Quasi-static Terms Research Articles

Evaluation of the Instability Risk of the Dam Slopes Simulated with Monte Carlo method (Case Study: Alborz Dam)

Embankment dams are one of the most important geotechnical structures that their failures can lead to disastrous damages. One of the main causes of dam failure is its slope instability. Slope Stability analysis has traditionally been performed using the deterministic approaches. These approaches show the safety of slope only with factor of safety that this factor cannot take into account the uncertainty in soil parameters. Hence, to investigate the impact of uncertainties in soil parameters on slope stability, probabilistic analysis by Monte Carlo Simulation (MCS) method was used in this research. MCS method is a computational algorithm that uses random sampling to compute the results. This method studies the probability of slope failure using the distribution function of soil parameters. Stability analysis of upstream and downstream slopes of Alborz dam in all different design modes was done in both static and quasi-static condition. Probability of failure and reliability index were investigated for critical failure surfaces. Based on the reliability index obtained in different conditions, it can be said that the downstream and upstream slope of the Alborz dam is stable. The results show that although the factor of safety for upstream slope in the state of earthquake loading was enough, but the results derived from probabilistic analysis indicate that the factor of safety is not adequate. Also the upstream slope of the Alborz dam is unstable under high and uncontrolled explosions conditions in steady seepage from different levels under quasi-static terms.

Sub-wavelength sensing of bi-periodic materials using topological sensitivity of second-order homogenized model

We aim to detect defects or perturbations of periodic media, e.g. due to a defective manufacturing process. To this end, we consider scalar waves in such media through the lens of a second-order macroscopic description, and we compute the sensitivities of the germane effective parameters due to topological perturbations of a microscopic unit cell. Specifically, our analysis focuses on the tensorial coefficients in the governing mean-field equation – including both the leading order (i.e. quasi-static) terms, and their second-order companions bearing the effects of incipient wave dispersion. Then, we present a method that permits sub-wavelength sensing of periodic media, given the (anisotropic) phase velocity of plane waves illuminating the considered medium for several angles and wavenumbers.

Microstructural Topological Sensitivities of the Second-Order Macroscopic Model for Waves in Periodic Media

We consider scalar waves in periodic media through the lens of a second-order effective i.e. macroscopic description, and we aim to compute the sensitivities of the germane effective parameters due to topological perturbations of a microscopic unit cell. Specifically, our analysis focuses on the tensorial coefficients in the governing mean-field equation – including both the leading order (i.e. quasi-static) terms, and their second-order companions bearing the effects of incipient wave dispersion. The results demonstrate that the sought sensitivities are computable in terms of (i) three unit-cell solutions used to formulate the unperturbed macroscopic model; (ii) two adoint-field solutions driven by the mass density variation inside the unperturbed unit cell; and (iii) the usual polarization tensor, appearing in the related studies of non-periodic media, that synthesizes the geometric and constitutive features of a point-like perturbation. The proposed developments may be useful toward (a) the design of periodic media to manipulate macroscopic waves via the microstructure-generated effects of dispersion and anisotropy, and (b) sub-wavelength sensing of periodic defects or perturbations.

Coupling Analysis of Complex-Layout Traces Using a Circuit-Concept Approach

An analytical method is studied for estimating coupling between arbitrarily directed multiple finite-length lines with different line lengths and heights. Coupling or crosstalk analysis is performed by developing an expanded circuit-concept approach based on modified telegrapher's equations of the Agrawal approach instead of the Taylor approach, providing some computational advantages. An electric image method using the quasi-static terms of the accurate Green's function is used to estimate the electromagnetic fields in an inhomogeneous medium such as a printed circuit board. The approach is applied to the analysis of parallel and nonparallel or bent microstrip models, and embedded-line models in which one line is embedded and the other is on the surface layer. To verify the proposed approach, we conducted some experiments and compared the results of our approach with the results of measurements and a commercial electromagnetic solver.

