Equations In Frequency Domain Research Articles

Non-linear free periodic vibrations of variable stiffness composite laminated plates

Steady-state free vibrations, with large amplitude displacements, of variable stiffness composite laminated plates (VSCL) are analysed. The intentions of this research are: (1) to find out how the natural frequencies and (mode) shapes evolve with the displacement amplitude in this new type of laminated composite material; (2) to describe modal interactions in VSCL due to energy interchanges under the coupling induced by non-linearity; (3) to compare the VSCL with traditional, constant stiffness, laminated plates. The VSCL of interest here have curvilinear fibres and the numerical analysis carried out is based on a recently developed p-version finite element with hierarchic basis functions. The element follows first-order shear deformation theory and considers Von Karman’s non-linear terms. The time domain equations of motion are first reduced using the linear modes of vibration and then transformed to the frequency domain via the harmonic balance method. These frequency domain equations are solved by an arc-length continuation method.

Study on Sound Field of High Intensity Focused Ultrasound with Short Focal Length

In this paper, numerical simulation of sound field with short focal length is performed, which is based on spheroidal beam equation (SBE) in frequency-domain for transducer with a wide aperture angle. And we made some experiments on vitro bovine liver to explore the characteristic of sound pressure and-3dB sound focal region at different positions of incident interface. It is found that with a fixed curvature radius if the focal length is shorter under the skin, the amplitude of sound pressure will be higher on the focus and the shape of-3dB sound focal region will be smaller. When the incident interface is in the range of planar wave, nonlinear effect is strong and the focus will change with the interface position. Especially when the position is near to transition location between planar wave and spheroidal wave, the nonlinear effect is lowered. While the focus is closer to the sound source so as to burn the scarfskin easily. When the interface is in the range of spheroidal wave, the focus position changes little but the side lobe effect due to refraction is obvious. And the focusing performance of transducer will be affected. The experimental results validate the accuracy of theoretical results. It is concluded that the position of incident interface should be selected reasonably with short focal length in the treatment of superficial tissue.

Finite elements parameterization of optical tomography with the radiative transfer equation in frequency domain

Optical tomography is a technique of probing semi-transparent media with the help of light sources. In this method, the spatial distribution of the optical properties inside the probed medium is reconstructed by minimizing a cost function based on the errors between the measurements and the predictions of a numerical model of light transport (also called forward/direct model) within the medium at the detectors locations. Optical tomography with finite elements methods involves generally continuous formulations where the optical properties are constant per mesh elements. This study proposes a numerical analysis in the parameterization of the finite elements space of the optical properties in order to improve the accuracy and the contrast of the reconstruction. Numerical tests with noised data using the same algorithm show that continuous finite elements spaces give better results than discontinuous ones by allowing a better transfer of the information between the whole computational nodes of the inversion. It is seen that the results are more accurate when the number of degrees of freedom of the finite element space of the optical properties (number of unknowns) is lowered. This shows that reducing the number of unknowns decreases the ill-posed nature of the inverse problem, thus it is a promising way of regularizing the inversion.

A preconditioned MinRes solver for time‐periodic parabolic optimal control problems

SUMMARYThis work is devoted to the multiharmonic analysis of parabolic optimal control problems in a time‐periodic setting. In contrast to previous approaches, we include the cases of different control and observation domains, the observation in certain energy spaces, and the presence of control constraints. In all these cases, we propose a new preconditioned MinRes solver for the frequency domain equations and show that this solver is robust with respect to the space and time discretization parameters as well as the involved ‘bad’ model parameters of the state equation. Copyright © 2012 John Wiley & Sons, Ltd.

Optical tomography with the discontinuous Galerkin formulation of the radiative transfer equation in frequency domain

Optical tomography is an inverse method of probing semi-transparent media with the help of light sources. The reconstruction of the optical properties usually employs finite volumes or continuous finite elements formulations of light transport as a forward model for the predictions. In a previous study, we have introduced a generalization of the inversion approach with finite elements formulations by using an integral form of the objective function. The novelty is that the surfaces of the detectors are taken into account in the reconstruction and compatibility is obtained for all finite element formulations. This present paper illustrates this new approach by developing a Discontinuous Galerkin formulation as a forward model for an optical tomography application in the frequency domain framework. Numerical tests are performed to gauge the accuracy of the method in recovering optical properties distribution with a gradient-based algorithm where the adjoint method is used to fastly compute the objective function gradient. It is seen that the reconstruction is accurate and can be affected by noise on the measurements as expected. Filtering of the gradient at each iteration of the reconstruction is used to cope with the ill-posed nature of the inverse problem and to improves the quality and accuracy of the reconstruction.

