NDLI: Nonlinear response of flapping beams to resonant excitations under nonlinear damping

Content Provider	Springer Nature Link
Author	Ozcelik, Orhan Attar, Peter J.
Copyright Year	2015
Abstract	The effect of excitation and damping parameters on the superharmonic and primary resonance responses of a slender cantilever beam undergoing flapping motion is investigated. The problem is cast into mathematical form using a nonlinear inextensible beam model which is subjected to time-dependent boundary conditions and linear or nonlinear damping forces. The flapping excitation is assumed to be non-harmonic, composed of two sine waves with different amplitudes. We employ a combination of Galerkin and perturbation methods to arrive at the frequency–response relationships associated with the second- and third-order superharmonic and primary resonances. The resonance solutions of the spatially discretized equation of motion, which involves both quadratic and cubic nonlinear terms, are constructed as first-order uniform asymptotic expansions via the method of multiple timescales. The effect of excitation and damping parameters on the steady-state resonance responses and their stability is described quantitatively using approximate analytical expressions. The critical excitation amplitudes leading to bistable solutions are identified. For the second-order superharmonic resonance, the critical excitation amplitude is determined to be dependent on the first-harmonic amplitude in the case of nonlinear damping. The third-order superharmonic resonance is determined to be independent of the second-harmonic excitation amplitude regardless of the damping types considered. The perturbation solutions are compared with numerical time-spectral solutions for different flapping amplitudes. The first-order perturbation solution is determined to be in very good agreement with the numerical solution up to 5° while above this amplitude differences in the two solutions develop, which are attributed to phase estimation accuracy.
Starting Page	4281
Ending Page	4307
Page Count	27
File Format	PDF
ISSN	00015970
Journal	Acta Mechanica
Volume Number	226
Issue Number	12
e-ISSN	16196937
Language	English
Publisher	Springer Vienna
Publisher Date	2015-09-08
Publisher Place	Vienna
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Theoretical and Applied Mechanics Classical Continuum Physics Continuum Mechanics and Mechanics of Materials Structural Mechanics Vibration, Dynamical Systems, Control Engineering Thermodynamics, Heat and Mass Transfer
Content Type	Text
Resource Type	Article
Subject	Mechanical Engineering Computational Mechanics

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