Analysis of Periodicity Termination in Phononic Crystals

2011 ◽  
Author(s):  
Bruce L. Davis ◽  
Andrew S. Tomchek ◽  
Edgar A. Flores ◽  
Liao Liu ◽  
Mahmoud I. Hussein
Keyword(s):  
Band Gap ◽  
Timoshenko Beam ◽  
Periodic Structures ◽  
Beam Theory ◽  
Phononic Crystals ◽  
Timoshenko Beam Theory ◽  
Band Gaps ◽  
Pass Band ◽  
Unit Cells

While resonant propagation modes are non-existent within band gaps in infinite periodic structures, it is possible for anomalous band-gap resonances to appear in finite periodic structures. We establish two criteria for the characterization of band-gap resonances and propose approaches for their elimination. By considering flexural periodic beams, we show that as the number of unit-cells is increased the vibration response corresponding to band-gap resonances (1) does not shift in frequency, and (2) drops in amplitude. Both these outcomes are not exhibited by regular pass-band resonances, nor by resonances in finite homogenous beams when the length is changed. Our conclusions stem from predictions based on Timoshenko beam theory coupled with matching experimental observations.

Flexural Vibration Band Gap in a Periodic Fluid-Conveying Pipe System Based on the Timoshenko Beam Theory

2011 ◽  
Vol 133 (1) ◽  
Author(s):  
Dianlong Yu ◽  
Jihong Wen ◽  
Honggang Zhao ◽  
Yaozong Liu ◽  
Xisen Wen
Keyword(s):  
Finite Element Method ◽  
Band Gap ◽  
Timoshenko Beam ◽  
Beam Theory ◽  
Flexural Vibration ◽  
Timoshenko Beam Theory ◽  
Flexural Wave ◽  
Vibration Band ◽  
Frequency Range ◽  
Pipe System

The flexural vibration band gap in a periodic fluid-conveying pipe system is studied based on the Timoshenko beam theory. The band structure of the flexural wave is calculated with a transfer matrix method to investigate the gap frequency range. The effects of the rotary inertia and shear deformation on the gap frequency range are considered. The frequency response of finite periodic pipe is calculated with a finite element method to validate the gap frequency ranges.

Study of the bending vibration characteristic of phononic crystals beam-foundation structures by Timoshenko beam theory

2015 ◽  
Vol 29 (20) ◽  
pp. 1550136 ◽  
Author(s):  
Yan Zhang ◽  
Zhi-Qiang Ni ◽  
Lin-Hua Jiang ◽  
Lin Han ◽  
Xue-Wei Kang
Keyword(s):  
Timoshenko Beam ◽  
Beam Theory ◽  
Phononic Crystals ◽  
Timoshenko Beam Theory ◽  
Winkler Foundation ◽  
Vibration Characteristic ◽  
Bending Vibration ◽  
Periodic Composites ◽  
Beam Foundation ◽  
Foundation Structure

Vibration problems wildly exist in beam-foundation structures. In this paper, finite periodic composites inspired by the concept of ideal phononic crystals (PCs), as well as Timoshenko beam theory (TBT), are proposed to the beam anchored on Winkler foundation. The bending vibration band structure of the PCs Timoshenko beam-foundation structure is derived from the modified transfer matrix method (MTMM) and Bloch's theorem. Then, the frequency response of the finite periodic composite Timoshenko beam-foundation structure by the finite element method (FEM) is performed to verify the above theoretical deduction. Study shows that the Timoshenko beam-foundation structure with periodic composites has wider attenuation zones compared with homogeneous ones. It is concluded that TBT is more available than Euler beam theory (EBT) in the study of the bending vibration characteristic of PCs beam-foundation structures with different length-to-height ratios.

Vibration isolation characteristics of finite periodic tetra-chiral lattice coating filled with internal resonators

2016 ◽  
Vol 230 (16) ◽  
pp. 2840-2850 ◽  
Author(s):  
Dawei Zhu ◽  
Xiuchang Huang ◽  
Hongxing Hua ◽  
Hui Zheng
Keyword(s):  
Band Gap ◽  
Vibration Isolation ◽  
Periodic Structures ◽  
Low Frequency ◽  
Band Gaps ◽  
Stiffened Plate ◽  
Frequency Range ◽  
Vibration Attenuation ◽  
Unit Cells ◽  
Internal Resonators