Computer Analysis of Electromagnetic Transients in Grounding Systems Considering Variation of Soil Parameters with Frequency

This paper presents a mathematical model to calculate transients in grounding systems. The derived equations arise from direct application of basic electromagnetic equations in frequency domain, whose solution is obtained by the application of the Moment Methods. A formulation based on experimental measurements is applied to quantify the soil parameters for each frequency. The unified approach is applied in the calculation of the grounding impedance of horizontal electrodes. Results show that the inclusion of frequency dependence of the soil parameters leads to a reduction of the values of grounding impedance, in comparison with results for soils with parameters independent of frequency.

Modeling of Coaxial Slot Waveguides Using Analytical and Numerical Approaches: Revisited

Our reviews of analytical methods and numerical methods for coaxial slot waveguides are presented. The theories, background, and physical principles related to frequency-domain electromagnetic equations for coaxial waveguides are reassessed. Comparisons of the accuracies of various types of admittance and impedance equations and numerical simulations are made, and the fringing field at the aperture sensor, which is represented by the lumped capacitance circuit, is evaluated. The accuracy and limitations of the analytical equations are explained in detail. The reasons for the replacement of analytical methods by numerical methods are outlined.

A Robust Preconditioned MinRes Solver for Distributed Time-Periodic Eddy Current Optimal Control Problems

This work is devoted to the construction and analysis of robust solvers for some distributed optimal control problems for time-periodic eddy current problems. We apply the multiharmonic approach to the optimality system and construct a new preconditioned MinRes solver for the system of frequency domain equations. We show that this solver is robust with respect to the space discretization and time discretization parameters as well as all involved “bad” parameters, like the conductivity, the reluctivity, and the regularization and cost parameters.

국부진동모드가 플러터해석에 미치는 영향연구

고속 비행체의 날개 구조물은 스킨과 튼튼한 골격으로 구성되어 있다. 플러터 해석시 날개 구조물의 고유진동모드를 이용하여 비정상공기력을 계산하고 모달접근법을 이용하여 시간영역이나 주파수 영역에서 구조물의 진동안정성을 분석하게 되므로, 사용되는 고유 진동 모드는 신중하게 선정되어야 한다. 이를 위해 날개 구조물과 같이 고차에서 스킨의 국부진동모드가 있는 경우 이러한 모드가 비정상공기력 및 플러터 특성에 미치는 영향을 분석하였다. The fin of high speed air vehicle is composed of skins and strong skeletons. In the flutter analysis, the eigenmodes of a fin are used for evaluating the unsteady aerodynamic force and the modal approach is applied for solving the flutter equation in both time and frequency domain. Therefore, the proper eigenmodes used for a modal flutter analysis should be chosen. For the appropriate choice of eigenmodes, when there exist local modes of a skin in the high modes, the effects of those modes on the unsteady aerodynamic force and flutter characteristics are anlalyzed.

Structural Nonlinear Flutter Characteristics Analysis for an Actuator-fin System with Dynamic Stiffness

The flutter characteristics of an actuator-fin system are investigated with structural nonlinearity and dynamic stiffness of the electric motor. The component mode substitution method is used to establish the nonlinear governing equations in time domain and frequency domain based on the fundamental dynamic equations of the electric motor and decelerator. The existing describing function method and a proposed iterative method are used to obtain the flutter characteristics containing preload freeplay nonlinearity when the control command is zero. A comparison between the results of frequency domain and those of time domain is studied. Simulations are carried out when the control command is not zero and further analysis is conducted when the freeplay angle is changed. The results show that structural nonlinearity and dynamic stiffness have a significant influence on the flutter characteristics. Limit cycle oscillations (LCOs) are observed within linear flutter boundary. The response of the actuator-fin system is related to the initial disturbance. In the nonlinear condition, the amplitude of the control command has an influence on the flutter characteristics.

