Natural Frequencies and Band Gaps of Periodically Corrugated Beams

2020 ◽  
Vol 143 (4) ◽  
Author(s):  
Rhamy Salim Bachour ◽  
Rodrigo Nicoletti
Keyword(s):  
Natural Frequencies ◽  
Periodic Structures ◽  
Dynamic Properties ◽  
Band Gaps ◽  
Transverse Waves ◽  
Large Bandwidth ◽  
Straight Beam ◽  
Propagating Waves ◽  
Corrugated Beam ◽  
Straight Segments

Abstract Structures with geometric periodicity can present interesting dynamic properties like stop and pass frequency bands. In this case, the geometric periodicity has the effect of filtering the propagating waves in the structure, in a similar way to that of phononic crystals and metamaterials (non-homogeneous materials). Hence, by adopting such structures, we can design systems that present dynamic characteristics of interest, e.g., with minimum dynamic response in a given frequency range with large bandwidth. In the present work, we show that corrugated beams also present the dynamic properties of periodic structures due to their periodic geometry only (no need of changing mass or material properties along the beam). Two types of corrugated beams are studied analytically: beams with curved bumps of constant radii and beams with bumps composed of straight segments. The results show that, as we change the proportions of the bump, the natural frequencies change and tend to form large band gaps in the frequency spectrum of the beam. Such shifting of the natural frequencies is related to the coupling between longitudinal and transverse waves in the curved beam. The results also show that it is possible to predict the position and the limits of the first band gap (at least) as a function of the fundamental frequency of the straight beam (without bumps), irrespective of the total length of the corrugated beam.

Vibrations of an Intermediately Supported U-Bend Tube

1975 ◽  
Vol 97 (1) ◽  
pp. 23-32 ◽  
Author(s):  
L. S. S. Lee
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Experimental Tests ◽  
Bending Stiffness ◽  
Stiffness Ratio ◽  
Plane Vibration ◽  
Straight Beam ◽  
Out Of Plane ◽  
Straight Segments ◽  
Good Agreement

Vibrations of an intermediately supported U-bend tube fall into two independent classes as an incomplete ring of single span does, namely, the in-plane vibration and the coupled twist-bending out-of-plane vibration. Natural frequencies may be expressed in terms of a coefficient p which depends on the stiffness ratio k, the ratio of lengths of spans, and the supporting conditions. The effect of the torsional flexibility of a curved bar acts to release the bending stiffness of a straight beam and hence decrease the natural frequency. Some conclusions for an incomplete ring of single span may not be equally well applicable to the U-tube case due to the effects of intermediate supports and the presence of the supporting straight segments. Results of the analytical predictions and the experimental tests of an intermediately supported U-tube are in good agreement.

MODIFICATION OF CASIMIR FORCES DUE TO BAND GAPS IN PERIODIC STRUCTURES

2002 ◽  
Vol 17 (06n07) ◽  
pp. 798-803 ◽  
Author(s):  
C. VILLARREAL ◽  
R. ESQUIVEL-SIRVENT ◽  
G. H. COCOLETZI
Keyword(s):  
Density Of States ◽  
Casimir Force ◽  
Periodic Structures ◽  
Local Density ◽  
Band Gaps ◽  
Basic Unit ◽  
Local Density Of States ◽  
Casimir Forces ◽  
Unit Cells ◽  
The Difference

The Casimir force between inhomogeneous slabs that exhibit a band-like structure is calculated. The slabs are made of basic unit cells each made of two layers of different materials. As the number of unit cells increases the Casimir force between the slabs changes, since the reflectivity develops a band-like structure characterized by frequency regions of high reflectivity. This is also evident in the difference of the local density of states between free and boundary distorted vacuum, that becomes maximum at frequencies corresponding to the band gaps. The calculations are restricted to vacuum modes with wave vectors perpendicular to the slabs.

