Analytical and numerical study of the influence of different support types in the nonlinear vibrations of beams

Rincón-Casado, A.; González-Carbajal, Javier; García-Vallejo, Daniel; Domínguez, José Ferreirós

doi:10.1016/j.euromechsol.2020.104113

Cited by 12 publications

(11 citation statements)

References 22 publications

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“…This is why this condition is imposed in Equation (1). On the other hand, θ 0 ∈ R is said to be an equilibrium point of Equation (1) provided that the constant function θ(t) := θ 0 is a solution of Equation (1). It is trivial to check that θ 0 ∈ R is an equilibrium point of Equation (1) if and only if θ 0 is a solution of g(t, θ, 0) − kθ = 0 for all t ∈ [a, b].…”

Section: Methodsmentioning

confidence: 99%

“…This paper originates from and is motivated by a recently published manuscript [1], where the influence of different support types in the nonlinear vibrations of beams is analyzed. During the development of this latter paper, the authors searched for a mathematical proof of the Straightforward Expansion Perturbation Method (SEPM), not reaching any manuscript containing a proper and rigorous definition and proof of the method.…”

Section: Introductionmentioning

confidence: 99%

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Convergence Analysis of the Straightforward Expansion Perturbation Method for Weakly Nonlinear Vibrations

et al. 2021

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There are typically several perturbation methods for approaching the solution of weakly nonlinear vibrations (where the nonlinear terms are “small” compared to the linear ones): the Method of Strained Parameters, the Naive Singular Perturbation Method, the Method of Multiple Scales, the Method of Harmonic Balance and the Method of Averaging. The Straightforward Expansion Perturbation Method (SEPM) applied to weakly nonlinear vibrations does not usually yield to correct solutions. In this manuscript, we provide mathematical proof of the inaccuracy of the SEPM in general cases. Nevertheless, we also provide a sufficient condition for the SEPM to be successfully applied to weakly nonlinear vibrations. This mathematical formalism is written in the syntax of the first-order formal language of Set Theory under the methodology framework provided by the Category Theory.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Convergence Analysis of the Straightforward Expansion Perturbation Method for Weakly Nonlinear Vibrations

et al. 2021

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“…The dynamics of ongoing research in the field of composite materials is reflected in numerous papers [39][40][41][42][43][44][45]. The results published to date repeatedly mention the use of carbon fibers as reinforcement for polymer composites.…”

Section: Heat Aerogelmentioning

confidence: 99%

“…Dynamic behavior has been investigated in the context of nonlinear parametric resonance [39], where the authors investigated the cubic nonlinear response of beams subjected to a spring force in longitudinal direction. The nonlinear vibrations of beams were also analyzed in [40]. The authors discussed the influence of different support types on free nonlinear vibration frequency.…”

Section: Heat Aerogelmentioning

confidence: 99%

Dynamic Behavior of Aviation Polymer Composites at Various Weight Fractions of Physical Modifier

et al. 2021

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The aim of this study was to determine the effect of a selected physical modifier with different granularity and mass percentage on the dynamics of aerospace polymer composites. The tests were carried out on samples made of certified aerospace materials used, among other purposes, for the manufacture of aircraft skin components. The hybrid composites were prepared from L285 resin, H286 hardener, GG 280T carbon fabric in twill 2/2 and alumina (Al2O3, designated as EA in this work). The manufactured composites contained alumina with grain sizes of F220, F240, F280, F320 and F360. The mass proportion of the modifier in the tested samples was 5% and 15%. The tested specimens, as cantilever beams fixed unilaterally, were subjected to kinematic excitation with defined parameters of amplitude and frequency excitation in the basic resonance zone of the structure. The results, obtained as dynamic responses, are presented in the form of amplitude–frequency characteristics. These relationships clearly indicate the variable nature of composite materials due to modifier density and grain size. The novelty of this study is the investigation of the influence of the alumina properties on system dynamics responses.

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“…In our study, we are limited only to beams, which have a very rich dynamic behavior depending on boundary conditions. For instance, numerical Finite Element (FE) simulations on clamped–clamped and hinged–hinged planar beams with homogeneous material properties show a hardening nature, while simply supported boundary conditions cause the softening of the frequency response for the first flexural mode [ 1 ]. This phenomenon has been investigated analytically and numerically in planar beams by means of axial–transversal coupling in nonlinear frequency amplitude response via implementing an additional axial spring [ 2 ], lumped tip mass [ 3 ], and higher-order resonances [ 4 ].…”

Section: Introductionmentioning

confidence: 99%

Influence of Mechanical Couplings on the Dynamical Behavior and Energy Harvesting of a Composite Structure

2020

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In this paper, the dynamical behavior of composite material is analyzed, including the energy harvesting effect. The composite is modeled by the Finite Element Method (FEM) and is made of pre-impregnate with a matrix of thermosetting epoxy resin reinforced with high-strength R-type glass fibers, and it is designed as a beam structure that is exposed to mechanical vibrations. The structure assumed the form of a beam with a substantially rectangular cross section. The couplings of motion occurring between mode shapes at properly selected fiber orientations are investigated. The beams with determined sets of composite layers and a coupling effect are used to recover electricity from the mechanical vibrations in the vicinity of the first resonance zone. The composite with a certain number of fiber glass layers has assumed an orientation relative to the beam axis. The new values found in this paper are the intensity of the coupling between the bending in the stiff and flexible directions of the beam for a chosen fiber layer stacking sequence. Additionally, the influence of layer configuration on the energy harvesting efficiency of the Macro-Fiber Composite (MFC) piezoelectric element is assessed.

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Analytical and numerical study of the influence of different support types in the nonlinear vibrations of beams

Cited by 12 publications

References 22 publications

Convergence Analysis of the Straightforward Expansion Perturbation Method for Weakly Nonlinear Vibrations

Convergence Analysis of the Straightforward Expansion Perturbation Method for Weakly Nonlinear Vibrations

Dynamic Behavior of Aviation Polymer Composites at Various Weight Fractions of Physical Modifier

Influence of Mechanical Couplings on the Dynamical Behavior and Energy Harvesting of a Composite Structure

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