An accurate substructural synthesis approach to random responses

An accurate substructural synthesis method including random responses synthesis, frequencyresponse functions synthesis and mid-order modes synthesis is developed based on rigorous substructure description, dynamic condensation and coupling. An entire structure can firstly be divided into several substructures according to different functions, geometric and dynamic characteristics. Substructural displacements are expressed exactly by retained mid-order fixed-interfacial normal modes and residual constraint modes. Substructural interfacial degree-of-freedoms are eliminated by interfacial displacements compatibility and forces equilibrium between adjacent substructures. Then substructural mode vibration equations are coupled to form an exact-condensed synthesized structure equation, from which structural mid-order modes are calculated accurately. Furthermore, substructural frequency-response function equations are coupled to yield an exact-condensed synthesized structure vibration equation in frequency domain, from which the generalized structural frequency-response functions are obtained. Substructural frequency-response functions are calculated separately by using the generalized frequency-response functions, which can be assembled into an entire-structural frequency-response function matrix. Substructural power spectral density functions are expressed by the exact-synthesized substructural frequency-response functions, and substructural random responses such as correlation functions and meansquare responses can be calculated separately. The accuracy and capacity of the proposed substructure synthesis method is verified by numerical examples.

A geometric framework for black hole perturbations

Black hole perturbation theory is typically studied on time surfaces that extend between the bifurcation sphere and spatial infinity. From a physical point of view, however, it may be favorable to employ time surfaces that extend between the future event horizon and future null infinity. This framework resolves problems regarding the representation of quasinormal mode eigenfunctions and the construction of short-ranged potentials for the perturbation equations in frequency domain.

Head- and Flow-Based Formulations for Frequency Domain Analysis of Fluid Transients in Arbitrary Pipe Networks

Applications of frequency-domain analysis in pipelines and pipe networks include resonance analysis, time-domain simulation, and fault detection. Current frequency-domain analysis methods are restricted to series pipelines, single-branching pipelines, and single-loop networks and are not suited to complex networks. This paper presents a number of formulations for the frequency-domain solution in pipe networks of arbitrary topology and size. The formulations focus on the topology of arbitrary networks and do not consider any complex network devices or boundary conditions other than head and flow boundaries. The frequency-domain equations are presented for node elements and pipe elements, which correspond to the continuity of flow at a node and the unsteady flow in a pipe, respectively. Additionally, a pipe-node-pipe and reservoir-pipe pair set of equations are derived. A matrix-based approach is used to display the solution to entire networks in a systematic and powerful way. Three different formulations are derived based on the unknown variables of interest that are to be solved: head-formulation, flow-formulation, and head-flow-formulation. These hold significant analogies to different steady-state network solutions. The frequency-domain models are tested against the method of characteristics (a commonly used time-domain model) with good result. The computational efficiency of each formulation is discussed with the most efficient formulation being the head- formulation. DOI: 10.1061/(ASCE)HY.1943-7900.0000338. © 2011 American Society of Civil Engineers. CE Database subject headings: Hydraulic transients; Unsteady flow; Pipe networks; Numerical analysis; Fourier analysis. Author keywords: Transients; Unsteady flow; Pipes; Networks; Numerical analysis; Fourier analysis.

Development of a convection–diffusion–reaction model for solving Maxwell's equations in frequency domain

SUMMARYWe propose in this study a numerically accurate and computationally efficient convection–diffusion–reaction finite difference scheme to discretize the full‐vector and semi‐vector optical waveguide equations. The scheme formulated in a grid stencil of five nodal points for solving the three‐dimensional waveguide equations employs the locally analytic solution. In this three‐dimensional study, calculations were carried out for the investigation of wave propagation in diffused channel, rectangular and rib types of optical waveguide. Copyright © 2011 John Wiley & Sons, Ltd.

