Kornyeyev O. Methods and means of mathematical modeling dynamics structural elements with viscoelastic properties based integra-differential equations

Object of research - mathematical modeling of the dynamic processes of vmehanicheskih objects with viscoelastic properties. Goal of improving the efficiency of mathematical and computer research dynamics problems of mechanical objects by creating methods and means of numerical modeling processes in structural elements with viscoelastic properties based on integral and differential equations. First proposed version of a numerical solution of integro-differential equations by using the method of variation of parameters to obtain an equivalent Volterra integral equation II-the first kind, which allows for effective and regular aprobovanye quadrature algorithms inherent integral formulation of problems of dynamics, improved operational method for solving a linear integral equation by using the modified solutions of the image is a function that makes it easy to analytical solution of the integral equation in the real domain, improved computational scheme simple iteration method for solving integral equations, methods find the first approximation, which reduces the number of teratsy. The practical significance of these results is to increase the effectiveness of computer simulations in problem solving research and design of structural elements with viscoelastic properties based on integral and differential equations, developed by the software tools used in computer modeling of tasks. Degree of application - the results of research have been implemented in PJSC "Budivelno-assembly upravlinnya on gazifikatsii" Khmelnitsky. Scope (branch) of mathematical modeling and software tools.