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Nonlinear Vibration and Stability Analysis of a Flexible Beam-ring Structure with One-to-one Internal Resonance by R.Q. Wu; W. Zhang; J.E. Chen; J.J. Feng; W.H. Hu is a Engineering article available to read on EtoBox.

What is Nonlinear Vibration and Stability Analysis of a Flexible Beam-ring Structure with One-to-one Internal Resonance about?

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 non

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Author

R.Q. Wu; W. Zhang; J.E. Chen; J.J. Feng; W.H. Hu

Publisher

Elsevier BV

Published

2023

Language

EN

Field

Engineering (Physical Sciences)