Locally resonant periodic structures with low-frequency band gaps

2013 ◽  
Vol 114 (3) ◽  
pp. 033532 ◽  
Author(s):  
Zhibao Cheng ◽  
Zhifei Shi ◽  
Y. L. Mo ◽  
Hongjun Xiang
Keyword(s):  
Frequency Band ◽  
Periodic Structures ◽  
Low Frequency ◽  
Band Gaps

Periodic Materials-Based 3D Seismic Base Isolators for Nuclear Power Plants

2014 ◽  
Author(s):  
Y. Yan ◽  
A. Laskar ◽  
Z. Cheng ◽  
F. Menq ◽  
Y. Tang ◽  
...  
Keyword(s):  
Earthquake Engineering ◽  
Structural Damage ◽  
Nuclear Power ◽  
Power Plants ◽  
Seismic Waves ◽  
Natural Frequencies ◽  
Field Tests ◽  
Band Gaps ◽  
Solid State Physics ◽  
Periodic Materials

The concept of periodic materials, based on solid state physics theory, is applied to earthquake engineering. The periodic material is a material which possesses distinct characteristics that do not allow waves with certain frequencies to be transmitted through; therefore, this material can be used in structural foundations to block unwanted seismic waves with certain frequencies. The frequency band of periodic material that can filter out waves is called the band gap, and the structural foundation made of periodic material is referred to as the periodic foundation. In designing a periodic foundation, the first step is to match band gaps of the periodic foundation with the natural frequencies of the superstructure. This is an iterative process. Starting with a design of the periodic foundation, the band gaps are identified by performing finite element analyses using ABAQUS. This design process is repeated until the band gaps match natural frequencies of the superstructure, and the field tests of a scaled specimen are conducted to validate the design. This is an on-going research project. Presented in this paper are the preliminary results, which show that the three dimensional periodic foundation is a promising and effective way to mitigate structural damage caused by earthquake excitations.

scholarly journals Influence of the flexibility of beams and slabs in static response and dynamic properties

2016 ◽  
Vol 9 (6) ◽  
pp. 842-855 ◽  
Author(s):  
J. R. BUENO ◽  
◽  
D. D. LORIGGIO ◽  
Keyword(s):  
Finite Element Method ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Vibration Modes ◽  
Linear Regime ◽  
Static Response ◽  
The Finite Element Method ◽  
Standard Code ◽  
The Relationship ◽  
Brazilian Standard

Abstract This article examines numerically the flexibility influence of support beams in static response and dynamic properties of a symmetric plate formed by massive slabs of reinforced concrete in elastic linear regime, using the Finite Element Method. In the static response the variation of bending mo-ments and displacements are evaluated, which depend on the relationship between the flexibility of the slab and the beam. The evaluation of dynamic properties is held in undamped free vibration, through which the vibration modes and the values of the natural frequencies is obtained, which are compared with the limits of the Brazilian standard code for design of concrete structures. Results show that the response may show great variation due to the change in the relationship between bending stiffness of the slabs and the beams.

scholarly journals Phononic Band Gaps of Elastic Periodic Structures: A Homogenization Theory Study

2007 ◽  
Author(s):  
Ying-Hong Liu ◽  
Chien C. Chang ◽  
Ruey-Lin Chern ◽  
C. Chung Chang
Keyword(s):  
Elastic Constants ◽  
Periodic Structures ◽  
Mass Density ◽  
Density Ratio ◽  
Low Frequency ◽  
Phononic Crystals ◽  
Band Gaps ◽  
Homogenization Theory ◽  
Dominant Factor ◽  
Phononic Band Gaps

In this study, we investigate band structures of phononic crystals with particular emphasis on the effects of the mass density ratio and of the contrast of elastic constants. The phononic crystals consist of arrays of different media embedded in a rubber or epoxy. It is shown that the density ratio rather than the contrast of elastic constants is the dominant factor that opens up phononic band gaps. The physical background of this observation is explained by applying the theory of homogenization to investigate the group velocities of the low-frequency bands at the center of symmetry Γ.

