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.

Broadband Seismic Isolation of Periodic Ladder Frame Structure

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Rajan Prasad ◽  
Abhijit Sarkar
Keyword(s):  
Periodic Structure ◽  
Seismic Isolation ◽  
Periodic Structures ◽  
Stop Band ◽  
Design Guidelines ◽  
Unit Cell ◽  
Frame Structure ◽  
Design Parameters ◽  
Pictorial Presentation ◽  
Selection Of

Abstract Ladder frame structures are used as models for multistorey buildings. These periodic structures exhibit alternating propagating and attenuating frequency bands. Of the six different wave modes of propagation, two modes strongly attenuate at all frequencies. The other four modes have nonoverlapping stop band characteristics. Thus, it is challenging to isolate such structures when subjected to broadband, multimodal base excitation. In this study, we seek to synthesize a periodic ladder frame structure that has attenuation characteristics over the maximal range of frequencies for all the modes of wave propagation. We synthesize a unit cell of the periodic structure, which comprises two distinct regions having different inertial, stiffness, and geometric properties. The eigenvalues of the transfer matrix of the unit cell determines the attenuating or the nonattenuating characteristics of the structure. A novel pictorial presentation in the form of eigenvalue map is developed. This is used to synthesize the optimal unit cell. Also, design guidelines for suitable selection of the design parameters are presented. It is shown that a large finite periodic structure comprising a unit cell synthesized using the present approach has significantly better isolation characteristics in comparison to the homogeneous or any other arbitrarily chosen periodic structure.

(Generalized) Bloch mode synthesis for the fast dispersion curve calculation of 3D periodic metamaterials

2021 ◽  
Vol 263 (4) ◽  
pp. 2102-2113
Author(s):  
Vanessa Cool ◽  
Lucas Van Belle ◽  
Claus Claeys ◽  
Elke Deckers ◽  
Wim Desmet
Keyword(s):  
Dispersion Curve ◽  
Periodic Structures ◽  
Cell Model ◽  
Stop Band ◽  
Computational Cost ◽  
Order Reduction ◽  
Element Model ◽  
Unit Cell ◽  
Reduction Techniques ◽  
Bloch Mode

Metamaterials, i.e. artificial structures with unconventional properties, have shown to be highly potential lightweight and compact solutions for the attenuation of noise and vibrations in targeted frequency ranges, called stop bands. In order to analyze the performance of these metamaterials, their stop band behavior is typically predicted by means of dispersion curves, which describe the wave propagation in the corresponding infinite periodic structure. The input for these calculations is usually a finite element model of the corresponding unit cell. Most common in literature are 2D plane metamaterials, which often consist of a plate host structure with periodically added masses or resonators. In recent literature, however, full 3D metamaterials are encountered which are periodic in all three directions and which enable complete, omnidirectional stop bands. Although these 3D metamaterials have favorable vibro-acoustic characteristics, the computational cost to analyze them quickly increases with unit cell model size. Model order reduction techniques are important enablers to overcome this problem. In this work, the Bloch Mode Synthesis (BMS) and generalized BMS (GBMS) reduction techniques are extended from 2D to 3D periodic structures. Through several verifications, it is demonstrated that dispersion curve calculation times can be strongly reduced, while accurate stop band predictions are maintained.

Energy harvesting using an array of multifunctional resonators

2012 ◽  
Vol 24 (2) ◽  
pp. 168-179 ◽  
Author(s):  
Kota Mikoshiba ◽  
James M Manimala ◽  
CT Sun
Keyword(s):  
Energy Harvesting ◽  
Kinetic Energy ◽  
Resonance Frequency ◽  
Band Gap ◽  
Vibration Isolation ◽  
Microelectromechanical Systems ◽  
Stop Band ◽  
Unit Cell ◽  
External Work ◽  
Local Resonance

Energy harvesting from structural vibrations using an array of multifunctional resonators based on the theory of locally resonant materials is demonstrated. Such locally resonant structures exhibit a stop band for elastic wave propagation. The band gap frequency range depends on the local resonance frequency of the microstructure. One method to realize this is through the use of an array of embedded resonators where the external work done is stored as kinetic energy of the internal mass when the forcing frequency is close to the local resonance frequency. This mechanism can be used to harvest energy by converting the kinetic energy into electrical energy, thus bestowing a multifunctional utility to the structure. We use a spring-loaded magnet enclosed in a capped poly(methyl methacrylate) tube equipped with copper coils to create a unit cell that acts both as a resonator and as a linear generator. Experiments on a serial array of seven unit cells exhibit a band gap between 146.5 (local resonance frequency) and 171 Hz with a peak voltage generation of 3.03 V at steady state. The continuous effective power generated by a single unit cell across a 1-Ω load resistor is 36 mW, indicating the feasibility of constructing vibration isolation structures that can power simple electronic and microelectromechanical systems devices. The applicability of using the device as a transducer to measure the local resonance frequency and the global resonance frequency of the structure is also discussed.

