scholarly journals Non-Debye Relaxations: The Ups and Downs of the Stretched Exponential vs. Mittag–Leffler’s Matchings

2021 ◽  
Vol 5 (4) ◽  
pp. 265
Author(s):  
Katarzyna Górska ◽  
Andrzej Horzela ◽  
Karol A. Penson
Keyword(s):  
Point Of View ◽  
Characteristic Functions ◽  
Elementary Functions ◽  
Depolarization Current ◽  
Frequency Dependent ◽  
Broadband Dielectric Spectroscopy ◽  
The Laplace Transform ◽  
The Time Domain ◽  
Debye Frequency ◽  
Comparability Of Results

Experimental data collected to provide us with information on the course of dielectric relaxation phenomena are obtained according to two distinct schemes: one can measure either the time decay of depolarization current or use methods of the broadband dielectric spectroscopy. Both sets of data are usually fitted by time or frequency dependent functions which, in turn, may be analytically transformed among themselves using the Laplace transform. This leads to the question on comparability of results obtained using just mentioned experimental procedures. If we would like to do that in the time domain we have to go beyond widely accepted Kohlrausch–Williams–Watts approximation and become acquainted with description using the Mittag–Leffler functions. To convince the reader that the latter is not difficult to understand we propose to look at the problem from the point of view of objects which appear in the stochastic processes approach to relaxation. These are the characteristic exponents which are read out from the standard non-Debye frequency dependent patterns. Characteristic functions appear to be expressed in terms of elementary functions whose asymptotics is simple. This opens new possibility to compare behavior of functions used to describe non-Debye relaxations. It turnes out that the use of Mittag-Leffler function proves very convenient for such a comparison.

scholarly journals Solution of the problems of quasi-statics for an elastic body with double porosity

2021 ◽  
Vol 1 (3) ◽  
pp. 1-5
Author(s):  
Ivane Tsagareli
Keyword(s):  
Boundary Value Problems ◽  
Elastic Body ◽  
Boundary Value ◽  
Original System ◽  
Double Porosity ◽  
Point Of View ◽  
Static Case ◽  
Elementary Functions ◽  
The Laplace Transform ◽  
Dimensional Boundary

The construction of solutions in explicit form is especially important from the point of view of its application, since it makes it possible to effectively carry out a quantitative analysis of the problem under study. This paper investigates the processes of deformation of solids in the quasi-static case. Two-dimensional boundary value problems of Dirichlet and Neumann for an elastic body with double porosity are considered. In Using the Laplace transform, these problems are reduced to auxiliary boundary value problems. Special representations of solutions to auxiliary boundary value problems are constructed using elementary functions that allow reducing the original system of equations to equations of a simple structure and facilitate the solution of the original problems. Auxiliary boundary value problems are solved for a specific elastic body - a porous disk. Solutions to these problems are obtained in the form of series. Conditions are provided that ensure the absolute and uniform convergence of these series and the use of the inverse Laplace theorem. It is proved that the inverse transforms provide a solution to the initial problems.

scholarly journals Research on the Time-Domain Dielectric Response of Multiple Impulse Voltage Aging Oil-Film Dielectrics

Energies ◽  
2021 ◽  
Vol 14 (7) ◽  
pp. 1948
Author(s):  
Chenmeng Zhang ◽  
Kailin Zhao ◽  
Shijun Xie ◽  
Can Hu ◽  
Yu Zhang ◽  
...  
Keyword(s):  
Time Domain ◽  
Dielectric Response ◽  
Early Stage ◽  
Debye Model ◽  
Polarization Current ◽  
Depolarization Current ◽  
Oil Film ◽  
Impulse Voltage ◽  
The Time Domain ◽  
Film Dielectric