Vibration analysis of liquid-filled pipelines with elastic constraints

In this paper, a transfer matrix method (TMM) in frequency domain considering fluid–structure interaction of liquid-filled pipelines with elastic constraints is proposed. The time-domain equations considering fluid–structure interaction, are transformed into frequency domain by Laplace transformation, and then twelve fourth-order ordinary differential equations and two second-order ordinary differential equations are deduced from the frequency-domain equations. The results of the fourteen frequency-domain equations are assembled into a transfer matrix, which represents the motion of a single pipe section. Combined with point matrices that describe specified boundary conditions, an overall transfer matrix for liquid-filled pipeline system can be assembled. Using the method, all the pipeline with no and rigid constraints can be easily calculated by simply setting the stiffness of the restraining springs from zero to a large number. Taking into account the longitudinal vibration, transverse vibration and torsional vibration, the proposed method can be used to analyze the pipelines with bends. Several numerical examples with different constraints are presented here to illustrate the application of the proposed method. The results are validated by measured and simulation data. Through the numerical examples, it is shown that the proposed method is efficient.

Frequency domain analyses of a thin liquid film surface by repetitively applied stress (dynamic response analyses by the long wave equation)

Numerical results were calculated for the dynamic behavior of an ultrathin liquid (lubricant) surface resulting from repetitively applied pressure and shear stress using the frequency domain equation and compared with those obtained using the time domain equation. Frequency domain analyses of the dynamic behavior of the ultrathin liquid (lubricant) surface produced by sinusoidally applied pressure and shear stress clarified the dependence of the liquid surface deformation on the frequency of the stresses and the disk speed. The dynamic behavior resulting from sinusoidally applied pressure and shear stress calculated using the time domain equation were found to gradually coincide with those obtained using the frequency domain equation.

Multimedia Educational Material and Remote Laboratory for Sliding Mode Control Measurements

The paper presents a multimedia educational program of DC servo drives for distant learning with a special emphasis on sliding mode control. The program contains of three parts: animation, simulation and internet based measurement. The animation program explains the operation of DC motors, gives its time- and frequency-domain equations, transfer functions and the theoretical background necessary for controller design for DC servo motors. The simulation model of the DC servo motor and the controller can be designed by the students based on the animation program. The students can also test their controllers through the internet based measurement, which is the most important part from engineering point of view. After the measurements are executed, the students can download the measured data and compare them to the simulation results.

Sound Field Reproduction Using Planar and Linear Arrays of Loudspeakers

In this paper, we consider physical reproduction of sound fields via planar and linear distributions of secondary sources (i.e., loudspeakers). The presented approach employs a formulation of the reproduction equation in spatial frequency domain which is explicitly solved for the secondary source driving signals. Wave field synthesis (WFS), the alternative formulation, can be shown to be equivalent under equal assumptions. Unlike the WFS formulation, the presented approach does not employ a far-field approximation when linear secondary source distributions are considered but provides exact results. We focus on the investigation of the spatial truncation and discretization of the secondary source distribution occurring in real-world implementations and present a rigorous analysis of evanescent and propagating components in the reproduced sound field.

Control of an Embedded System via Internet

This paper presents our experience with a complete multimedia educational program of dc servo drives for distant learning. The program contains three parts: animation, simulation, and Internet-based measurement. The animation program helps to understand the operation of dc motors as well as its time- and frequency-domain equations, transfer functions, and the theoretical background necessary to design a controller for dc servo motors. The simulation model of the dc servo motor and the controller can be designed by the students based on the animation program. The students can also test their controllers through the Internet-based measurement, which is the most important part from an engineering point of view. Students can then perform various exercises such as programming the D/A and A/D cards in the embedded system and designing different types of controllers. First, a simple PI controller can be designed, but advanced students can also design more sophisticated controllers such as the sliding mode controller. After the measurements are executed, the students can download the measured data and compare them to the simulation results.

PDE-Constrained Fluorescence Tomography With the Frequency-Domain Equation of Radiative Transfer

We present the first fluorescence tomography algorithm that is based on a partial differential equation (PDE) constrained approach. PDE methods have been increasingly employed in many numerical applications, as they often lead to faster and more robust solutions of many inverse problems. In particular, we use a sequential quadratic programming (SQP) method, which allows solving the two forward problems in fluorescence tomography (one for the excitation and one for the emission radiances) and one inverse problem (for recovering the spatial distribution of the fluorescent sources) simultaneously by updating both forward and inverse variables in simultaneously at each of iteration of the optimization process. We evaluate the performance of this approach with numerical and experimental data using a transport-theory frequency-domain algorithm as forward model for light propagation in tissue. The results show that the PDE-constrained approach is computationally stable and accelerates the image reconstruction process up to a factor of 15 when compared to commonly employed unconstrained methods.