Nonlinear resonant response of a buckled beam coupled with a boundary massive oscillator

This study focuses on nonlinear modal resonant dynamics of a buckled beam coupled with a boundary massive oscillator. To reveal buckled beam–boundary oscillator coupling effect, extended Hamilton principle is employed to derive a dynamic model with geometric nonlinearity included, and direct multipl...

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Bibliographic Details
Published in:Nonlinear dynamics 2024-03, Vol.112 (5), p.3217-3240
Main Authors: Chen, Hao, Guo, Tieding, Qiao, Wanzhi, Cong, Yunyue, Kang, Houjun
Format: Article
Language:English
Subjects:
Automotive Engineering
Boundary conditions
Classical Mechanics
Control
Dynamic models
Dynamic stability
Dynamical Systems
Engineering
Geometric nonlinearity
Hamilton's principle
Investigations
Mechanical Engineering
Nonlinear dynamics
Nonlinear response
Original Paper
Oscillators
Partial differential equations
Poincare maps
Vibration
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Summary:This study focuses on nonlinear modal resonant dynamics of a buckled beam coupled with a boundary massive oscillator. To reveal buckled beam–boundary oscillator coupling effect, extended Hamilton principle is employed to derive a dynamic model with geometric nonlinearity included, and direct multiple-scale method (i.e., attacking directly partial differential equations) is then applied to reduce the original infinite-dimensional beam–support coupled system, leading to nonlinear modulation equations characterizing reduced slow dynamics of the coupled system, by focusing on beam’s one-to-one internally resonant dynamics around its first buckled shape. Time history responses, frequency responses, and Poincaré mapping are employed to investigate stability/bifurcation of nonlinear forced coupled dynamics, with one-to-one internal resonance activated or not.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-023-09239-3