Stochastic response of fractionally damped beams

This paper aims at introducing the governing equation of motion of a continuous fractionally damped system under generic input loads, no matter the order of the fractional derivative. Moreover, particularizing the excitation as a random noise, the evaluation of the power spectral density performed in frequency domain highlights relevant features of such a system.Numerical results have been carried out considering a cantilever beam under stochastic loads. The influence of the fractional derivative order on the power spectral density response has been investigated, underscoring the damping effect in reducing the power spectral density amplitude for higher values of the fractional derivative order. Finally, the fractional derivative term introduces in the system dynamics both effective damping and effective stiffness frequency dependent terms.     

Prioritizing of wind farm locations for hydrogen production: A case study

Many advantages of renewable energies, especially wind energy, such as abundance, permanence, and lack of pollution has encouraged many industrialized and developing countries to focus more on these clean and economic sources of energy. Identifying a good location that is suitable for the construction of a wind farm is one of the important initial steps in harnessing wind energy which is assessed this study. The purpose of this study is to prioritize and rank 13 cities of Fars province in Iran, in terms of their suitability for the construction of a wind farm. Six important criteria were used to prioritize and rank the cities. Wind power density is the most important criterion among these criteria which is calculated by obtaining the 3-h wind speed data between 2004 and 2013. DEA (Data Envelopment Analysis) method is used for prioritizing and ranking cities, and then AHP (Analytical Hierarchy Process), and FTOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) methods are used to assess the validity of results. It is concluded that Izadkhast city is the suggested location for the construction of wind farm. The utilizing a wind-hydrogen energy conversion system will result in a substantial amount of hydrogen production (averagely 21.9 ton/year) when a 900 kW wind turbine is installed in this location.     

Dressed in Blue: The Impact of Woad on English Clothing,c. 1350–c. 1670

Abstract

This paper seeks to explore the changing importance of blue colours, blue dyes and woad in particular in England in the late Middle Ages and early modern period. It does so by considering six themes — the popularity and fashionability of blue; blue and its significance within the Order of the Garter; blue as a colour worn by the lower social groups and its association with poverty and livery; colour symbolism of blue; blue and court entertainments; blue and the liturgy — but it will start with a review of blue colours and blue dyes.     

A new identification method of viscoelastic behavior: Application to the generalized Maxwell model

This paper focuses on the generalized Maxwell model (GMM) identification. The formulation of the transfer function of the GMM is defined, as well as its asymptotes. To compare identification methods of the parameters of the GMM, a test transfer function and two quality indicators are defined. Then, three graphical methods are described, the enclosing curve method, the CRONE method and an original one. But the results of graphical methods are not good enough. Thus, two optimization recursive processes are described to improve the results of graphical methods. The first one is based on an unconstrained non-linear optimization algorithm and the second one is original and allows constraining identified parameters. This new process uses the asymptotes of the modulus and the phase of the transfer function of the GMM. The result of the graphical method optimized with the new process is very accurate and fast.     

UNIQUENESS OF DISPLACEMENT-HEAT FLUX AND STRESS-TEMPERATURE PROBLEMS IN THERMOELASTICITY WITH ONE RELAXATION TIME

Two uniqueness theorems of linear thermoelasticity with one relaxation time corresponding to natural initial boundary value problems described in terms of two different pairs of thermoelastic variables: displacement-heat flux and stress-temperature are proved.     

Arbitrary real-order cost functions for signals and systems

This work focuses on a new type of cost function based on fractional operators. To do so, the concept of definite integral is extended to arbitrary real-order. Some properties of this new fractional-order definite integral are studied and a fractional-order Barrow's rule is proposed. It is illustrated by an example (the design of an IIR filter) how this new kind of cost function can be a valuable tool in problems where optimal design methods are involved.     

Chaotic dynamics in Bonhoffer-van der Pol fractional reaction-diffusion system

In this article we analyze the linear stability of nonlinear fractional reaction-diffusion systems. As an example, the reaction-diffusion model with cubic nonlinearity is considered. By computer simulation, it was shown that in such simplest system, a complex nonlinear dynamics, which includes spatially non-homogeneous oscillations and spatio-temporal chaos, takes place. Possible applications of the fractional reaction-diffusion system for signal processing and pattern recognition systems are presented.     

Variable-order fractional derivatives and their numerical approximations

This paper addresses the different possible definitions of variable-order derivatives and their numerical approximations; both approximations based upon the definitions and approximations consisting of non-linear transfer functions (in particular combining existing approximations of constant-order fractional derivatives, such as the Crone approximation, with fuzzy logic) are considered. There are different possible configurations, implementing variable-order fractional derivatives both with and without memory of past values of the time-dependent differentiation order.     

Stability preservation analysis in direct discretization of fractional order transfer functions

In this paper, a class of the direct methods for discretization of fractional order transfer functions is studied in the sense of stability preservation. The stability boundary curve is exactly determined for these discretization methods. Having this boundary helps us to recognize whether the original system and its discretized model are the same in the sense of stability. Finally, some illustrative examples are presented to evaluate achievements of the paper.     

On distributed order integrator/differentiator

In this paper, we derive the impulse response of the distributed order integrator/differentiator and its asymptotic property by using the complex path integral. Based on the derived analytical impulse response, we present a technique to perform the discretization of the above distributed order integrator/differentiator. The derived asymptotic property can be applied to verify the feasibility of this method. Some new features of the distributed order integrator/differentiator are shown in time and frequency domains. A number of illustrated figures are presented to validate the concepts.