On quasistatics and correcting functions in the dynamics of elastic structures

A new method is proposed for constructing quasistatic terms that are required to refine the solution of the problem of dynamic loading of an elastic structure with energy scattering taken into account and a bounded number of coordinate functions used in the modal expansion. The quasistatic terms introduced are orthogonal to the mode shapes taken into account in the calculations of the vibration harmonics and compensate the quasistatic contribution of the neglected vibration harmonics. The identity between the procedures of introducing correcting functions (correcting series) and refining the quasistatics is discussed.

LOW-FREQUENCY SCATTERING ANALYSIS AND HOMOGENISATION OF SPLIT-RING ELEMENTS

A key structure in so-called metamaterial mediums is the elementary split-ring resonator. We consider in this paper the low-frequency electromagnetic scattering by a split-ring particle modelled as a perfectly conducting wire ring, furnished with a narrow gap, and derive analytical solutions for the electric and magnetic dipole moments for different kinds of incidence and polarisation in the quasi-static approximation. Through a vectorial homogenisation process, the expressions discovered for the dipole moments and the related polarisability dyadics are linked with the macroscopic constitutive equations for the medium. We further show that the condition for resonance of a medium consisting of simple split-rings cannot be achieved by means of the given quasi-static terms without violating the underlying assumptions of homogenisation. Nevertheless, the results are applicable for sparse medium of rings, and we derive numerical guidelines for the applicability with some examples of the effect of the considered split-ring medium on electromagnetic wave propagation. (Less)

On the efficient computation of closed-form Green's functions in planar stratified media

The spatial-domain Green's functions for the vector and scalar potentials in planar stratified media are cast into closed forms via a two-level approximation of their spectral-domain counterparts. The proposed methodology begins with the approximation of the spectral-domain Green's functions over large values of the spectral variable by complex exponentials, and continues with the approximation of the remainder by rational functions. Finally, the closed-form Green's functions in terms of spherical and cylindrical waves are derived, making use of some well-known integral identities. A key-feature of the proposed approach is that although it does not call for an analytical extraction of the quasistatic terms and the surface wave poles, it provides the means for the accurate description of both the near-field and far-field physics. Moreover, the rational function spectrum fitting proposed here overcomes the problem of the spurious singular behavior of the spatial-domain Green's functions because of the use of Hankel functions. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2008.

A Robust Method for the Computation of Green's Functions in Stratified Media

Closed-form Green's functions for unbounded planar stratified media are derived in terms of cylindrical and spherical waves. The methodology is based on a two-level approximation of the spectral-domain representation of Green's functions. This robust, efficient, and fully numerical approach does not call for an analytical extraction of ldquoproblematicrdquo behaviors, such as the quasi-static terms and the surface wave poles, prior to the spectrum fitting. Instead, the spatial-domain Green's functions derived in this paper provide an accurate description of both the near-field singularity in the vicinity of the source and the far-field dominant behavior of the surface waves.

Crosstalk Analysis Method for Two Bent Lines on a PCB Using a Circuit Model

We propose a method of crosstalk analysis for two bent transmission lines with vias at both ends on a PCB using a circuit-concept approach in the quasi-static condition. In this condition, the electromagnetic fields can be approximately estimated by the quasi-static terms of the accurate Green's function in an inhomogeneous medium. Thus we obtain a circuit model in an ABCD matrix by taking account of the fields generated by a longitudinal line and a vertical via on a PCB. To verify the proposed approach, we conducted some experiments and compared our approach's results with measured results and a commercial electromagnetic solver's results.

Free-surface granular flows down heaps

The present paper extends the granular-flow constitutive model of Savage (1998 J Fluid Mech 377:1–26) to treat spherical particles. Savage accounted for both quasi-static and collisional stresses by considering: (i) strain-rate fluctuations embodied in a critical state plasticity model, as well as, (ii) individual particle velocity fluctuations modelled by granular-flow kinetic theory. In the present work, the governing equations of the kinetic theory of Jenkins (1998 In: Hermann HJ, Luding S (eds) Physics of Dry Granular Media. Kluwer Academic pp. 353–370) for identical spherical, smooth, inelastic particles are supplemented with additional quasi-static terms that have forms patterned after the corresponding terms in the equations of Savage for two-dimensional disk-like particles. The resulting equations along with side-wall and free-surface boundary conditions are applied to examine free-surface granular flow down a heap contained between two frictional vertical side walls. Width-averaged equations of motion are integrated to obtain depth profiles of mean velocity, granular temperature, solids fraction and the Savage–Jeffrey parameter. Detailed comparisons are made with particle-tracking experiments. When the gap between the vertical side walls is fairly narrow, good agreement is found between the predicted and the measured profiles of mean velocity and granular temperature.

