On geometrically nonlinear mechanics of nanocomposite beams

Vaccaro, Marzia Sara

doi:10.1016/j.ijengsci.2022.103653

Cited by 21 publications

(7 citation statements)

References 71 publications

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“…First, we obtain numerically minimum values of f 0 for locking instability under different values of the system parameters ω and α (see the red "×" in Figure 10). As mentioned in Section 3, locking instability can be depicted by fractal erosion of safe basin of system (2).…”

Section: Numerical Examplesmentioning

confidence: 98%

“…According to the theoretical results and numerical ones in Figures 3 and 6, it is clear that when ω � 1, 0.1 ≤ α ≤ 0.28, and 0.24 ≤ f 0 ≤ 0.5, system (2) will undergo a unique periodic motion or locking. It means that the safe basin in Figure 11 is the basin of attraction of the only periodic attractor of system (2). In Figures 11 and 12, as the parameter f 0 increases, the safe basin will become fractal, and its area will be reduced, implying that locking instability becomes more and more obvious.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…e pitchfork bifurcation along α is shown in Figure 2. In order to address more abundant dynamical behaviors of system (2), in what follows, we suppose 0 < α < 1.…”

Section: Dynamical Modelmentioning

confidence: 99%

“…where f cri 0 is the threshold for heteroclinic bifurcation of system (2). e variation of the threshold f cri 0 with the parameter α under ω � 1 is shown in Figure 10(…”

Section: Necessary Conditions For Heteroclinic Bifurcationmentioning

confidence: 99%

“…ere are also some oscillators whose nonlinearities are irrational terms due to the changes in their geometric con guration [1,2]. Such oscillatory systems have received increasing attentions for being commonly used in the design and applications of machinery such as energy harvesters, turbine structures, and industrial robots [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

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Initial-Sensitive Dynamical Behaviors of a Class of Geometrically Nonlinear Oscillators

Qin

Shang

Huimin

2022

Shock and Vibration

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The vibrating system of a class of linkage-slider structure is considered, and its initial-sensitive dynamical behaviors such as safe jump, locking instability, and chaos are studied. First, static bifurcation of the dynamical system is discussed. Then, via analyzing the effect of the external excitation on the periodic solutions under primary resonance, it is found that the change of the excitation frequency may lead to bistability and safe jump. Furthermore, it follows from the investigation of the heteroclinic bifurcation that the increase of the external excitation amplitude may lead to locking instability, chaos, and static locking. The results have some potential values in the design of geometrically nonlinear oscillators.

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Section: Numerical Examplesmentioning

confidence: 98%

Section: Numerical Examplesmentioning

confidence: 99%

“…e pitchfork bifurcation along α is shown in Figure 2. In order to address more abundant dynamical behaviors of system (2), in what follows, we suppose 0 < α < 1.…”

Section: Dynamical Modelmentioning

confidence: 99%

“…where f cri 0 is the threshold for heteroclinic bifurcation of system (2). e variation of the threshold f cri 0 with the parameter α under ω � 1 is shown in Figure 10(…”

Section: Necessary Conditions For Heteroclinic Bifurcationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Initial-Sensitive Dynamical Behaviors of a Class of Geometrically Nonlinear Oscillators

Qin

Shang

Huimin

2022

Shock and Vibration

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Newton vs. Euler–Lagrange approach, or how and when beam equations are variational

Babilio,

Lenci

2024

Meccanica

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There is a clear and compelling need to correctly write the equations of motion of structures in order to adequately describe their dynamics. Two routes, indeed very different from a philosophical standpoint, can be used in classical mechanics to derive such equations, namely the Newton vectorial approach (i.e., roughly, sum of forces equal to mass times acceleration) or the Euler–Lagrange variational formulation (i.e., roughly, stationarity of a certain functional). However, it is desirable that whichever derivation strategy is chosen, the equations are the same. Since many structures of interest often consist of slender and highly flexible beams operating in regimes of large displacement and large rotation, we restrict our attention to the Euler-Bernoulli assumptions with a generic initial configuration. In this setting, the question that arises is: What conditions must the constitutive assumptions satisfy in order for the equations of motion obtained by Newton’s approach to be identical to the Euler–Lagrange equations derived from an appropriate Lagrangian, natural or virtual, for any arbitrary initial configuration? The aim of this paper is to try to answer this basic question, which indeed does not have an immediate and simple answer, in particular as a consequence of the fact that bending moment could be related to two different notions of flexural curvature.

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Hygro-thermal vibration study of nanobeams on size-dependent visco-Pasternak foundation via stress-driven nonlocal theory in conjunction with two-variable shear deformation assumption

Zhang¹,

Schiavone²,

Qing³

2023

Composite Structures

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On geometrically nonlinear mechanics of nanocomposite beams

Cited by 21 publications

References 71 publications

Initial-Sensitive Dynamical Behaviors of a Class of Geometrically Nonlinear Oscillators

Initial-Sensitive Dynamical Behaviors of a Class of Geometrically Nonlinear Oscillators

Newton vs. Euler–Lagrange approach, or how and when beam equations are variational

Hygro-thermal vibration study of nanobeams on size-dependent visco-Pasternak foundation via stress-driven nonlocal theory in conjunction with two-variable shear deformation assumption

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