Power capacitors suffer multiple impulse voltages during their lifetime. With the multiple impulse voltage aging, the internal insulation, oil-film dielectric may deteriorate and even fail in the early stage, which is called accumulative effect. Hence, the time-domain dielectric response of oil-film dielectric with multiple impulse voltage aging is studied in this paper. At first, the procedure of the preparation of the tested samples were introduced. Secondly, an aging platform, impulse voltage generator was built to test the accumulative effect of capacitor under multiple impulse voltage. Then, a device was used to test the time-domain dielectric response (polarization depolarization current, PDC) of oil-film dielectric in different aging states. And finally, according to the PDC data, extended Debye model and characteristic parameters were obtained by matrix pencil algorithm identification. The results indicated that with the increase of impulse voltage times, the time-domain dielectric response of oil-film dielectric changed accordingly. The polarization current curve moved up gradually, the insulation resistance decreased when subjected to the repeated impulses. In frequency domain, the frequency spectrum of tan δ changed along with the impulse accumulation aging, especially at low frequency. At last, combined with the aging mechanism of oil-film dielectric under multiple impulse voltage, the test results were discussed.

Time-Domain Nonlinear SSI Analysis of Foundation Sliding Using Frequency-Dependent Foundation Impedance Derived From SASSI

2008 ◽  
Author(s):  
Mansour Tabatabaie ◽  
Thomas Ballard
Keyword(s):  
Frequency Domain ◽  
Linear Systems ◽  
Time Domain ◽  
Soil Structure ◽  
Wave Radiation ◽  
Far Field ◽  
Frequency Dependent ◽  
Nonlinear Springs ◽  
Mat Foundation ◽  
The Time Domain

Dynamic soil-structure interaction (SSI) analysis of nuclear power plants is often performed in frequency domain using programs such as SASSI [1]. This enables the analyst to properly a) address the effects of wave radiation in an unbounded soil media, b) incorporate strain-compatible soil shear modulus and damping properties and c) specify input motion in the free field using the de-convolution method and/or spatially variable ground motions. For structures that exhibit nonlinearities such as potential base sliding and/or uplift, the frequency-domain procedure is not applicable as it is limited to linear systems. For such problems, it is necessary to solve the problem in the time domain using the direct integration method in programs such as ADINA [2]. The authors recently introduced a sub-structuring technique called distributed parameter foundation impedance (DPFI) model that allows the structure to be partitioned from the total SSI system and analyzed in the time domain while the foundation soil is modeled using the frequency-domain procedure [3]. This procedure has been validated for linear systems. In this paper we have expanded the DPFI model to incorporate nonlinearities at the soil/structure interface by introducing nonlinear shear and normal springs arranged in series between the DPFI and structure model. This combination of the linear far-field impedance (DPFI) plus nonlinear near-field soil springs allows the foundation sliding and/or uplift behavior be analyzed in time domain while maintaining the frequency-dependent stiffness and radiation damping nature of the far-field foundation impedance. To check the accuracy of this procedure, a typical NPP foundation mat supported at the surface of a layered soil system and subjected to harmonic forced vibration was first analyzed in the frequency domain using SASSI to calculate the target linear response and derive a linear, far-field DPFI model. The target linear solution was then used to validate two linear time-domain ADINA models: Model 1 consisting of the mat foundation+DPFI derived from the linear SASSI model and Model 2 consisting of the total SSI system (mat foundation plus a soil block). After linear alignment, the nonlinear springs were added to both ADINA models and re-analyzed in time domain. Model 2 provided the target nonlinear solution while Model 1 provided the results using the DPFI+nonlinear springs. By increasing the amplitude of the vibration load, different levels of foundation sliding were simulated. Good agreement between the results of two models in terms of the displacement response of the mat and cyclic force-displacement behavior of the springs validates the accuracy of the procedure presented herein.

