Non-monotonic dynamics (mixed hardening/softening) in nonlinear continuous structures: An asymptotic formulation

Non-monotonic dynamics of nonlinear continuous structures, i.e., mixed hardening(H)/softening(S) behavior in the vicinity of H/S transition, is comprehensively investigated by developing a generic asymptotic formulation. Non-monotonic dynamics is due to high-order competition between cubic and quint...

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Bibliographic Details
Published in:Nonlinear dynamics 2024-09, Vol.112 (17), p.14745-14772
Main Authors: Lan, Fangyan, Guo, Tieding
Format: Article
Language:English
Subjects:
Approximation
Asymptotic properties
Automotive Engineering
Behavior
Cables
Classical Mechanics
Control
Dispersion hardening
Dynamic structural analysis
Dynamical Systems
Engineering
Frequency response
Investigations
Mechanical Engineering
Nonlinear dynamics
Parameter identification
Physics
Shallow foundations
Softening
Vibration
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Summary:Non-monotonic dynamics of nonlinear continuous structures, i.e., mixed hardening(H)/softening(S) behavior in the vicinity of H/S transition, is comprehensively investigated by developing a generic asymptotic formulation. Non-monotonic dynamics is due to high-order competition between cubic and quintic mechanisms and thus qualitatively distinct from routine monotonic dynamics (either softening or hardening) associated with Duffing-type cubic mechanism. The general theoretical formulation is applied to both a nonlinear foundation beam model and a nonlinear shallow sagged cable model, with various non-monotonic responses found. In particular, by leveraging frequency response curves (FRCs) and backbone curves (BBCs), reversal of FRCs/BBCs in the mixed softening/hardening dynamics is further connected to zero dispersion phenomenon, with its activation condition also established.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-024-09666-w