A direct discrete complex image method from the closed-form Green's functions in multilayered media

Sommerfeld integration is introduced to calculate the spatial-domain Green's functions (GF) for the method of moments in multilayered media. To avoid time-consuming numerical integration, the discrete complex image method (DCIM) was introduced by approximating the spectral-domain GF by a sum of exponentials. However, traditional DCIM is not accurate in the far- and/or near-field region. Quasi-static and surface-wave terms need to be extracted before the approximation and it is complicated to extract the surface-wave terms. In this paper, some features of the matrix pencil method (MPM) are clarified. A new direct DCIM without any quasi-static and surface-wave extraction is introduced. Instead of avoiding large variations of the spectral kernel, we introduce a novel path to include more variation before we apply the MPM. The spatial-domain GF obtained by the new DCIM is accurate both in the near- and far-field regions. The CPU time used to perform the new DCIM is less than 1 s for computing the fields with a horizontal source-field separation from 1.6/spl times/10/sup -4//spl lambda/ to 16/spl lambda/. The new DCIM can be even accurate up to 160/spl lambda/ provided the variation of the spectral kernel is large enough and we have accounted for a sufficient number of complex images.

Treatment of singularities and quasi-static terms in the EFIE analysis of planar structures

This paper reports on some mathematical and numerical details of the application of the electric field integral equation (EFIE) method to the analysis of planar structures printed on multilayered substrates. Closed-form expressions for singular and hypersingular terms of the transverse electric field Green's dyadic (TEFGD) are identified so that they can be explicitly extracted out before solving the EFIE. The problems due to the presence of the hypersingular contribution, usually argued to preclude the application of the EFIE to planar structures, are solved. In addition, a low-frequency expansion of the TEFGD corresponding to a single layer substrate is carried out to recognize nonsingular electrostatic-type contributions that can eventually become very important for computational purposes.

Computation of response moments of high dimensional MDOF structure excited by stationary non-Gaussian random fields

Output moments of a non-linear dynamical system excited by a non-Gaussian random field can be obtained in practice only by simulation techniques. When the dynamical system can be decomposed in a low dimension non-linear part acting on a high dimension linear part, the original problem reduces to calculate output moments of a high dimension linear system. The proposed method suggests that work should be directed in the frequency domain. Time trajectories are then obtained through Fourier transform. Such a procedure does not introduce any approximation errors due to the time integration numerical scheme nor does it introduce any transient state. Further quasi-static correction terms can be introduced when a truncated modal basis is utilized in order to describe the low frequency dynamic response.

Two techniques for the efficient numerical calculation of the Green's functions for planar shielded circuits and antennas

In this paper we present new contributions to the computation of the Green's functions arising in the analysis of multilayered shielded printed circuits and antennas. First the quasistatic term of the spectral domain Green's functions is extracted so that the convergence of the reminder dynamic modal series is enhanced. Moreover, it is shown that by extracting a second-order quasi-static term the convergence is further improved. In regard to the quasi-static terms, they are computed in the spatial domain by numerically evaluating the associated spatial images series. Then a new and efficient technique is developed for the summation of the slowly convergent modal series. The technique can be viewed as the application of the integration by parts technique to discrete sequences and greatly accelerates the convergence rate of the series involved. It is shown that the new algorithm is numerically very robust and leads to a drastic reduction in the computational effort and time usually required for the numerical evaluation of the shielded Green's functions.

