Chaotic dynamics of the size-dependent non-linear micro-beam model

Chaotic dynamics of the size-dependent non-linear micro-beam model

Bibliographic Details
Parent link:Communications in Nonlinear Science and Numerical Simulation
Vol. 50.— 2017.— [P. 16-28]
Corporate Author: Национальный исследовательский Томский политехнический университет (ТПУ) Институт кибернетики (ИК) Кафедра инженерной графики и промышленного дизайна (ИГПД) Научно-учебная лаборатория 3D моделирования (НУЛ 3DМ)
Other Authors: Krysko A. V. Anton Vadimovich, Awrejcewicz J. Jan, Pavlov S. P., Zhigalov M. V. Maksim, Krysko V. A. Vadim
Summary:Title screen
In this work, a size-dependent model of a Sheremetev-Pelekh-Reddy-Levinson micro-beam is proposed and validated using the couple stress theory, taking into account large deformations. The applied Hamilton's principle yields the governing PDEs and boundary conditions. A comparison of statics and dynamics of beams with and without size-dependent components is carried out. It is shown that the proposed model results in significant, both qualitative and quantitative, changes in the nature of beam deformations, in comparison to the so far employed standard models. A novel scenario of transition from regular to chaotic vibrations of the size-dependent Sheremetev-Pelekh model, following the Pomeau-Manneville route to chaos, is also detected and illustrated, among others.
Режим доступа: по договору с организацией-держателем ресурса
Published: 2017
Subjects:
электронный ресурс
труды учёных ТПУ
Micro-beam
Couple stress theory
PDEs
Chaos
микроволны
принцип Гамильтона
хаотические колебания
пучки
деформации
Online Access:https://doi.org/10.1016/j.cnsns.2017.02.015
Format: Electronic Book Chapter
KOHA link:https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=656134
Description
Summary:Title screen
In this work, a size-dependent model of a Sheremetev-Pelekh-Reddy-Levinson micro-beam is proposed and validated using the couple stress theory, taking into account large deformations. The applied Hamilton's principle yields the governing PDEs and boundary conditions. A comparison of statics and dynamics of beams with and without size-dependent components is carried out. It is shown that the proposed model results in significant, both qualitative and quantitative, changes in the nature of beam deformations, in comparison to the so far employed standard models. A novel scenario of transition from regular to chaotic vibrations of the size-dependent Sheremetev-Pelekh model, following the Pomeau-Manneville route to chaos, is also detected and illustrated, among others.
Режим доступа: по договору с организацией-держателем ресурса
DOI:10.1016/j.cnsns.2017.02.015

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