Vibration isolation from irregularity in a nearly periodic structure: Theory and measurements

1983 ◽  
Vol 74 (3) ◽  
pp. 894-905 ◽  
Author(s):  
C. H. Hodges ◽  
J. Woodhouse
Keyword(s):  
Periodic Structure ◽  
Vibration Isolation ◽  
Structure Theory

Broadband Vibration Isolation for Rods and Beams Using Periodic Structure Theory

2018 ◽  
Vol 86 (2) ◽  
Author(s):  
Rajan Prasad ◽  
Abhijit Sarkar
Keyword(s):  
Periodic Structure ◽  
Vibration Isolation ◽  
Periodic Structures ◽  
Stop Band ◽  
Extreme Case ◽  
Unit Cell ◽  
Structure Theory ◽  
Seismic Excitations ◽  
Stiffness Properties ◽  
Selection Of

The alternating stop-band characteristics of periodic structures have been widely used for narrow band vibration control applications. The objective of this work is to extend this idea for broadband excitations. Toward this end, we seek to synthesize a longitudinal and a flexural periodic structure having the largest fraction of the frequencies falling in the attenuation bands of the structure. Such a periodic structure when subjected to broadband excitation has minimal transmission of the response away from the source of excitation. The unit cell of such a periodic structure is constituted of two distinct regions having different inertial and stiffness properties. We derive guidelines for suitable selection of inertial and stiffness properties of the two regions in the unit cell such that the maximal frequency region corresponds to attenuation bands of the periodic structure. It is found that maximal dissimilarity between the neighboring regions of the unit cell leads to maximal attenuating frequencies. In the extreme case, it is found that more than 98% of the frequencies are blocked. For seismic excitations, it is shown that large, finite periodic structures corresponding to the optimal unit cell derived using the infinite periodic structure theory has significant vibration isolation benefits in comparison to a homogeneous structure or an arbitrarily chosen periodic structure.

scholarly journals Numerical Study on Propagative Waves in a Periodically Supported Rail Using Periodic Structure Theory

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Xi Sheng ◽  
Huike Zeng ◽  
Sara Ying Zhang ◽  
Ping Wang
Keyword(s):  
Periodic Structure ◽  
Numerical Study ◽  
Stop Band ◽  
Standing Waves ◽  
Dispersion Curves ◽  
Structure Theory ◽  
Cross Sectional ◽  
Quarter Wavelength ◽  
Calculation Results ◽  
Wave Modes

This paper presents the numerical study on propagative waves in a periodically supported rail below 6000 Hz. A periodic rail model, which considers the effects of both the periodic supports and the rail cross section deformation, has been established based on the periodic structure theory and the finite element method. Two selection approaches are proposed to obtain the concerned dispersion curves from the original calculation results of dispersion relations. The differences between the dispersion curves of different support conditions are studied. The propagative waves corresponding to the dispersion curves are identified by the wave modes. The influences of periodic supports on wave modes in pass bands are revealed. Further, the stop band behaviors are investigated in terms of the bounding frequencies, the standing wave characteristics, and the cross-sectional modes. The results show that eight propagative waves with distinct modes exist in a periodically supported rail below 6000 Hz. The differences between the dispersion curves of periodically and continuously supported rails are not obvious, apart from the stop band behaviors. All the bounding-frequency modes of the stop bands are associated with the standing waves. Two bounding-frequency modes of the same stop band can be regarded as two identical standing waves with the longitudinal translation of the quarter-wavelength, one of which is the so-called pinned-pinned resonance.

scholarly journals Implications of Nonsub-Wavelength Resonator Spacing on the Sound Transmission Loss Predictions of Locally Resonant Metamaterial Partitions

2020 ◽  
Vol 143 (4) ◽  
Author(s):  
Lucas Van Belle ◽  
Claus Claeys ◽  
Elke Deckers ◽  
Wim Desmet
Keyword(s):  
Periodic Structure ◽  
Transmission Loss ◽  
Sound Transmission ◽  
Structure Theory ◽  
Structure Modeling ◽  
Sound Transmission Loss ◽  
Control Engineering ◽  
Resonant Structures ◽  
Wavelength Scale ◽  
Sub Wavelength

Abstract Locally resonant metamaterials have recently emerged and gained attention in the field of noise control engineering. The addition of resonant structures to a flexible partition on a sub-wavelength scale enables a targeted frequency range of strongly reduced vibration and sound transmission. These structures have been widely studied and are typically analyzed using infinite periodic structure theory. The implications of nonsub-wavelength resonator spacing on the sound transmission loss of metamaterial partitions as well as on the representativeness of the infinite periodic structure modeling are, however, less well known. In this technical brief, it is shown that, although a shifted sound transmission loss peak can be predicted for partitions with nonsub-wavelength resonator spacing when using infinite periodic structure modeling, the sound transmission loss enhancement is not guaranteed for their finite structure counterparts.

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