Speciality:
01.02.01 (Theoretical mechanics)
Birth date:
21.08.1947
E-mail: Website: https://users.kpi.kharkov.ua/apm Keywords: nonlinear vibrations of finite-dimensional systems; stability of nonlinear vibrations; homoclinic and heteroclinic trajectories and chaotic behavior of dynamical systems; dynamics of vibro-impact systems; vibrations and waves in nonlinear elastic systems; rational fractional approximations in theory of non-linear vibrations.
Subject:
New methods of analysis of nonlinear normal vibration modes of essentially nonlinear finite-dimensional conservative systems are developed. A problem of construction of normal vibrations in nonautonomous and self-oscillating finite-dimensional systems close to conservative ones is solved. Methods of the stability investigation of normal vibration modes in systems with a single and several equilibrium positions are developed. New methods of construction of homo- and heteroclinic trajectories as well of matching of local expansions with using fractional rational approximations, are developed. Normal vibrations and stationary traveling waves in some discrete and continuous vibro-impact systems are investigated. New results on problems of dynamics of nonlinear elastic systems (rods, shells, arches) are obtained.
Main publications:
A. F. Vakakis, L. I. Manevich, Yu. V. Mikhlin,V. N. Pilipchuk, and A. A. Zevin. Normal Modes and Localization in Nonlinear Systems. NY: Wiley, 1996.
Yu. V. Mikhlin and B. I. Morgunov. Normal vibrations in near-conservative self-excited and viscoelastic nonlinear systems // Nonlinear Dynamics, 2001, 25, 33–48.
Yu. V. Mikhlin, A. M. Volok. Solitary transversal waves and vibro-impact motions in infinite chains and rods // Int. Journal of Solids and Structure, 2000, 37, 3403–3420.
Yu. V. Mikhlin and A. L. Zhupiev. An application of the Ince algebraization to the stability of non-linear normal vibration modes // Int. Journal of Nonlinear Mechanics, 1997, 32(1), 393–409.