Owing to their locally resonant mechanism, internal resonators are usually used to provide band gaps in low-frequency region for many types of periodic structures. In this study, internal resonators are used to improve the vibration attenuation ability of finite periodic tetra-chiral coating, enabling high reduction of the radiated sound power by a vibrating stiffened plate. Based on the Bloch theorem and finite element method, the band gap characteristics of tetra-chiral unit cells filled with and without internal resonators are analysed and compared to reveal the relationship between band gaps and vibration modes of such tetra-chiral unit cells. The rotational vibration of internal resonators can effectively strengthen the vibration attenuation ability of tetra-chiral lattice and extend the effective frequency range of vibration attenuation. Two tetra-chiral lattices with and without internal resonators are respectively designed and their vibration transmissibilities are measured using the hammering method. The experimental results confirm the vibration isolation effect of the internal resonators on the finite periodic tetra-chiral lattice. The tetra-chiral lattice as an acoustic coating is applied to a stiffened plate, and analysis results indicate that the internal resonators can obviously enhance the vibration attenuation ability of tetra-chiral lattice coating in the frequency range of the band gap corresponding to the rotating vibration mode of internal resonators. When the soft rubber with the internal resonators in tetra-chiral layers has gradient elastic modulus, the vibration attenuation ability and noise reduction of the tetra-chiral lattice coating are basically enhanced in the frequency range of the corresponding band gaps of tetra-chiral unit cells.

scholarly journals Improving the accuracy of analytical relationships for mechanical properties of additively manufactured lattice structures

2020 ◽  
Author(s):  
Reza Hedayati ◽  
Naeim Ghavidelnia ◽  
Mojtaba Sadighi ◽  
Bodaghi
Keyword(s):  
Timoshenko Beam ◽  
Beam Theory ◽  
Cell Types ◽  
Timoshenko Beam Theory ◽  
Unit Cell ◽  
Lattice Structures ◽  
Starting Point ◽  
Unit Cells ◽  
Order Of Magnitude ◽  
The Difference

Porous implants must satisfy several physical and biological requirements in order to be promising materials for orthopedic application: they should have the proper levels of stiffness, permeability, and fatigue resistance and in proximity to how much they are in bone tissues. In recent years, several experimental, numerical, and analytical studies have been carried out on the influence of unit cell geometry on such properties. Even though experimental and numerical techniques can effectively study and predict the behavior of different micro-structure, they lack the ease the analytical relationships provide for such predictions. Even though it is well-known that Timoshenko beam theory gives much better accuracy in predicting the deformation of a beam (and as a result lattice structures), many of the already-existing relationships in the literature have been derived based on Euler-Bernoulli beam theory. The question that arises here is that can there be a convenient way to convert the already-existing relationships based on Euler-Bernoulli to relationships based on Timoshenko beam theory without the need to rewrite all the derivations from the starting point. In this paper, this question is addressed and answered, and a simple approach is presented. This technique is applied to six unit cells for which Euler-Bernoulli analytical relationships could be found in the literature, but Timoshenko theories could not be found: BCC, hexagonal packing, rhombicuboctahedron, diamond, truncated cube, and truncated octahedron. The results of this study demonstrated that converting analytical relationships based on Euler-Bernoulli to equivalent Timoshenko ones can decrease the difference between the analytical and numerical values for one order of magnitude which is a significant improvement in accuracy of the analytical formulas. The methodology presented in this study is not only beneficial to the already-existing analytical relationships but also facilitates derivation of accurate analytical relationships for other, yet unexplored, unit cell types.

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.

Exact Dynamic Analysis of Space Structures Using Timoshenko Beam Theory

AIAA Journal ◽  
2004 ◽  
Vol 42 (4) ◽  
pp. 833-839 ◽  
Author(s):  
Jen-Fang Yu ◽  
Hsin-Chung Lien ◽  
B. P. Wang
Keyword(s):  
Dynamic Analysis ◽  
Timoshenko Beam ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Space Structures

Optimal design of high-g MEMS piezoresistive accelerometer based on Timoshenko beam theory

2017 ◽  
Vol 24 (2) ◽  
pp. 855-867 ◽  
Author(s):  
Feng Liu ◽  
Shiqiao Gao ◽  
Shaohua Niu ◽  
Yan Zhang ◽  
Yanwei Guan ◽  
...  
Keyword(s):  
Optimal Design ◽  
Timoshenko Beam ◽  
Beam Theory ◽  
Timoshenko Beam Theory
Sign in / Sign up

Export Citation Format

Share Document