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Author:

Wu, R.Q. (Wu, R.Q..) | Zhang, W. (Zhang, W..) | Chen, J.E. (Chen, J.E..) | Feng, J.J. (Feng, J.J..) | Hu, W.H. (Hu, W.H..)

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EI Scopus SCIE

Abstract:

The nonlinear dynamic characteristics of a flexible beam-ring structure under fundamental harmonic excitation are systematically investigated. The nonlinear partial differential governing equations of motion for the beam-ring structure are derived by using Hamilton's principle and discretized into two coupled ordinary differential equations including quadratic and cubic nonlinearities by Galerkin's technique. The potential internal resonance relationship of the beam-ring structure is recognized through analyzing the mode shapes and linear frequencies. The method of multiple scales is utilized to approximately analyze the dynamic system and yield a set of autonomous equations under the case of 1:1 internal resonance and a primary resonance. The amplitude-frequency characteristics and the stability of the steady-state responses are studied numerically. The frequency-response curves show that some parameters of the amplitude-frequency equations have significant contributions to the nonlinear responses near resonance of the beam-ring structure. Finally, the bifurcation diagram is obtained and the Poincare map, power spectra and the largest Lyapunov exponent are used to identify the nonlinear dynamic behaviors of the beam-ring structure. From the numerical simulations, it is found that there exist typical nonlinear phenomena such as multi-value solutions, jumps, bifurcations, multiple periodic and chaotic motions in the beam-ring system. This work also proposes a reference for nonlinear modeling and dynamic analysis of similar complex structures. © 2023

Keyword:

Beam-ring structure Bifurcation Nonlinear vibration Internal resonance Amplitude-frequency characteristics

Author Community:

  • [ 1 ] [Wu R.Q.]Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, School of Mechanical Engineering, Tianjin University of Technology, Tianjin, 300384, China
  • [ 2 ] [Wu R.Q.]National Demonstration Center for Experimental Mechanical and Electrical Engineering Education, Tianjin University of Technology, Tianjin, 300384, China
  • [ 3 ] [Zhang W.]Beijing Key Laboratory on Nonlinear Vibrations and Strength of Mechanical Structures, College of Mechanical Engineering, Beijing University of Technology, Beijing, 100124, China
  • [ 4 ] [Chen J.E.]Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, School of Mechanical Engineering, Tianjin University of Technology, Tianjin, 300384, China
  • [ 5 ] [Chen J.E.]National Demonstration Center for Experimental Mechanical and Electrical Engineering Education, Tianjin University of Technology, Tianjin, 300384, China
  • [ 6 ] [Feng J.J.]Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, School of Mechanical Engineering, Tianjin University of Technology, Tianjin, 300384, China
  • [ 7 ] [Feng J.J.]National Demonstration Center for Experimental Mechanical and Electrical Engineering Education, Tianjin University of Technology, Tianjin, 300384, China
  • [ 8 ] [Hu W.H.]Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control, School of Mechanical Engineering, Tianjin University of Technology, Tianjin, 300384, China
  • [ 9 ] [Hu W.H.]National Demonstration Center for Experimental Mechanical and Electrical Engineering Education, Tianjin University of Technology, Tianjin, 300384, China

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Source :

Applied Mathematical Modelling

ISSN: 0307-904X

Year: 2023

Volume: 119

Page: 316-337

5 . 0 0 0

JCR@2022

ESI Discipline: ENGINEERING;

ESI HC Threshold:19

Cited Count:

WoS CC Cited Count: 0

SCOPUS Cited Count: 8

ESI Highly Cited Papers on the List: 0 Unfold All

WanFang Cited Count:

Chinese Cited Count:

30 Days PV: 3

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