A novel wave propagation method for measuring viscoelastic properties of pre-strained materials

2021 ◽  
pp. 1-19
Author(s):  
Pierre Lemerle
Keyword(s):  
Wave Propagation ◽  
Viscoelastic Properties ◽  
Time History ◽  
Main Concept ◽  
Frequency Dependent ◽  
Damping Characteristics ◽  
History Of ◽  
Propagation Methods ◽  
The Time Domain ◽  
Waveform Pattern

Abstract Viscoelastic materials are widely used for vibroacoustic solutions due to their ability to mitigate vibration and sound. Wave propagation methods are based on the measurement of the waveform pattern of a transitory pulse in one-dimensional structures. The time evolution of the pattern can be used to deduce the material elasticity and damping characteristics. The most popular propagation methods, namely Hopkinson bar methods, assume no dispersion, i.e. the complex elasticity modulus is not frequency-dependent. This is not significant for resilient materials such as elastomers. More recent approaches have been developed to measure frequency-dependent properties from a pulse propagating in a slender bar. We showed in previous works how to adapt these techniques for shorter samples of materials, representing a real advance, as extrusion is a cumbersome process for many materials. The main concept was to reconstruct the time history of the wave propagating in a composite structure composed of a long incident bar made of a known material and extended by a shorter sample bar. Then the viscoelastic properties of the sample material were determined in the frequency domain within an inverse method held in the time domain. In industry, most isolation solutions using mounts or bushings must support structural weights. This is why it is particularly interesting to know the viscoelastic properties of the material in stressed state. Here, we show how to overcome this challenging issue. The theoretical framework of the computational approach is detailed and the method is experimentally verified.

scholarly journals Discrete-time inverse optimal control for a reaction wheel pendulum: a passivity-based control approach

2020 ◽  
Vol 19 (4) ◽  
pp. 123-132 ◽  
Author(s):  
Oscar Danilo Montoya ◽  
Walter Gil-González ◽  
Federico Martin Serra
Keyword(s):  
Optimal Control ◽  
Discrete Time ◽  
Point Of View ◽  
Control Analysis ◽  
Inverse Optimal Control ◽  
Reaction Wheel ◽  
Control Approach ◽  
Control Functions ◽  
Passivity Based Control ◽  
The Time Domain

In this paper it is presented the design of a controller for a reaction wheel pendulum using a discrete-time representation via optimal control from the point of view of passivity-based control analysis. The main advantage of the proposed approach is that it allows to guarantee asymptotic stability convergence using a quadratic candidate Lyapunovfunction. Numerical simulations show that the proposed inverse optimal control design permits to reach superiornumerical performance reported by continuous approaches such as Lyapunov control functions and interconnection,and damping assignment passivity-based controllers. An additional advantageof the proposed inverse optimal controlmethod is its easy implementation since it does not employ additional states. It is only required a basic discretizationof the time-domain dynamical model based on the backward representation. All the simulations are carried out inMATLAB/OCTAVE software using a codification on the script environment.

scholarly journals Convergence of the uniaxial PML method for time-domain electromagnetic scattering problems

2021 ◽  
Author(s):  
Changkun Wei ◽  
Jiaqing Yang ◽  
Bo Zhang
Keyword(s):  
Time Domain ◽  
Electromagnetic Scattering ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Scattering Problems ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Time Domain Electromagnetic ◽  
Numer Anal ◽  
The Time Domain

In this paper, we propose and study the uniaxial perfectly matched layer (PML) method for three-dimensional time-domain electromagnetic scattering problems, which has a great advantage over the spherical one in dealing with problems involving anisotropic scatterers. The truncated uniaxial PML problem is proved to be well-posed and stable, based on the Laplace transform technique and the energy method. Moreover, the $L^2$-norm and $L^{\infty}$-norm error estimates in time are given between the solutions of the original scattering problem and the truncated PML problem, leading to the exponential convergence of the time-domain uniaxial PML method in terms of the thickness and absorbing parameters of the PML layer. The proof depends on the error analysis between the EtM operators for the original scattering problem and the truncated PML problem, which is different from our previous work (SIAM J. Numer. Anal. 58(3) (2020), 1918-1940).

