http://doi.org/10.35668/978-966-479-146-2
Glukhivskyi L. Yo. Nonlinear oscillations: numerical polyharmonic simulating [Electronic resource] / L. Glukhivskyi ; Translation from Ukrainian and editors L. Yo. Glukhivskyi. – Kyiv : UkrISTEI, 2024. – 199 p.
ISBN 978-966-479-146-2 (online)
UDC 534 : 621.3.021:681.3.068.004.4
Author's translation from the book Л. Й. Глухівського «Нелінійні коливання: чисельне полігармонічне моделювання», Київ : «Альфа Пік», 2008.
Glukhivskyi Lev Yosypovych – Doctor of Technical Sciences, Professor, Honored Worker of Science and Technology of Ukraine, Kyiv, Ukraine; +38(050) 309-08-57; gl.lev42@gmail.com
Abstract. The book describes the basics of the differential harmonic method, which belongs to the class of methods for numerical modeling of nonlinear oscillations, that is, periodic processes, in systems of one or another physical nature, the variables of which are connected by nonlinear connections.The method is based on finding periodic solutions of systems of nonlinear differential equations with their approximation by Fourier series and taking into account the required number of higher harmonics.
The basic software of the differential harmonic method, developed in the FORTRAN-90 language, is described. It consists of 24 software modules. When modeling a specific nonlinear oscillation, it is necessary to develop three more modules, the development principle of which is given. Ten examples of computer modeling of various types of nonlinear oscillations are given, in particular: forced, parametric and free.
The book is intended for specialists in the field of computer modeling and analysis of periodic processes in nonlinear systems of mechanics, electrical engineering, automatic control, radio physics, acoustics, etc., and can also be used as a study guide for graduate students and doctoral students in the relevant sciences.
Keywords: nonlinear systems, periodic processes, numerical modeling, nonlinear differential equations, periodic solutions, numerical methods, algorithms for finding periodic solutions, differential harmonic method, software, computer programs for finding periodic solutions
