Науковий вісник НГУ

Resonance phenomena in quasi-zero stiffness vibration isolation systems

User Rating:  / 0

Details

Category: Mining mechanics

Last Updated on Friday, 30 October 2015 22:35

Published on Friday, 30 October 2015 22:35

Hits: 3342

Authors:

P.Ya. Pukach, Dr. Sci. (Tech.), Associate Professor, Lviv Polytechnic National University, Senior Lecturer of the Higher Mathematics Department, Lviv, Ukraine.

I.V. Kuzio, Dr. Sci. (Tech.), Professor, Lviv Polytechnic National University, Head of the Department of Mechanics and Mechanical Engineering Automation, Lviv, Ukraine.

Abstract:

Purpose. To study dynamic processes in nonlinear oscillatory systems with quasi-zero stiffness and with one or many degrees of freedom, which are widely used in industry for cargo and personnel vibration isolation during transportation. The previous studies of such systems were based only on the numerical approaches. In this paper, we propose to investigate thoroughly the dynamics of the above mentioned systems and the conditions for the occurrence of resonance phenomena in them using the asymptotic methods of nonlinear mechanics and applying the apparatus of special periodic functions.

Methodology. The methods of studying resonance oscillations of vibration isolation equipment are based on the asymptotic methods of nonlinear mechanics, wave theory of motion and the use of special Ateb-functions.

Findings. In this work, for the nonlinear quasi-zero stiffness vibration isolation systems with one and two degrees of freedom, we analytically obtained the conditions of resonance oscillations, threshold values of resonance amplitudes depending on the system parameters.

Originality. For the first time, the dynamic processes in systems with concentrated masses and quasi-zero stiffness were analyzed based on analytical approaches. In contrast to numerical approaches, the analytical approaches allow investigating the features of the dynamics of such systems more precisely.

Practical value. The proposed method may solve the problems of analysis, and the problems oscillatory systems synthesis at the design stage, as they allow us to choose such elastic properties of dynamical systems that prevent resonance phenomena. These modes of equipment operation may assure efficient and safe transportation.

References:

1. Loveykin, V.S., Chovnyuk, Yu.V. and Dikteruk, M.G. (2007), “Design and optimization of the movement of rough nonlinear mechanical systems”, Víbratsii v tekhnitsi ta tekhnologíyakh, issue 3(48), pp. 68–71.

Ловейкин В.С. Проектирование и оптимизация режимов движения грубых нелинейных механических систем / В.С. Ловейкин, Ю.В. Човнюк, М.Г. Диктерук // Вібрації в техніці та технологіях. – Дніпропетровськ, 2007. – № 3(48). – С.68–71.

2. Mitropolskii, Yu. A. (1994), Nelineynye krayevye zadachi matematicheskoy fiziki i ikh prilozheniya [Nonlinear Boundary Value Problems of Mathematical Physics and Their Applications], Іnstitute of Mathematics of NAS of Ukraine, Kiev, Ukraine.

Митропольский Ю.А. Нелинейные краевые задачи математической физики и их приложения / Митропольский Ю.А. – К.: Ін-т математики НАН України, 1994. – 231 c.

3. Sokil, B.I. and Sokil, M.B. (2002), “Periodic Ateb-function in the study of nonlinear systems with impulse disturbance”, Scientific Bulletin: Collection of scientific works UDLTU, issue 12.8, pp. 304–311.

Сокіл Б.І. Періодичні Ateb-функції у дослідженні нелінійних систем з імпульсним збуренням / Б.І. Сокіл, М.Б. Сокіл // Науковий вісник: Збірник науково-технічних праць. – Львів: УДЛТУ, 2002.– Вип. 12.8.– С. 304–311.

4. Sokil, B.I., (2001), “Nonlinear vibrations of mechanical systems and analytical methods for their research”, Abstract of Dr. Sci. (Tech.) dissertation, Dynamics and Strength of Machines, Lviv Polytechnic National University, Lviv, Ukraine.

Сокіл Б.І. Нелінійні коливання механічних систем і аналітичні методи їх досліджень: автореф. дис. на здобуття наук. ступеня д-ра техн. наук: спец. 05.02.09 “Динаміка та міцність машин” / Сокіл Б.І.; Національний ун-т "Львівська політехніка".– Львів, 2001.– 36 с.

5. Pukach, P.Ya., (2014), “Methods for the analysis of dynamic processes in nonlinear nonautonomus mechanical systems with different structures”, Abstract of Dr. Sci. (Tech.) dissertation, Dynamics and Strength of Machines, Lviv Polytechnic National University, Lviv, Ukraine.

Пукач П.Я. Методи аналізу динамічних процесів у нелінійних неавтономних механічних системах різної структури: автореф. дис. на здобуття наук. ступеня д-ра техн. наук: спец. 05.02.09 “Динаміка та міцність машин” / Пукач П.Я. //Нац. ун-т „Львівська політехніка“. – Львів, 2014.– 40 с.

2015_03_pukach
2015-10-29  506.41 KB  986

• < Prev
• Next >