scholarly journals Computer-Aided Numerical Inversion of Laplace Transform

2000 ◽  
Vol 22 (3) ◽  
pp. 189-213 ◽  
Author(s):  
Umesh Kumar
Keyword(s):  
Laplace Transform ◽  
Probability Density Functions ◽  
Numerical Inversion ◽  
Time Varying ◽  
Inversion Technique ◽  
Computer Aided ◽  
The Laplace Transform ◽  
The Time Domain ◽  
Time Invariant ◽  
Exponential Probability

This paper explores the technique for the computer aided numerical inversion of Laplace transform. The inversion technique is based on the properties of a family of three parameter exponential probability density functions. The only limitation in the technique is the word length of the computer being used. The Laplace transform has been used extensively in the frequency domain solution of linear, lumped time invariant networks but its application to the time domain has been limited, mainly because of the difficulty in finding the necessary poles and residues. The numerical inversion technique mentioned above does away with the poles and residues but uses precomputed numbers to find the time response. This technique is applicable to the solution of partially differentiable equations and certain classes of linear systems with time varying components.

Dynamic Response for a Functionally Graded Rectangular Plate Subjected to Thermal Shock Based on LS Theory

2013 ◽  
Vol 332 ◽  
pp. 381-395 ◽  
Author(s):  
Seyed Mohsen Nowruzpour Mehrian ◽  
Mohammad Hasan Naei ◽  
Shahla Zamani Mehrian
Keyword(s):  
Thermal Shock ◽  
Rectangular Plate ◽  
Time Domain ◽  
Sudden Change ◽  
Functionally Graded ◽  
State Equations ◽  
The Laplace Transform ◽  
Graded Material ◽  
Thermoelastic Response ◽  
The Time Domain

Thermal shock describes the way that a material exposed to a sudden change in temperature. These conditions usually take place in aerospace industry, when aircraft encounter the atmosphere layers. It also happens in combustion chamber of engines when mixture of fuel and air ignite in cylinder. Classical thermoelasticity is not capable to analyze such a problem. Therefore, generalized coupled thermoelasticity theories arose. In this article, the dynamic coupled thermoelastic response of a rectangular plate made of functionally graded material subjected to a thermal shock based on Lord-Shulman theory is studied. Using state space approach, the state equations of the problem are obtained. The plate’s boundary condition is simply support on the edges and the variation of mechanical properties is assumed to change along the thickness of the plate. The Laplace transform is applied to transform governing equations from time domain to the Laplace domain. Then by using a numerical method, the equations are solved and the results are inversed to the time domain displacement and temperature field are acquired. Results are presented for different power law indices and they are validated by previous reported literature.

Travelers’ exposure to vibrations and noise depending on the type of transport – the results of pilot research

2019 ◽  
Vol 570 (3) ◽  
pp. 23-27
Author(s):  
Magdalena Matys ◽  
Kamil Piotrowski ◽  
Dominik Mleczko ◽  
Paweł Pawlik
Keyword(s):  
Air Pollution ◽  
Time Domain ◽  
Public Transport ◽  
Sound Pressure ◽  
Heavy Traffic ◽  
Pressure Level ◽  
Point Of View ◽  
Vibration Acceleration ◽  
Passenger Cars ◽  
The Time Domain

For some time residents of big cities have been encouraged to change their means of transport, that is, to swap passenger cars for public transport vehicles. This is meant to help to reduce the problems associated with heavy traffic and air pollution. The authors of the article decided to check if such a change is also beneficial from the point of view of comfort and health of a person who uses public transport. For this purpose values of vibration acceleration and sound pressure level to which Cracow’s commuters are exposed to have been analyzed, depending on the type of vehicle they choose. In this respect measurements have been carried out for passenger cars, buses and trams. Two vehicle models of each type, significantly different from each other (old and new) have been selected for the tests. The measurements during a few trips in each type of vehicle on a predetermined route have been conducted. This article presents a comparison of measured values of vibroacoustic parameters in the time domain. It attempts to assess vibration and noise parameters, taking into account their impact on the health and comfort of the traveler.

Sign in / Sign up

Export Citation Format

Share Document