Distributed order fractional constitutive stress-strain relation in wave propagation modeling

Distributed order fractional model of viscoelastic body is used in order to describe wave propagation in infinite media. Existence and uniqueness of fundamental solution to the generalized Cauchy problem, corresponding to fractional wave equation, is studied. The explicit form of fundamental solution is calculated, and wave propagation speed, arising from solution's support, is found to be connected with the material properties at initial time instant. Existence and uniqueness of the fundamental solutions to the fractional wave equations corresponding to four thermodynamically acceptable classes of linear fractional constitutive models, as well as to power type distributed order model, are established and explicit forms of the corresponding fundamental solutions are obtained

Forced oscillations of a body attached to a viscoelastic rod of fractional derivative type

We study forced oscillations of a rod with a body attached to its free end so that the motion of a system is described by two sets of equations, one of integer and the other of the fractional order. To the constitutive equation we associate a single function of complex variable that plays a key role in finding the solution of the system and in determining its properties. This function could be defined for a linear viscoelastic bodies of integer/fractional derivative type

Nano and viscoelastic Beck's column on elastic foundation

Beck's type column on Winkler type foundation is the subject of the present analysis. Instead of the Bernoulli-Euler model describing the rod, two generalized models will be adopted: Eringen non-local model corresponding to nano-rods and viscoelastic model of fractional Kelvin-Voigt type. The analysis shows that for nano-rod, the Herrmann-Smith paradox holds while for viscoelastic rod it does not

On a system of equations arising in viscoelasticity theory of fractional type

We study a system of partial differential equations with integer and fractional derivatives arising in the study of forced oscillatory motion of a viscoelastic rod. We propose a new approach considering a quotient of relations appearing in the constitutive equation instead the constitutive equation itself. Both, a rod and a body are assumed to have finite mass. The motion of a body is assumed to be translatory. Existence and uniqueness for the corresponding initial-boundary value problem is proved within the spaces of functions and distributions

Space-time fractional Zener wave equation

Space-time fractional Zener wave equation, describing viscoelastic materials obeying the time-fractional Zener model and the space-fractional strain measure, is derived and analyzed. This model includes waves with finite speed, as well as non-propagating disturbances. The existence and the uniqueness of the solution to the generalized Cauchy problem are proved. Special cases are investigated and numerical examples are presented

Alternative approaches to financial and sporting performance measurement in English professional football

The purpose of this thesis is to combine, in a new way, variables of financial performance and sporting performance in professional football clubs to provide a new measure of overall performance. Previous literature on the topic indicates that the choice of variables used to measure sporting and financial performance has been haphazard and inconsistent. Subsequently, this thesis devises and tests a model that provides a new holistic measure of overall performance and can be used to evaluate the performance of professional football clubs in England. The model was produced using statistical analysis techniques to ensure that the correct variables were included and weighting factors on each variable added a further robustness to the model. The model is also timely in relation to new regulations throughout the European game such as Financial Fair Play which aims to alleviate the debt problem across professional football and encourage clubs to spend within their means. The thesis concluded a number of findings in relation to English professional football clubs since 1992. First, there has been a move towards utility maximisation among English clubs. Second, the foreign ownership model has led to an improvement in sporting performance and a decline in financial performance. Third, there is evidence to suggest that there has been a relationship between rising revenues and rising costs in English football during the last twenty years and that this shows no signs of abating. The central contribution to knowledge o f this thesis is the production of the model. The model highlights, for the first time, the relationship between variables. The thesis also provides a contribution to knowledge when analysing the performance o f clubs in the English football industry since the formation of the English Premier League in 1992. A further contribution is the potential application of the model to other professional team leagues and sports both in the UK and overseas. Such a model can be used by professional sports clubs, academics and practitioners alike to ascertain how a given club is performing in relation to its closest competitors. The model can also be used by governing bodies to inform and implement changes at policy level. Furthermore, the model and its uses are not exclusively limited to the UK given the Eurocentric nature of the work

