Free and Forced Wave Motion in a Two-Dimensional Plate with Radial Periodicity

In many practical engineering situations, a source of vibrations may excite a large and flexible structure such as a ship’s deck, an aeroplane fuselage, a satellite antenna, a wall panel. To avoid transmission of the vibration and structure-borne sound, radial or polar periodicity may be used. In th...

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Autores principales:	Elisabetta Manconi, Sergey V. Sorokin, Rinaldo Garziera, Matheus Mikael Quartaroli
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	periodic structures polar coordinates wave propagation forced response of plates and shells finite element analysis unbounded structures Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
Acceso en línea:	https://doaj.org/article/584c21a4395b41a8899350b42473e3bd
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spelling	oai:doaj.org-article:584c21a4395b41a8899350b42473e3bd2021-11-25T16:41:42ZFree and Forced Wave Motion in a Two-Dimensional Plate with Radial Periodicity10.3390/app1122109482076-3417https://doaj.org/article/584c21a4395b41a8899350b42473e3bd2021-11-01T00:00:00Zhttps://www.mdpi.com/2076-3417/11/22/10948https://doaj.org/toc/2076-3417In many practical engineering situations, a source of vibrations may excite a large and flexible structure such as a ship’s deck, an aeroplane fuselage, a satellite antenna, a wall panel. To avoid transmission of the vibration and structure-borne sound, radial or polar periodicity may be used. In these cases, numerical approaches to study free and forced wave propagation close to the excitation source in polar coordinates are desirable. This is the paper’s aim, where a numerical method based on Floquet-theory and the FE discretision of a finite slice of the radial periodic structure is presented and verified. Only a small slice of the structure is analysed, which is approximated using piecewise Cartesian segments. Wave characteristics in each segment are obtained by the theory of wave propagation in periodic Cartesian structures and Finite Element analysis, while wave amplitude change due to the changes in the geometry of the slice is accommodated in the model assuming that the energy flow through the segments is the same. Forced response of the structure is then evaluated in the wave domain. Results are verified for an infinite isotropic thin plate excited by a point harmonic force. A plate with a periodic radial change of thickness is then studied. Free waves propagation are shown, and the forced response in the nearfield is evaluated, showing the validity of the method and the computational advantage compared to FE harmonic analysis for infinite structures.Elisabetta ManconiSergey V. SorokinRinaldo GarzieraMatheus Mikael QuartaroliMDPI AGarticleperiodic structurespolar coordinateswave propagationforced response of plates and shellsfinite element analysisunbounded structuresTechnologyTEngineering (General). Civil engineering (General)TA1-2040Biology (General)QH301-705.5PhysicsQC1-999ChemistryQD1-999ENApplied Sciences, Vol 11, Iss 10948, p 10948 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	periodic structures polar coordinates wave propagation forced response of plates and shells finite element analysis unbounded structures Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999
spellingShingle	periodic structures polar coordinates wave propagation forced response of plates and shells finite element analysis unbounded structures Technology T Engineering (General). Civil engineering (General) TA1-2040 Biology (General) QH301-705.5 Physics QC1-999 Chemistry QD1-999 Elisabetta Manconi Sergey V. Sorokin Rinaldo Garziera Matheus Mikael Quartaroli Free and Forced Wave Motion in a Two-Dimensional Plate with Radial Periodicity
description	In many practical engineering situations, a source of vibrations may excite a large and flexible structure such as a ship’s deck, an aeroplane fuselage, a satellite antenna, a wall panel. To avoid transmission of the vibration and structure-borne sound, radial or polar periodicity may be used. In these cases, numerical approaches to study free and forced wave propagation close to the excitation source in polar coordinates are desirable. This is the paper’s aim, where a numerical method based on Floquet-theory and the FE discretision of a finite slice of the radial periodic structure is presented and verified. Only a small slice of the structure is analysed, which is approximated using piecewise Cartesian segments. Wave characteristics in each segment are obtained by the theory of wave propagation in periodic Cartesian structures and Finite Element analysis, while wave amplitude change due to the changes in the geometry of the slice is accommodated in the model assuming that the energy flow through the segments is the same. Forced response of the structure is then evaluated in the wave domain. Results are verified for an infinite isotropic thin plate excited by a point harmonic force. A plate with a periodic radial change of thickness is then studied. Free waves propagation are shown, and the forced response in the nearfield is evaluated, showing the validity of the method and the computational advantage compared to FE harmonic analysis for infinite structures.
format	article
author	Elisabetta Manconi Sergey V. Sorokin Rinaldo Garziera Matheus Mikael Quartaroli
author_facet	Elisabetta Manconi Sergey V. Sorokin Rinaldo Garziera Matheus Mikael Quartaroli
author_sort	Elisabetta Manconi
title	Free and Forced Wave Motion in a Two-Dimensional Plate with Radial Periodicity
title_short	Free and Forced Wave Motion in a Two-Dimensional Plate with Radial Periodicity
title_full	Free and Forced Wave Motion in a Two-Dimensional Plate with Radial Periodicity
title_fullStr	Free and Forced Wave Motion in a Two-Dimensional Plate with Radial Periodicity
title_full_unstemmed	Free and Forced Wave Motion in a Two-Dimensional Plate with Radial Periodicity
title_sort	free and forced wave motion in a two-dimensional plate with radial periodicity
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/584c21a4395b41a8899350b42473e3bd
work_keys_str_mv	AT elisabettamanconi freeandforcedwavemotioninatwodimensionalplatewithradialperiodicity AT sergeyvsorokin freeandforcedwavemotioninatwodimensionalplatewithradialperiodicity AT rinaldogarziera freeandforcedwavemotioninatwodimensionalplatewithradialperiodicity AT matheusmikaelquartaroli freeandforcedwavemotioninatwodimensionalplatewithradialperiodicity
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Free and Forced Wave Motion in a Two-Dimensional Plate with Radial Periodicity

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