Flexural vibration band gaps in Timoshenko beams with locally resonant structures

2006 ◽  
Vol 100 (12) ◽  
pp. 124901 ◽  
Author(s):  
Dianlong Yu ◽  
Yaozong Liu ◽  
Gang Wang ◽  
Honggang Zhao ◽  
Jing Qiu
Keyword(s):  
Flexural Vibration ◽  
Band Gaps ◽  
Vibration Band ◽  
Timoshenko Beams ◽  
Resonant Structures

Flexural vibration band gaps in thin plates with two-dimensional binary locally resonant structures

2006 ◽  
Vol 15 (2) ◽  
pp. 266-271 ◽  
Author(s):  
Yu Dian-Long ◽  
Wang Gang ◽  
Liu Yao-Zong ◽  
Wen Ji-Hong ◽  
Qiu Jing
Keyword(s):  
Flexural Vibration ◽  
Band Gaps ◽  
Thin Plates ◽  
Vibration Band ◽  
Two Dimensional ◽  
Resonant Structures

Flexural Vibration Band Gaps in a Ternary Phononic Crystal Thin Plate

2011 ◽  
Vol 675-677 ◽  
pp. 1085-1088
Author(s):  
Zong Jian Yao ◽  
Gui Lan Yu ◽  
Jian Bao Li
Keyword(s):  
Band Gap ◽  
Thin Plate ◽  
Mass Density ◽  
Phononic Crystal ◽  
Flexural Vibration ◽  
Expansion Method ◽  
Band Gaps ◽  
Physical Parameters ◽  
Vibration Band ◽  
Filling Fraction

The band structures of flexural waves in a ternary locally resonant phononic crystal thin plate are studied using the improved plane wave expansion method. And the thin concrete plate composed of a square array of steel cylinders hemmed around by rubber is considered here. Absolute band gaps of flexural vibration with low frequency are shown. The calculation results show that the band gap width is strongly dependent on the filling fraction, the radius ratio, the mass density and the Young’s modulus contrasts between the core and the coating. So by changing these physical parameters, the required band gap could be obtained.

Complete flexural vibration band gaps in membrane-like lattice structures

2006 ◽  
Vol 357 (2) ◽  
pp. 154-158 ◽  
Author(s):  
Dianlong Yu ◽  
Yaozong Liu ◽  
Jing Qiu ◽  
Gang Wang ◽  
Honggang Zhao
Keyword(s):  
Flexural Vibration ◽  
Band Gaps ◽  
Vibration Band ◽  
Lattice Structures

Flexural vibration band gaps in periodic Timoshenko beams with oscillators in series resting on flexible supports

2020 ◽  
Vol 23 (14) ◽  
pp. 3117-3127
Author(s):  
Lan Ding ◽  
Zhi Ye ◽  
Qiao-Yun Wu
Keyword(s):  
Band Gap ◽  
Transfer Matrix ◽  
Propagation Constant ◽  
Dynamic Stiffness ◽  
Band Gaps ◽  
Vibration Band ◽  
Timoshenko Beams ◽  
Gap Formation ◽  
Flexible Supports ◽  
In Series

The propagation properties of waves in Timoshenko beams resting on flexible supports and with periodically attached harmonic locally resonant oscillators are studied by the transfer matrix methodology. Through calculating the differential equations of the beam for the flexible vibration and the dynamic equations of the oscillators in series, the matrix of dynamic stiffness and the resulting transfer matrix are derived. Accordingly, the band gap in infinite system characterized by the propagation constant can be verified by comparing to the curve of transmission property, determined with the finite element method for the finite system. The mechanism of each band gap formation is further explored. Numerical results show that different from the single degree-of-freedom mass-spring model, one more locally resonant band gap is generated in the system of two oscillators in series. The introduction of flexible supports, allowing for variable internal coupling between the adjacent cells, produces an extra band gap with a minimum frequency of zero. It is also found that the starting frequencies of the locally resonant gaps are related to the spring stiffness and mass of the oscillator. Therefore, the positions and widths of the band gaps can be tuned by properly adjusting the four parameters of the oscillators and also the stiffness of the flexible supports.

scholarly journals Band Gaps Characteristics Analysis of Periodic Oscillator Coupled Damping Beam

Materials ◽  
2020 ◽  
Vol 13 (24) ◽  
pp. 5748
Author(s):  
Li Tang ◽  
Xiongliang Yao ◽  
Guoxun Wu ◽  
Dong Tang
Keyword(s):  
Flexural Vibration ◽  
Wave Dispersion ◽  
Band Gaps ◽  
Structural Vibration ◽  
Flexural Wave ◽  
Beam Model ◽  
Vibration Band ◽  
Engineering Structures ◽  
Plate Structures ◽  
Characteristics Analysis

The vibration of the periodic oscillator coupled damping beam model is reduced through the band gaps designing method, which can be applied in equivalent engineering structures. In this paper, the flexural wave dispersion relations of the infinite long periodic oscillator coupled damping beam were calculated using the reverberation-ray matrix method combined with the Bloch theorem. The flexural wave vibration frequency response function of the finite long periodic oscillator coupled damping beam was carried out using the finite element method. The flexural wave vibration band gaps occur in the infinite long periodic oscillator coupled damping beam model in both the analytical and numerical results. In these band gaps, flexural waves’ propagation is prohibited, and flexural vibration is significantly suppressed. Furthermore, the effects of structure and material parameters on the flexural wave vibration band gaps characteristics are studied. Thus, the structural vibration reduction design can be realized by adjusting the related parameters of the periodic coupled damping beam structures and the equivalent 2D periodic stiffened plate structures.

Flexural vibration band gaps in Bragg acoustical hyperstructure beam with local-resonance system

2019 ◽  
Vol 33 (23) ◽  
pp. 1950278 ◽  
Author(s):  
X. F. Lei ◽  
H. P. Hou ◽  
P. Liu ◽  
Z. F. Xu ◽  
S. H. Liu ◽  
...  
Keyword(s):  
Theoretical Model ◽  
Transmission Spectrum ◽  
Composite Beam ◽  
Reaction Force ◽  
Flexural Vibration ◽  
Reversed Phase ◽  
Band Gaps ◽  
Vibration Band ◽  
Resonance System ◽  
Local Resonance

Bragg acoustical hyperstructure can scatter elastic wave, local resonance system can fight against vibration by the reaction force with reversed phase in low-frequency range, for improving the scattering performance of Bragg hyperstructure, a novel composite beam of Bragg beam with local resonator is investigated theoretically. Its dispersion relations and bang gaps are calculated by the established theoretical model. In order to confirm the veritable existence of band gaps, the transmission spectrum of flexural vibration waves are also studied by finite-element method, and comparing the relationship of vibration transmission spectrum and band gaps, the results indicate that the proposed theoretical model can accurately predict the band gaps of the proposed composite beam. For probing the dispersion mechanics, comparing the band gaps and modes shapes of the proposed composite beam with an unalloyed Bragg beam, the results denoted that local resonator can add two band gaps at the base of Bragg beam. Further, the changes of the band gaps that depend on the local resonator and on Bragg beam are studied. It is indicated that the total band gaps can be narrowed when the resonance frequency of the local resonators located at the band gaps of the Bragg beam and the branches will become approximately flat. The band gaps will broaden if the branch that depends on the local resonator gets closer to the branch on Bragg beam.

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