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In this contribution, free vibration of axially functionally graded beams is analysed within the framework of the Euler-Bernoulli beam theory. The beams with uniaxial variation of the elasticity modulus and mass density are approximated by an equivalent beam with piecewise exponentially varying geometrical and material properties. A numerical example for a beam with pinned ends is presented.
In this paper, a problem of transverse free vibration of a double-nanobeam-system is considered. The nanobeams of the system are coupled by an arbitrary number of translational springs. The solution of the problem by using the Green’s functions properties is obtained. A numerical example is presented.
The one-dimensional time-fractional advection-diffusion equation with the Caputo time derivative is considered. The fundamental solution to the Cauchy problem is obtained using the integral transform technique. The numerical results are illustrated graphically.
This article is a continuation of the discussion on the two-dimensional Fourier equation with Robin’s boundary condition. In the paper the Finite Difference Method is applied.
In this work we study the fractional forced pendulum equation with combined fractional derivatives -tDαT0Dαtu( t ) + g ( u ( t )) = f ( t ), t ∈ ( 0, T ) ( 0. 1 ) u ( 0 ) = u ( T ) = 0 where ½ < α < 1, g ∈ C ( R, R ), bounded f ∈ C [ 0, T ]. Using minimization techniques form variational calculus we show that ( 0. 1 ) has a nontrivial solution.
G-queueing network with positive messages and signals at transient behavior is considered. A system of difference-differential equations for the state probabilities of the network is obtained. To find them and the average characteristics of the network a technique was applied based on the use of apparatus of multivariate generating functions. An expression for the generating function was obtained...
This paper describes implementations of the Hough Circle Transform and the Radon Line Transform. The presented transforms were used to build a system for identifying road signs from selected images and recordings. This can be very important and especially useful for monitoring and prevention in driver assistance systems. The design of our system assumed that the objects should be found automatically...
The necessities of processing of spatial data require developing new feature-sensitive tools such as extensions of the wavelet transform. Considering the advantages of the application of complex wavelets and their extension to quaternionic wavelets for twodimensional data structures, the new octonion discrete wavelet transform for the analysis of three-dimensional data structures was introduced in...
In the paper the problem of thermal processes proceeding in the domain of biological tissue secured with protective clothing is discussed. In particular, the mathematical model of heat exchange corresponding to conditions of high temperature in the system environment - layer of protective clothing - air gap - skin tissue is formulated in the form of a certain boundary - initial problem. Next, the...
We consider a multi-channel queueing system with unlimited queue and with exponentially distributed service time and the intervals between the arrival of customers batches, which uses a hysteretic control mechanism of the input flow intensity. The system receives two independent flows of customers, one of which is blocked in an overload mode. An algorithm for finding the stationary distribution of...
In this text a new property of geometric nature of the Chebyshev polynomials is given. It is proven that the lengths of diagonals of a regular n-gon with the side of length equal to one are the sums of positive roots of the respective renormalized Chebyshev polynomials of one from among four types. Some new special decompositions of differences of values of the Chebyshev polynomials are also presented.
In this paper, the results of numerical studies on optimization of a geometrically nonlinear column with an internal crack by means of genetic algorithms are presented. The system is loaded by an axially applied external force P with a constant line of action. The presented problem is formulated on the basis of the principle of stationary total potential energy. The main purpose of this paper is to...
In this paper we present a numerical method to solve a one-dimensional, one-phase extended Stefan problem with fractional time derivative described in the Caputo sense. The proposed method is based on applying a similarity variable for the anomalous-diffusion equation and the finite difference method. In the final part, examples of numerical results are discussed.
The purpose of this research paper is to find the expected incomes in open Markov queueing networks with incomes, positive and negative messages at any time by the multidimensional transformations. Investigations were carried out in cases when incomes from the network transitions between the states are deterministic functions not dependent on network states and time. It is assumed that all network...
This paper deals with a new method of constructing mathematical models of complex processes aliquant vibration frequencies, based on the ideas of genetic algorithms. Compared with the method of data handling group, this method makes it possible to synthesize mathematical models of any complexity without selecting the number of rows selection. Moreover, the use of genetic algorithms will significantly...
In the paper the description of numerical analysis of the heat transfer process proceeding in a two-dimensional silicon thin film is presented. It is assumed that some parameters like relaxation time and boundary temperatures appearing in the mathematical model of the analyzed problem are given as intervals. The discussed problem has been solved using the interval form of the lattice Boltzmann method...
The paper presents the numerical analysis of stress occurring in the most wearable parts of knee joint endoprostheses. That applies to the pair: sled - spherical insert. The Finite Elements Method makes it possible to calculate the stress in particular elements of the tested model. The interaction between the two parts of endoprosthesis takes place on a comparatively small contact surface.
We consider solving the Cauchy problem with an abstract linear evolution equation by means of the Generalized Method of Lie-algebraic discrete approximations. Discretization of the equation is performed by all variables in equation and leads to a factorial rate of convergence if Lagrange interpolation is used for building quasi representation of differential operator. The rank of a finite dimensional...
The presented work is focused on the basis of mathematical and numerical descriptions of the binary alloy solidification problem. The mathematical formulation is based on the so-called substitute thermal capacity, which implies a change in the specific heat of solidifying material. In the literature one can find many ways to define this parameter. Five models, differing in the description of the substitute...
The report presents a study of the thermal boundary effect behaviour in the hexagonal-type rigid conductors. Every hexagonal cell of the conductor is made of three rhombus parts. Some special cases of a considered conductor with rhombus parts built of two layers of different isotropic material are analyzed. The tolerance averaging approach is used as a tool of modeling. The most important result of...
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