A METHOD OF ANALYZING FINITE PERIODIC STRUCTURES, PART 2: COMPARISON WITH INFINITE PERIODIC STRUCTURE THEORY

1997 ◽  
Vol 202 (4) ◽  
pp. 571-583 ◽  
Author(s):  
J. Wei ◽  
M. Petyt
Keyword(s):  
Periodic Structure ◽  
Periodic Structures ◽  
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.

Excitation of Rotationally Periodic Structures

1979 ◽  
Vol 46 (4) ◽  
pp. 878-882 ◽  
Author(s):  
S. J. Wildheim
Keyword(s):  
Periodic Structure ◽  
Periodic Structures ◽  
Resonance Condition ◽  
Forced Response ◽  
Closed Ring ◽  
Additional Resonance ◽  
Rotationally Symmetric ◽  
Deformation Patterns ◽  
Frequency Diagram ◽  
Rotationally Periodic Structure

A rotationally periodic structure consists of a finite number of identical substructures forming a closed ring. The vibrational behavior of such structures is considered, especially the forced response due to a rotating force. It is known that for a rotationally symmetric structure, excited by a rotating force, resonance for the n nodal diameters mode is obtained when the corresponding natural frequency is ωn = nΩ, where Ω is the angular velocity of the force. This resonance condition also holds for a rotationally periodic structure. But then additional resonance possibilities exist, given by ωn = (kN ± n)Ω, where N is the number of substructures and k = 0, 1, 2,… These resonance conditions give a zigzag line in the nodal diameters versus frequency diagram, which here is introduced as the ZZENF diagram. The deformation patterns at the resonances are both forward and backward traveling waves.

Parametric Study on Rectangular Sonic Crystal

2012 ◽  
Vol 152-154 ◽  
pp. 281-286 ◽  
Author(s):  
Arpan Gupta ◽  
Kian Meng Lim ◽  
Chye Heng Chew
Keyword(s):  
Band Gap ◽  
Periodic Structure ◽  
Parametric Study ◽  
Sound Propagation ◽  
Periodic Structures ◽  
Sound Attenuation ◽  
Experimental Results ◽  
Center Frequency ◽  
Sonic Crystal ◽  
Sonic Crystals

Sonic crystals are periodic structures made of sound hard scatterers which attenuate sound in a range of frequencies. For an infinite periodic structure, this range of frequencies is known as band gap, and is determined by the geometric arrangement of the scatterers. In this paper, a parametric study on rectangular sonic crystal is presented. It is found that geometric spacing between the scatterers in the direction of sound propagation affects the center frequency of the band gap. Reducing the geometric spacing between the scatterers in the direction perpendicular to the sound propagation helps in better sound attenuation. Such rectangular arrangement of scatterers gives better sound attenuation than the regular square arrangement of scatterers. The model for parametric study is also supported by some experimental results.

Optimization of Axial Vibration Attenuation of Periodic Structure With Nonlinear Stiffness Without Addition of Mass

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Diego P. Vasconcellos ◽  
Marcos Silveira
Keyword(s):  
Periodic Structure ◽  
Total Mass ◽  
Periodic Structures ◽  
Original Structure ◽  
Dynamical Response ◽  
Nonlinear Stiffness ◽  
Optimal Position ◽  
Simplified Approach ◽  
Vibration Attenuation ◽  
Linear And Nonlinear

Abstract We explore the vibration attenuation of a periodic structure when one absorber with nonlinear cubic stiffness is included without increasing the total mass. Metastructures, and specifically periodic structures, present interesting characteristics for vibration attenuation that are not found in classical structures. These characteristics have been explored for automotive and aerospace applications, among others, as structures with low mass are paramount for these industries, and keeping low vibration levels in wide frequency range is also desirable. It has been shown that the addition of vibration absorbers in a periodic arrangement can provide vibration attenuation for shock input without increasing the total mass of a structure. In this work, the dynamical response of a metastructure with one nonlinear vibration absorber, with same mass as original structure, optimized for vibration attenuation under harmonic input is compared with a base metastructure without absorbers and a metastructure with linear absorbers via the evaluation of the H2 norm of the frequency response. A simplified approach is used to compare linear and nonlinear stiffness based on deformation energy, by considering linear and nonlinear restoring forces to be equal at mean deformation. The dynamical response of the optimal system is obtained numerically, and an optimization procedure based on sequential quadratic programming (SQP) is proposed to find the optimal position and stiffness coefficients of only one nonlinear absorber, showing that it results in lower level of vibrations than original structure and than structure with linear absorbers, while almost the same level as a structure with all nonlinear absorbers.

Peptide-mediated deposition of nanostructured TiO2 into the periodic structure of diatom biosilica

2008 ◽  
Vol 23 (12) ◽  
pp. 3255-3262 ◽  
Author(s):  
Clayton Jeffryes ◽  
Timothy Gutu ◽  
Jun Jiao ◽  
Gregory L. Rorrer
Keyword(s):  
Titanium Dioxide ◽  
Electron Diffraction ◽  
Thermal Annealing ◽  
Periodic Structure ◽  
Outer Surface ◽  
Periodic Structures ◽  
Diatom Frustule ◽  
X Ray Diffraction ◽  
X Ray ◽  
Reported Study

Diatoms are single-celled algae that make silica shells called frustules that possess periodic structures ordered at the micro- and nanoscale. Nanostructured titanium dioxide (TiO2) was deposited onto the frustule biosilica of the diatom Pinnularia sp. Poly-l-lysine (PLL) conformally adsorbed onto surface of the frustule biosilica. The condensation of soluble Ti-BALDH to TiO2 by PLL-adsorbed diatom biosilica deposited 1.32 ± 0.17 g TiO2/g SiO2 onto the frustule. The periodic pore array of the diatom frustule served as a template for the deposition of the TiO2 nanoparticles, which completely filled the 200-nm frustule pores and also coated the frustule outer surface. Thermal annealing at 680 °C converted the as-deposited TiO2 to its anatase form with an average nanocrystal size of 19 nm, as verified by x-ray diffraction, electron diffraction, and SEM/TEM. This is the first reported study of directing the peptide-mediated deposition of TiO2 into a hierarchical nanostructure using a biologically fabricated template.

scholarly journals Number of Wavevectors for Each Frequency in a Periodic Structure

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Farhad Farzbod
Keyword(s):  
Periodic Structure ◽  
Degrees Of Freedom ◽  
Phonon Dispersion ◽  
Periodic Structures ◽  
Dispersion Curves ◽  
Neighbor Interaction ◽  
Phonon Dispersion Curves ◽  
Hexagonal Form ◽  
Vibration Properties ◽  
Unit Cells

Periodic structures have interesting acoustic and vibration properties making them suitable for a wide variety of applications. In a periodic structure, the number of frequencies for each wavevector depends on the degrees-of-freedom of the unit cell. In this paper, we study the number of wavevectors available at each frequency in a band diagram. This analysis defines the upper bound for the maximum number of wavevectors for each frequency in a general periodic structure which might include damping. Investigation presented in this paper can also provide an insight for designing materials in which the interaction between unit cells is not limited to the closest neighbor. As an example application of this work, we investigate phonon dispersion curves in hexagonal form of boron nitride to show that first neighbor interaction is not sufficient to model dispersion curves with force-constant model.

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