A FORM OF AERODYNAMIC ADMITTANCE FOR USE IN BRIDGE AEROELASTIC ANALYSIS

This paper returns to, and addresses, the question of identifying the nature of aerodynamic admittance in relation to extended-span bridges in wind. Theoretical formulations for the sectional aerodynamic forces acting upon the deck girder of a long-span bridge have conventionally been composed of the sum of two kinds of terms: aeroelastic terms and buffeting terms. The former employ frequency-dependent coefficients (“flutter derivatives”) associated with sinusoidal displacements of the structure, while the latter have typically been expressed in quasi-static terms with fixed lift, drag and moment coefficients. This inconsistency of formulation has required that at some point the buffeting terms, functions of gust velocity, be adjusted to a more compatible form through the introduction of the so-called aerodynamic admittance factors that are frequency-dependent. The present paper identifies a form of these several section-force factors as functions of the flutter derivatives themselves.

An efficient nonquasi-static diode model for circuit simulation

Based on the partitioned-charge-based modeling approach, a general nonquasi-static dynamic charge element is derived to simulate both transient behavior and high-frequency characteristics of a semiconductor diode. A new model parameter /spl tau/ is introduced to describe the dynamic charge redistribution time for a diode. By partitioning the total base charge into quasi-static (QS) and nonquasi-static (NQS) terms, a single-/spl tau/ (level 2) diode model is first derived. By further dividing the NQS charge, a double-/spl tau/ (level 3) diode model is proposed to describe different reverse recovery processes. In addition, a voltage-dependent equation is incorporated to the double-/spl tau/ model into account for the dynamic charge partitioning. We show that the SPICE diode (level 1) model is included by setting /spl tau/ to zero as a special case of the proposed models. The new diode model has been implemented in MISIM, a model independent SPICE-like simulation framework. Significant improvement in accuracy over the traditional SPICE diode model in both time and frequency domain has been demonstrated, while achieving the same or even better simulation speed and reliability.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Forerunners on conducting surfaces: the infinitesimal vertical magnetic dipole with displacement terms

The transient behaviour of the electric fields and the time derivative of the magnetic fields on the surface of a conductor are derived when a steady state infinitesimally small vertical magnetic dipole on the surface of a uniformly conducting half-space is impulsively switched off. Explicit expressions are obtained for the speed of light terms, the long-time behaviour of which are shown to match the short-time behaviour of the associated quasi-static terms. A relaxational effect dependent on the electric susceptibility of the conductor allows the forerunners associated with the free space light speed to travel along the surface essentially undamped, and so is responsible for the short-time behaviour of the quasi-static fields. The other forerunners travelling at the conductor light speed are of insignificant magnitude, and the electromagnetic field finally decays as in the quasi-static approximation.

Relativistic ponderomotive Hamiltonian of two interacting electromagnetic waves.

An expression for the ponderomotive Hamiltonian for a relativistic particle gyrating in a quasistatic magnetic field and in the presence of two interacting electromagnetic waves is derived. The frequencies of the waves are of the order of the gyrofrequency meaning that an average is performed over the gyration and the rapid oscillations of the waves leading to the ponderomotive Hamiltonian which contains only quasistatic and slow oscillatory terms. The derivation is systematic and allows for arbitrary k\ensuremath{\rho}, v/c, ${E}_{\mathrm{para}}$/${E}_{\ensuremath{\perp}}$, polarizations, and for slowly growing and spatially modulated waves. Nonuniformities in the background magnetic and electric fields are also included.

On determining the relation between the mean stress and deformation tensors in structurally inhomogeneous elastic media

The paper deals with establishing a rheological equation connecting the mean stress and deformation tensors in a structurally inhomogeneous elastic medium. The problem is formulated in the dynamic terms, and the defining equations are sought in the form of linear operator relations. The expression for the elastic operator is obtained in the form of a perturbation series, the terms of which represent a superposition of the linear integral operators. Partial sums of the series are obtained using the method of changing the field variables (taking into account the multiple scattering). An expression for the elastic operator kernel is obtained consisting of three different type terms, namely the quasi-static, couple stress and nonlocal terms.