scholarly journals Higher order interfacial effects for elastic waves in one dimensional phononic crystals via the Lagrange-Hamilton's principle

2018 ◽  
Vol 67 ◽  
pp. 58-70 ◽  
Author(s):  
F. Lebon ◽  
R. Rizzoni
Keyword(s):  
Elastic Waves ◽  
Higher Order ◽  
Phononic Crystals ◽  
Hamilton’S Principle ◽  
Hamilton's Principle ◽  
Interfacial Effects ◽  
One Dimensional

scholarly journals Topologically protected elastic waves in one-dimensional phononic crystals of continuous media

2017 ◽  
Vol 11 (1) ◽  
pp. 017201 ◽  
Author(s):  
Ingi Kim ◽  
Satoshi Iwamoto ◽  
Yasuhiko Arakawa
Keyword(s):  
Elastic Waves ◽  
Continuous Media ◽  
Phononic Crystals ◽  
One Dimensional

Quasi-One-Dimensional Periodic Structure with Locally Resonant Band Gap

2005 ◽  
Vol 73 (1) ◽  
pp. 167-170 ◽  
Author(s):  
Gang Wang ◽  
Xisen Wen ◽  
Jihong Wen ◽  
Yaozong Liu
Keyword(s):  
Band Gap ◽  
Periodic Structure ◽  
Elastic Waves ◽  
Phononic Crystals ◽  
Experimental Results ◽  
Harmonic Oscillators ◽  
Dimensional Structure ◽  
Stiffness Ratio ◽  
One Dimensional ◽  
Two Factors

The propagation of longitudinal elastic waves in quasi one-dimensional structure consisting of harmonic oscillators periodically jointed on a slender beam is studied. Sub-frequency locally resonant band gap with highly asymmetric attenuation is observed in both theoretical and experimental results, and both results match well. The stiffness and mass ratios are found analytically as two factors that influence the actual attenuation in the band gap of the locally resonant phononic crystals. The study on the weights of the two factors shows that the stiffness ratio is the key one. Thus, the reason for the mismatch between the regions of the sharp attenuation and the theoretical band gap in the locally resonant phononic crystals is discovered.

scholarly journals Hamilton’s Principle for Circuits with Dissipative Elements

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Zdeněk Biolek ◽  
Dalibor Biolek ◽  
Viera Biolková
Keyword(s):  
Variational Principle ◽  
Higher Order ◽  
Hamilton’S Principle ◽  
Hamilton's Principle ◽  
Frequency Dependent ◽  
Nearest Neighbours ◽  
Classic Form

The classic form of Hamilton’s variational principle does not hold for circuits with dissipative elements. It is shown in the paper that this may not be true in the case of systems consisting of the so-called higher-order elements. Hamilton’s principle is then extended to circuits containing the classical resistors and Frequency Dependent Negative Resistors (FDNRs). The extension is also made to any pair of elements which are the nearest neighbours on any Σ-diagonal of Chua’s table.

The scattering matrix approach: A study of elastic waves propagation in one-dimensional disordered phononic crystals

2015 ◽  
Vol 118 (23) ◽  
pp. 234302 ◽  
Author(s):  
R. Pernas-Salomón ◽  
R. Pérez-Álvarez ◽  
Z. Lazcano ◽  
J. Arriaga
Keyword(s):  
Elastic Waves ◽  
Scattering Matrix ◽  
Phononic Crystals ◽  
Matrix Approach ◽  
One Dimensional ◽  
Waves Propagation

Elastic Wave Localization in Two-Dimensional Phononic Crystals with One-Dimensional Aperiodicity

2011 ◽  
Vol 52-54 ◽  
pp. 1131-1136
Author(s):  
Zhi Zhong Yan ◽  
Chuan Zeng Zhang ◽  
Yue Sheng Wang
Keyword(s):  
Elastic Waves ◽  
Periodic Sequence ◽  
Phononic Crystals ◽  
Two Dimensional ◽  
Wave Localization ◽  
Band Structures ◽  
One Dimensional ◽  
Transmission Coefficients ◽  
Localization Factor ◽  
Match Theory

The band structures of in-plane elastic waves propagating in two-dimensional phononic crystals with one-dimensional aperiodicity are analyzed in this paper. The localization of wave propagation is discussed by introducing the concept of the localization factor that is calculated by the plane-wave-based transfer-matrix method. By treating the aperiodicity as the deviation from the periodicity in a special way, two kinds of aperiodic phononic crystals that have Thue-Morse and Rudin-Shapiro sequence in one direction and translational symmetry in the other direction are considered. The transmission coefficients based on eigenmode match theory are also calculated and the results show the same behaviors as the localization factor does. In the case of Thue-Morse and Rudin-Shapiro structures, the band structures of Thue-Morse sequence exhibit similarities with quasi-periodic sequence not present in the results of Rudin-Shapiro sequence.

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