1993
DOI: 10.1007/bf00162232
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Nonlinear response of an initially buckled beam with 1:1 internal resonance to sinusoidal excitation

Abstract: The nonlinear response of an initially buckled beam in the neighborhood of 1 : I internal resonance is investigated analytically, numerically, and experimentally. The method of multiple time scales is applied to derive the equations in amplitudes and phase angles. Within a small range of the internal detuning parameter, the first mode; which is externally excited, is found to transfer energy to the second mode. Outside this region, the response is governed by a unimodal response of the first mode. Stability bo… Show more

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Cited by 50 publications
(18 citation statements)
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“…where a dot denotes differentiation with respect to time t and wi, C, Kij and fi are defined in Afaneh [10]. The signs 4-appearing in equations (17a), (17c) and the natural frequency calculation indicate the nature of the axial P force where the upper sign is used for compression and the lower for a tension force.…”
Section: (T2 -}-W2q2(t) + Kmq~(t)q2(t) -K22ql(t)q2(t)q3(t)mentioning
confidence: 99%
See 1 more Smart Citation
“…where a dot denotes differentiation with respect to time t and wi, C, Kij and fi are defined in Afaneh [10]. The signs 4-appearing in equations (17a), (17c) and the natural frequency calculation indicate the nature of the axial P force where the upper sign is used for compression and the lower for a tension force.…”
Section: (T2 -}-W2q2(t) + Kmq~(t)q2(t) -K22ql(t)q2(t)q3(t)mentioning
confidence: 99%
“…The study uses constrained flexibility [9] and introduces a checking function derived from Gauss' principle of least constraint to monitor formulation error. The reduced multibody dynamics solution is compared to experimental test results [ 10] and time integration of Galerkin's method.…”
Section: Introductionmentioning
confidence: 99%
“…Contrary to veering, modes at crossing are not known to hybridize or transfer energy. In the classical structural dynamics, crossover was primarily explored in cables and curved beams [13,14,[23][24][25][26].…”
Section: Introductionmentioning
confidence: 99%
“…The authors found that the beam exhibits a threeto-one internal resonance resulting in an energy exchange between these modes. Based on an initially buckled beam with clamped ends, Afaneh and Ibrahim found that the first mode transfers energy to the second mode in the presence of the 1 : 1 internal resonance [9]. Chin et al analyzed the response of a buckled beam possessing a two-to-one internal resonance to a principal parametric resonance of the higher mode [10].…”
Section: Introductionmentioning
confidence: 99%