Effects of “Finiteness” on Wave Propagation and Vibration in Elastic Periodic Structures

Aerospace ◽  
2004 ◽  
Author(s):  
Mahmoud I. Hussein ◽  
Gregory M. Hulbert ◽  
Richard A. Scott
Keyword(s):  
Frequency Band ◽  
Vibration Isolation ◽  
Wave Attenuation ◽  
Periodic Structures ◽  
Stop Band ◽  
Forced Response ◽  
Band Frequency ◽  
Mode Localization ◽  
Unit Cells ◽  
Frequency Behavior

The dynamics of finite elastic periodically layered structures is compared to that of the constituent periodic media. The focus is on both the frequency behavior and the spatial response. Through simulations of harmonically induced wave motion within a finite number of unit cells, the frequency band structure and attenuation characteristics of infinite and finite periodic systems are shown to conform under certain conditions. It is concluded that only one or two unit cells of a periodic material are required for “frequency bandness” to carry through to a finite structure, and only three to four unit cells are necessary for significant wave attenuation to take place when the structure is excited at a stop-band frequency. Furthermore, vibration analyses are conducted on a bounded fully periodic structure. The natural frequency spread is shown to conform with the frequency band layout of the infinite periodic material, and the steady-state forced response is observed to exhibit mode localization patterns that resemble those of the infinite periodic medium. These results could be used for setting guidelines for the design of periodic structures for vibration isolation and frequency filtering.

scholarly journals Phase-resonance Exploitation in Full-Metal 3D Periodic Structures for Single- and Multi- Wideband Applications

2021 ◽  
Author(s):  
Carlos Molero Jiménez
Keyword(s):  
Periodic Structure ◽  
Periodic Structures ◽  
Circuit Model ◽  
Unit Cell ◽  
Equivalent Circuits ◽  
Cell Architecture ◽  
Complex Unit Cell ◽  
Phase Resonance

This paper presents a versatile full-metal 3D periodic structure based on square waveguides with non-closed resonators perforated on their walls. The complex unit-cell architecture is modelled via accurate equivalent circuits, previously characterized. The circuit model predicts the excitation of phase resonance, which will be used to optimize and design different functionalities, such as polarisation converters or absorption.

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 Phase-resonance Exploitation in Full-Metal 3D Periodic Structures for Single- and Multi- Wideband Applications

2021 ◽  
Author(s):  
Carlos Molero Jiménez
Keyword(s):  
Periodic Structure ◽  
Periodic Structures ◽  
Circuit Model ◽  
Unit Cell ◽  
Equivalent Circuits ◽  
Cell Architecture ◽  
Complex Unit Cell ◽  
Phase Resonance

This paper presents a versatile full-metal 3D periodic structure based on square waveguides with non-closed resonators perforated on their walls. The complex unit-cell architecture is modelled via accurate equivalent circuits, previously characterized. The circuit model predicts the excitation of phase resonance, which will be used to optimize and design different functionalities, such as polarisation converters or absorption.

Wave Finite Element Method Based on Reduced Model for One-Dimensional Periodic Structures

2015 ◽  
Vol 07 (02) ◽  
pp. 1550018 ◽  
Author(s):  
C. W. Zhou ◽  
J. P. Lainé ◽  
M. N. Ichchou ◽  
A. M. Zine
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Periodic Structures ◽  
Numerical Approach ◽  
Unit Cell ◽  
Cell Dynamics ◽  
One Dimensional ◽  
Ill Conditioning ◽  
Selection Of ◽  
Element Method

In this paper, an efficient numerical approach is proposed to study free and forced vibration of complex one-dimensional (1D) periodic structures. The proposed method combines the advantages of component mode synthesis (CMS) and wave finite element method. It exploits the periodicity of the structure since only one unit cell is modelled. The model reduction based on CMS improves the computational efficiency of unit cell dynamics, avoiding ill-conditioning issues. The selection of reduced modal basis can reveal the influence of local dynamics on global behavior. The effectiveness of the proposed approach is illustrated via numerical examples.

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