us to split the tomographic problem into two subproblems. The first is a linear inverse problem. The data are the measured projections and the linear operator is described by a Gram matrix, and provides a set of coefficients. The second consists of computing the solution of the tomographic problem as a linear combination of the elements of the NP basis with respect to the coefficients obtained by solving the first problem, and it provides a solution for any given grid of points. The spatially varying geometric response of the system is taken into account by properly choosing the elements of the basis. The rotational invariance shown by the elements of the considered basis induces a block circulant structure in the Gram matrix. This structure can be used to reduce the computational efforts needed for solving the inverse problem. In particular, we diagonalize (blockwise) the Gram matrix by applying the discrete Fourier transform and we solve the inverse problem in the frequency domain associated with the rotation angles. We develop numerical validation with synthetic data in order to test the performance of the NP approach and to assess the reliability of the results. A reconstruction of a two‐dimensional image requires 45–94 s, which is an acceptable time for clinical purposes. Finally, we apply the method to acquired clinical data that consist of a three‐dimensional brain scan. © 2002 John Wiley & Sons, Inc. Int J Imaging Syst Technol 12, 1–8, 2002

On the Efficient Implementation of the Integral Equation Method in Elastodynamics

The authors deal with low-cost computer implementation of the integral equation method in application to wave excitation, propagation and diffraction phenomena in solids. Typically these are frequency domain problems of seismic and physical acoustics and of nondestructive testing. Fast codes are obtained basing on analytical extracting and taking account of singular and slowly converging components of the solution beforehand. The present paper gives ideas of several such approaches, which have already proved their efficiency in practical applications. More details including numerical examples and discussion of similar methods known from the literature can be found in the surveyed papers.1–12

ON THE EFFICIENT IMPLEMENTATION OF THE INTEGRAL EQUATION METHOD IN ELASTODYNAMICS

The authors deal with low-cost computer implementation of the integral equation method in application to wave excitation, propagation and diffraction phenomena in solids. Typically these are frequency domain problems of seismic and physical acoustics and of nondestructive testing. Fast codes are obtained basing on analytical extracting and taking account of singular and slowly converging components of the solution beforehand. The present paper gives ideas of several such approaches, which have already proved their efficiency in practical applications. More details including numerical examples and discussion of similar methods known from the literature can be found in the surveyed papers.1–12

An efficient BE iterative-solver-based substructuring algorithm for 3D time-harmonic problems in elastodynamics

This work is concerned with the development of an efficient and general algorithm to solve frequency-domain problems modelled by the boundary element method based on a sub-region technique. A specific feature of the algorithm discussed here is that the global sparse matrix of the coupled system is implicitly considered, i.e. problem quantities are not condensed into interface variables. The proposed algorithm requires that only the block matrices with non-zero complex-valued coefficients be stored and manipulated during the analysis process. In addition, the efficiency of the technique presented is improved by using iterative solvers. The good performance of pre-conditioned iterative solvers for systems of equations having real-valued coefficients, well demonstrated in the literature, is confirmed for the present case where the system matrix coefficients are complex. The efficiency of the algorithm described here is verified by analysing a soil–machine foundation interaction problem. CPU time and accuracy are the parameters used for estimating the computational efficiency.