Spatial Modulation of Repeated Vibration Modes in Rotationally Periodic Structures

1997 ◽  
Author(s):  
Mintae Kim ◽  
Joonho Moon ◽  
Jonathan A. Wickert
Keyword(s):  
Mode Shape ◽  
Natural Frequencies ◽  
Periodic Structures ◽  
Spatial Modulation ◽  
Vibration Modes ◽  
Algebraic Relation ◽  
Natural Frequencies And Modes ◽  
Axisymmetric Structure ◽  
Technical Interest ◽  
Model Features

Abstract When a structure deviates from axisymmetry because of circumferentially varying model features, significant changes can occur to its natural frequencies and modes, particularly for the doublet modes that have non-zero nodal diameters and repeated natural frequencies in the limit of axisymmetry. Of technical interest are configurations in which inertia, dissipation, stiffness, or domain features are evenly distributed around the structure. Aside from the well-studied phenomenon of eigenvalue splitting, whereby the natural frequencies of certain doublets split into distinct values, modes of the axisymmetric structure that are precisely harmonic become contaminated by certain additional wavenumbers in the presence of periodically spaced model features. From analytical, numerical, and experimental perspectives, this paper investigates spatial modulation of the doublet modes, particularly those retaining repeated natural frequencies for which modulation is most acute. In some cases, modulation can be sufficiently severe that a mode shape will beat spatially as harmonics with commensurate wavenumbers combine, just as the superposition of time records having nearly equal frequencies leads to classic temporal beating. A straightforward algebraic relation and a graphical checkerboard diagram are discussed with a view towards predicting the wavenumbers present in modulated eigenfunctions given the number of nodal diameters in the base mode and the number of equally spaced model features.

Elastic wave propagation in metamaterial rods with periodic shunted piezo-patches

2021 ◽  
Vol 263 (2) ◽  
pp. 4303-4311
Author(s):  
Edson J.P. de Miranda ◽  
Edilson D. Nobrega ◽  
Leopoldo P.R. de Oliveira ◽  
José M.C. Dos Santos
Keyword(s):  
Wave Propagation ◽  
Elastic Wave ◽  
Wave Attenuation ◽  
Periodic Structures ◽  
Band Gaps ◽  
Low Frequencies ◽  
Periodic Arrays ◽  
Extended Plane ◽  
Elastic Metamaterials ◽  
Piezoelectric Structures

The wave propagation attenuation in low frequencies by using piezoelectric elastic metamaterials has been developed in recent years. These piezoelectric structures exhibit abnormal properties, different from those found in nature, through the artificial design of the topology or exploring the shunt circuit parameters. In this study, the wave propagation in a 1-D elastic metamaterial rod with periodic arrays of shunted piezo-patches is investigated. This piezoelectric metamaterial rod is capable of filtering the propagation of longitudinal elastic waves over a specified range of frequency, called band gaps. The complex dispersion diagrams are obtained by the extended plane wave expansion (EPWE) and wave finite element (WFE) approaches. The comparison between these methods shows good agreement. The Bragg-type and locally resonant band gaps are opened up. The shunt circuits influence significantly the propagating and the evanescent modes. The results can be used for elastic wave attenuation using piezoelectric periodic structures.

Detection of Damage Extension in Cantilever Beams Using Change Ratio of Frequency Response Functions

2011 ◽  
Vol 50-51 ◽  
pp. 875-879
Author(s):  
Hai Lei Jia ◽  
Yin Zhao
Keyword(s):  
Frequency Response ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Damage Index ◽  
High Sensitivity ◽  
Cantilever Beams ◽  
Response Functions ◽  
Full Spectrum ◽  
Structural Dynamic ◽  
Low Dimensional

Frequency response function (FRF) is a fundamental dynamic index, which is capable of reflecting structural dynamic properties using full-spectrum information. In spite of distinct merits over conventional modal parameters, the FRF has an observable drawback of multi-dimensionality, unsuited for damage characterization. Such a situation motivates an interesting subject, i.e., extracting low-dimensional, high-sensitivity damage index from the FRF. This study focuses on developing a valid damage index, called FRF change ratio, to detect extension of damage. An experiment towards cantilever beams is systemically conducted. The results show that the FRF change ratio can effectively reflects damage extension, and it is more sensitive than conventional natural frequencies. This new damage index holds promise for practical damage detection in beam-like structures.

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