Analytical method to study a mathematical model of wave processes under twopoint time conditions
Journal Title: Восточно-Европейский журнал передовых технологий - Year 2019, Vol 1, Issue 7
Abstract
<p>Research and analysis of dynamic processes in oscillatory systems are closely connected to the establishment of exact or approximate analytical solutions to the problems of mathematical physics, which model such systems. The mathematical models of wave propagation in oscillatory systems under certain initial conditions at a fixed time are well known in the literature. However, wave processes in lengthy structures subject to an external force only and at the assigned states of the process at two points in time have been insufficiently studied. Such processes are modeled by a two-point time problem for the inhomogeneous wave equation in an unbounded domain t>0, x∈ℝ<sup>s</sup>. The model takes into consideration the assignment of a linear combination with unknown amplitude of oscillations and the rate of its change at two points in time. A two-point problem, generally speaking, is the ill-posed boundary value problem, since the respective homogeneous problem has non-trivial solutions. A class of quasi-polynomials has been established as the class of the existence of a single solution to the problem. This class does not contain the non-trivial elements from the problem's kernel, which ensures the uniqueness of solution to the problem. We have proposed a precise method to build the solution in the specified class. The essence of the method is that the problem's solution is represented as the action of a differential expression, whose symbol is the right-hand side of the equation, on some function of parameters. The function is constructed in a special way using the equation and two-point conditions, and has special features associated with zeroes of the denominator – the characteristic determinant of the problem.</p><p>The method is illustrated by the description of oscillatory processes within an infinite string and a membrane.</p>The main practical application of the constructed method is the possibility to adequately mathematically model the oscillatory systems, which takes into consideration a possibility to control the system's parameters. Such a control over parameters makes it possible to perform optimal synthesis and design of parameters for the relevant technical systems in order to analyze and account for special features in the dynamic modes of oscillations
Authors and Affiliations
Zinovii Nytrebych, Volodymyr Ilkiv, Petro Pukach, Oksana Malanchuk, Ihor Kohut, Andriy Senyk
Keywords
Related Articles
- EP ID EP666209
- DOI 10.15587/1729-4061.2019.155148
- Views 63
- Downloads 0
Development of trenchless technology of reconstruction of «pulling pig P» pipeline communications
<p>The technology of trenchless reconstruction of pipeline communications has been developed by pulling a new polyethylene pipeline into a worn-out steel traction by the pig. The pig moves under the pressure of air suppl...
Thermodynamic analysis of the schemecycle design of a heatingcoolingmachinefor an individual house
<p>The direction of the research is the thermodynamic analysis of the scheme-cycle designof a heating and cooling machine for an individual house powered by autonomous solar photovoltaic system of providing private consu...
Development of intelligent demographic forecasting system
The scientific methodological and functional principles of the intelligent decision support system for the management of demographic situation based on predictions are developed. Predictions (prognosis) of the changes in...
Geometrical synthesis of spatial six-link guiding mechanisms
<p><span lang="EN-GB">The study considers problems of geometric synthesis of spatial hinge-lever six-link mechanisms with linear displacement of the final link performing the guiding function. The variants of arranging t...
Ensuring comfort microclimate in the classrooms under condition of the required air exchange
<p>We performed comparative analysis of regulatory documents, which relate to ventilation of school premises and operate in European countries at present. We showed the essential difference of the recommended air exchang...