On natural frequencies of non-uniform beams modulated by finite periodic cells

Xu, Yiwei; Zhou, Xiaoling; Wang, Wei; Wang, Longqi; Peng, Fujun; Li, Bin

doi:10.1016/j.physleta.2016.07.057

Cited by 22 publications

(10 citation statements)

References 19 publications

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“…Most of the time, the involved geometrical and material designs of these taylored system are quite complex and make uneasy to establish some general links between the band gap features and the unit cell design parameters. By the way, some numerical parametric variations as in [5] illustrate possible tendencies.…”

Section: Introductionmentioning

confidence: 99%

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On the control of the first Bragg band gap in periodic continuously corrugated beam for flexural vibration

Pelat

Gallot

Gautier

2019

Journal of Sound and Vibration

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This work aims to provide better physical understanding of Bragg band gap effects in continuously periodic corrugated beams for flexural waves. The main outcome is the establishement of original algebraic formulas for the band gap width and central frequency. It is shown that the band gap width and central frequency only depend on a thickness contrast parameter. To do so, a so called two-skins geometry is proposed to approximate the usual solid beam cross section, in order to greatly simplify analytical derivations following the Plane Wave Expansion (PWE) method applied to Euler-Bernoulli theory. Theoretical predictions in the two-skins geometry successfully match the results in the practical case of a solid geometry obtained from both experiments on a beam demonstrator and numerical simulations done by classical PWE (1D Euler and Timoshenko theories) or finite element (3D elasticity theory) methods. The complete set of results is benchmarked in details so that the geometrical approximation is validated and the algebraic formulas are usable as design tools of such notch filters. Moreover, flexural and longitudinal motion coupling due to the non-symetrical thickness profile of the demonstrators leads to an additional band gap that is experimentally identified. A numerical study illustrates the resulting double filtering effect. Potential applications of the background provided by this work can concern Noise,Vibration and Harshness (NVH) engineering, for which meta-materials can be very relevant especially when structure lightening is required.

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Section: Introductionmentioning

confidence: 99%

“…This leads to many open questions for which the literature is very extensive. Among many others, some of the recent works typically focus on the optimization of periodic Euler-Bernoulli beams from Transfer Matrix Method [5], Plane Wave Expansion Method [6], Waveguide Finite Element method [7] or varying amplitudes method [8].…”

Section: Introductionmentioning

confidence: 99%

On the control of the first Bragg band gap in periodic continuously corrugated beam for flexural vibration

Pelat

Gallot

Gautier

2019

Journal of Sound and Vibration

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“…A comprehensive research on inhomogeneous beams vibrations was presented by Hajianmaleki and Qatu (2013). The transfer matrix method, adapted in analysis of flexural wave propagation in a beam on an elastic foundation and in investigating natural frequencies of non-uniform beams, can be found in Yu et al (2012) and Xu et al (2016), respectively. Wave propagation in beams with periodically varying stiffness is considered in Chen (2013) by the use of the multireflection method.…”

Section: Prefacementioning

confidence: 99%

Free vibrations spectrum of periodically inhomogeneous Rayleigh beams using the tolerance averaging technique

Świątek

Domagalski

Jędrysiak

2019

Journal of Theoretical and Applied Mechanics

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In this paper, linear-elastic Rayleigh beams with a periodic structure are considered. Dynamics of such beams is described by partial differential equations with non-continuous highly oscillating coefficients. The analysis of dynamic problems using the aforementioned equations is very often problematic to perform. Thus, other simplified models of Rayleigh beams are proposed. Some of these models are based on the concept of the effective stiffness. Among them, one can distinguish the theory of asymptotic homogenization. However, in these models, the size of the mesostructure parameter (the size of a periodicity cell) is often neglected. Therefore, a non-asymptotic averaged model of the periodic beam is introduced, called the tolerance model, which is derived by applying the tolerance averaging technique (TA). The obtained tolerance model equations have constant coefficients, and in contrast to other averaged models, some of them depend on the size of the periodicity cell.

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“…In [63] the flexural vibration band gaps in periodic beams is investigated using differential quadrature method, moreover the influence of shear deformation on the gaps is analyzed. Similarly, natural frequencies of structures made of period cells was presented for beams in [64,65] and for plates in [66,67]. In [68] the aim is the problem of vibration of band gaps in periodic Mindlin plates and it is solved using spectral element method.…”

Section: Introductionmentioning

confidence: 99%

Critical Temperatures for Vibrations and Buckling of Magneto-Electro-Elastic Nonlocal Strain Gradient Plates

2021

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An analytical method is presented in this work for the linear vibrations and buckling of nano-plates in a hygro-thermal environment. Nonlinear von Kármán terms are included in the plate kinematics in order to consider the instability phenomena. Strain gradient nonlocal theory is considered for its simplicity and applicability with respect to other nonlocal formulations which require more parameters in their analysis. Present nano-plates have a coupled magneto-electro-elastic constitutive equation in a hygro-thermal environment. Nano-scale effects on the vibrations and buckling behavior of magneto-electro-elastic plates is presented and hygro-thermal load outcomes are considered as well. In addition, critical temperatures for vibrations and buckling problems are analyzed and given for several nano-plate configurations.

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On natural frequencies of non-uniform beams modulated by finite periodic cells

Cited by 22 publications

References 19 publications

On the control of the first Bragg band gap in periodic continuously corrugated beam for flexural vibration

On the control of the first Bragg band gap in periodic continuously corrugated beam for flexural vibration

Free vibrations spectrum of periodically inhomogeneous Rayleigh beams using the tolerance averaging technique

Critical Temperatures for Vibrations and Buckling of Magneto-Electro-Elastic Nonlocal Strain Gradient Plates

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