Free vibrations of finite periodic structures in pass- and stop-bands of the counterpart infinite waveguides

The existence of frequency stop-bands, in which transmission of the vibro-acoustic energy is impossible, suggests that the periodic structures may be used for vibro-isolation. In any technical application, however, only a finite segment of such a structure can be used. This paper is concerned with c...

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Bibliographic Details
Published inJournal of sound and vibration Vol. 347; pp. 200 - 217
Main Authors Hvatov, Alexander, Sorokin, Sergey
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 07.07.2015
Subjects
Eigenfrequencies
Free vibration
Hierarchies
Mathematical analysis
Mathematical models
Periodic structures
Spectra
Vibration
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Summary:The existence of frequency stop-bands, in which transmission of the vibro-acoustic energy is impossible, suggests that the periodic structures may be used for vibro-isolation. In any technical application, however, only a finite segment of such a structure can be used. This paper is concerned with comparison of the eigenfrequency spectra of finite periodic structures with location of stop-bands for their infinite counterparts. A hierarchy of four mathematical models is considered. In each case, special attention is paid to eigenfrequencies and eigenmodes of a single periodicity cell with appropriate boundary conditions. The influence of the amount of periodicity cells in a finite compound structure on its eigenfrequency spectrum is analyzed. Several features common for the considered models are found and discussed in the context of the existing knowledge on the subject.
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ISSN:0022-460X
1095-8568
DOI:10.1016/j.jsv.2015.03.003