Troškovi korišćenja uređaja za aeraciju vode na toplovodnim ribnjacima

Modern fish production requires utilization of new technologies, which assumes application of appropriate mechanization and devices. In the process of the fish production in the warm-water fish-ponds it frequently appears a problem of lacking the oxygen dissolved in water. This problem may be solved by utilization of water aeration device. Selection of the water aeration device is usually carried out in our practice on the basis of its technological and exploitation characteristics, without knowledge of economic effects both of its provision and utilization of concrete technical solution. Economic effects of aeration device utilization suppose complete knowledge of methodological procedure for calculation of costs, as well as disposal of reliable initial data necessary for calculation of the costs for such devices.Savremena proizvodnja ribe podrazumeva primenu novih tehnologija, koje za sobom povlače i upotrebu odgovarajućih sredstava mehanizacije i uređaja. U uzgoju ribe na toplovodnim ribnjacima se kao čest problem javlja nedostatak kiseonika rastvorenog u vodi, što se može rešiti primenom uređaja za aeraciju vode. Odabir uređaja za aeraciju vode se u našoj praksi najčešće vrši na osnovu njegovih tehnološko-eksploatacionih karakteristika, bez poznavanja ekonomskih efekata nabavke i primene konkretnog tehničkog rešenja. Ekonomski efekti upotrebe uređaja za aeraciju podrazumevaju potpuno poznavanje metodološkog postupka za određivanje troškova, kao i raspolaganje pouzdanim polaznim podacima koji su neophodni za izračunavanje troškova eksploatacije ovakvih uređaja

On a initial value problem arising in mechanics

We study initial value problem for a system consisting of an integer order and distributed-order fractional differential equation describing forced oscillations of a body attached to a free end of a light viscoelastic rod. Explicit form of a solution for a class of linear viscoelastic solids is given in terms of a convolution integral. Restrictions on storage and loss moduli following from the Second Law of Thermodynamics play the crucial role in establishing the form of the solution. Some previous results are shown to be special cases of the present analysis

Mehanizovani postupci pripreme i obrade komposta od rezidbenih ostataka voćarsko-vinogradarske proizvodnje

This paper is part of research about the effects of mechanized process of fragmentation of pruning residues on the composting process. Compost, as a form of organic fertilizer, requires specific production treatment depending on the form of biomass. Pruning residues from fruit-vine production can be translated into quality organic fertilizer, but it is necessary to coordinate mechanized treatment of biomass and technology of composting process with microbiological processes for organic matter decomposition.Rad predstavlja deo istraživanja uticaja mehanizovanih procesa usitnjavanja rezidbenih ostataka na proces kompostiranja. Kompost kao vid organskog đubriva zahteva specifičan tretman proizvodnje u zavisnosti od vida biomase. Rezidbeni ostaci iz voćarsko-vinogradarske proizvodnje se mogu prevesti u kvalitetno organsko đubrivo, ali je potrebno uskladiti mehanizovane procese obrade biomase i tehnologiju kompostiranja sa mikrobiološkim procesima razlaganja organske materije

Sorption of different phenol derivatives on a functionalized macroporous nanocomposite of poly(glycidyl methacrylate-co-ethylene glycol dimethacrylate) and acid modified bentonite

Macroporous nanocomposite of poly(glycidyl methacrylate-co-ethylene glycol dimethacrylate) and acid modified bentonite was prepared by radical suspension copolymerization. Nanocomposite was functionalized with diethylenetriamine (DETA), by ring-opening reaction of the pendant epoxy groups. Functionalization was performed in order to enable phenol derivatives sorption. This new, not sufficiently investigated material, with developed porous structure was denoted CP-S-A-DETA. In this study, the influence of temperature on 4-nitrophenol (4NP) sorption on CP-S-A-DETA was investigated. The chemisorption was estimated as dominant process since activation energy of sorption of 4NP of 54.8 kJ mol(-1) was obtained. After determining the optimal sorption conditions for 4NP, the sorption of 2-nitrophenol (2NP) and 2-chloro-4-nitrophenol (2Cl4NP) on CP-S-A-DETA was investigated with respect to pH, initial concentration and contact time. The 2NP sorption was seldom tested, while according to our knowledge, the 2Cl4NP sorption was not investigated. The isotherm data were best fitted with Langmuir model, while the sorption dynamics obeyed the pseudo-second-order kinetic model for all derivatives