A modified transfer matrix method for the study of the bending vibration band structure in phononic crystal Euler beams

2012 ◽  
Vol 407 (23) ◽  
pp. 4579-4583 ◽  
Author(s):  
Lin Han ◽  
Yan Zhang ◽  
Zhi-Qiang Ni ◽  
Zi-Ming Zhang ◽  
Lin-Hua Jiang
Keyword(s):  
Band Structure ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Phononic Crystal ◽  
Vibration Band ◽  
Bending Vibration

Bending vibration band structure of phononic crystal beam by modified transfer matrix method

2014 ◽  
Vol 28 (15) ◽  
pp. 1450093 ◽  
Author(s):  
Zhi-Qiang Ni ◽  
Yan Zhang ◽  
Lin-Hua Jiang ◽  
Lin Han
Keyword(s):  
Band Structure ◽  
Transfer Matrix ◽  
Timoshenko Beam ◽  
Phononic Crystal ◽  
Vibration Band ◽  
Plane Wave Expansion ◽  
Matrix Operation ◽  
Bending Vibration ◽  
The Matrix ◽  
Constitutive Matrix

The bending vibration band structure of phononic crystal (PC) beam is solved by a unified formulation of the modified transfer matrix (MTM) method in this paper. The improvement of MTM method is the introduction of constitutive matrix U and matrix of derivative functions V, which standardizes and simplifies the deduction by the matrix operation. The band structure of an epoxy-aluminum PC Timoshenko beam is calculated by both MTM method and plane wave expansion (PWE) method. The results show that the present MTM method has a great advantage in the precision of the result. In addition, the formulation of transfer matrix derived from Timoshenko beam condition is a general form which is also suitable for other general beam structures just by replacing corresponding matrices.

A method for determining the minimum period number in finite locally resonant phononic crystal beams

2020 ◽  
Vol 26 (9-10) ◽  
pp. 801-813
Author(s):  
Panxue Liu ◽  
Shuguang Zuo ◽  
Xudong Wu ◽  
Minghai Zhang
Keyword(s):  
Band Gap ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Structural Parameters ◽  
Phononic Crystal ◽  
Minimum Period ◽  
Comprehensive Index ◽  
Vibration Attenuation ◽  
Vibration Transmissibility

To achieve the target band-gap in finite locally resonant phononic crystal beams, a method for determining the minimum period number is proposed. The vibration transmissibility method is extended to deal with the finite locally resonant phononic crystal beam. Comparing the vibration attenuation region obtained from the transmissibility method with the band-gap from the conventional transfer matrix method, the minimum period number can be calculated. Based on two forming patterns of locally resonant phononic crystal beams, the effects of the lattice constant and structural parameters of resonators on the band-gap as well as the influence of the period number on the vibration transmission characteristic are investigated. The minimum period number method can improve the applicability of the transmissibility method in the design of band-gaps and overcome the drawback that the transfer matrix method lacks the actual vibration attenuation. Finally, a comprehensive index is introduced to evaluate the effect of vibration reduction.

Electronic properties of superlattices

1990 ◽  
Vol 68 (3) ◽  
pp. 268-272 ◽  
Author(s):  
D. Aitelhabti ◽  
P. Vasilopoulos ◽  
J. F. Currie
Keyword(s):  
Wave Function ◽  
Dispersion Relation ◽  
Band Structure ◽  
Electronic Properties ◽  
Transfer Matrix ◽  
Current Density ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Tight Binding ◽  
Effective Masses

Using the transfer-matrix method, we evaluate the exact normalized wave function analytically, the band structure, and the current density associated with an electron in a superlattice, with different or equal effective masses between wells and barriers. Also, we evaluate numerically the dispersion relation, the bandwidth, and the current density (in the tight-binding limit) for both equal and different effective masses between wells and barriers.

A modified transfer matrix method for bending vibration of CFRP/Steel composite transmission shafting

2019 ◽  
Vol 90 (3) ◽  
pp. 603-614 ◽  
Author(s):  
Mo Yang ◽  
Xian Zhou ◽  
Wen Zhang ◽  
Jianmin Ye ◽  
Yefa Hu
Keyword(s):  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Bending Vibration ◽  
Steel Composite

One-Dimensional Phononic Crystal Dynamic Analysis by Spectral Transfer Matrix Method

2019 ◽  
Author(s):  
Adriano Goto ◽  
Edilson Dantas Nóbrega ◽  
Vilson Souza Pereira ◽  
Dalmo Inácio Galdez Costa ◽  
Jose Maria Campos dos Santos
Keyword(s):  
Dynamic Analysis ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Phononic Crystal ◽  
One Dimensional
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