On application of the Floquet theory for radially periodic membranes and plates

Hvatov, Alexander; Sorokin, Sergey

doi:10.1016/j.jsv.2017.11.003

Cited by 15 publications

(18 citation statements)

References 17 publications

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“…Since the energy flow evaluation is computationally expensive it is required to build the approximation that allows one to assess attenuation zones without computing insertion losses. One of the approximations are the eigenfrequencies of single periodicity cells [6][7]. The process of eigenfrequency obtaining is described below.…”

Section: =+mentioning

confidence: 99%

“…Together with interfacial conditions, they are forming A-type symmetrical boundary problem and B-type symmetrical boundary problem. It is shown in [6][7] that the symmetrical A and B type problems are covering all Floquet stop-band boundaries in the linear case.…”

Section: The Eigenfrequency Analysismentioning

confidence: 99%

“…It can be proved directly when one is considering the linear case ( 0 N = or 0  = ). In general case it is not proved, however, this fact is also valid for the radial periodic membrane case[7]. Dependencies 0 = could be plotted as shown inFig.8.…”

mentioning

confidence: 92%

“…From the other hand, one can use the eigenfrequency of a symmetrical periodicity cell approach as described in [6][7], which has no restrictions on a structure type. In [7] it is used for radially periodic structure, which also does not have the translational symmetry property. Therefore, it can be used for Floquet theory predictions quality assessment.…”

Section: Introductionmentioning

confidence: 99%

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Floquet Theory Analysis of a Weakly Non-Linear Periodic Structure

Hvatov¹,

Sorokin²

2019

Proceedings of the 7th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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In the paper, the question of applicability of Floquet theory in a weakly non-linear structure is considered. Usually, references contain numerical approaches for the simple non-linear spring masses case. Nevertheless, there is no readily available analytical solution for that problem. Moreover, the theory expansion to a continuous to a non-linear case is still questionable. In the paper, the structure consisting of a waveguide connected with a non-linear spring is considered. One can use the eigenfrequency of a symmetrical periodicity cell approach, which has no restrictions on a periodic structure form. Two approaches for the stop-band predictions in the infinite periodic weakly nonlinear structure on a simple example of rods connected with the non-linear spring are considered. The approaches considered in the paper such as force balance and symmetrical cell eigenfrequencies could be used for more complicated structures.

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Section: =+mentioning

confidence: 99%

Section: The Eigenfrequency Analysismentioning

confidence: 99%

mentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

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Floquet Theory Analysis of a Weakly Non-Linear Periodic Structure

Hvatov¹,

Sorokin²

2019

Proceedings of the 7th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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“…This paper deals with structures that exhibit periodicity in the circumferential and radial directions, whose cylindrical wave propagation is estimated using the Floquet theory formulation for an infinite periodic structure in one dimension. Approximation of the Floquet theory for radially periodic structures has been recently presented in [11]. Compared to this work, the approximation is here achieved in terms of the FE discretisation of a period of the structures to which the theory of wave propagation in periodic structures is applied according to the formulation of the WFE method.…”

Section: Introductionmentioning

confidence: 99%

Wave Propagation in Polar Periodic Structures Using Floquet Theory and Finite Element Analysis

Manconi¹,

Sorokin²,

Garziera³

2019

Proceedings of the 7th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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In this paper, a generalised approximated approach to study wave propagation in structures that exhibit radial and/or circumferential periodicity is presented. Only a circular sector of the structure is studied, which could be a circumferential period or an arbitrary slice according to the kind of periodicity of the structure (radial, circumferential, both radial and circumferential). The slice is then approximated using piecewise Cartesian waveguides, whose wave characteristics are obtained by the theory of wave propagation in periodic Cartesian structures and Finite Element analysis. Wave amplitudes change due to the changes in the geometry of the slice are accommodated in the model assuming that the energy flow through the interfaces of each Cartesian waveguide is the same. Results are validated considering the response of an infinite isotropic thin plate excited by a point harmonic force, showing the accuracy of the method and the computational advantage compared to a standard FE harmonic analysis for infinite structures. A numerical example of a polar periodic structure, mimicking a spider web, is also presented to investigate the potential applications of the method.

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On Unified Formulation of Floquet Propagator in Cartesian and Polar Coordinates

Hvatov

Sorokin²

2022

Mechanisms and Machine Science

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On application of the Floquet theory for radially periodic membranes and plates

Cited by 15 publications

References 17 publications

Floquet Theory Analysis of a Weakly Non-Linear Periodic Structure

Floquet Theory Analysis of a Weakly Non-Linear Periodic Structure

Wave Propagation in Polar Periodic Structures Using Floquet Theory and Finite Element Analysis

On Unified Formulation of Floquet Propagator in Cartesian and Polar Coordinates

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