scholarly journals Acoustic band fracture variation of low frequency transmission zone in one-dimensional solid-fluid periodic structures under omnidirectional incidence

2013 ◽  
Vol 62 (20) ◽  
pp. 204302
Author(s):  
Liu Cong ◽  
Xu Xiao-Dong ◽  
Liu Xiao-Jun
Keyword(s):  
Periodic Structures ◽  
Low Frequency ◽  
One Dimensional ◽  
Transmission Zone

scholarly journals Longitudinal wave propagation in a one-dimensional quasi-periodic waveguide

2019 ◽  
Vol 475 (2231) ◽  
pp. 20190392
Author(s):  
Vladislav S. Sorokin
Keyword(s):  
Wave Propagation ◽  
Wave Attenuation ◽  
Periodic Structures ◽  
Low Frequency ◽  
Periodic Waveguide ◽  
One Dimensional ◽  
Vibration Attenuation ◽  
Direct Separation ◽  
Longitudinal Wave Propagation ◽  
Spatial Modulations

The paper deals with the analysis of wave propagation in a general one-dimensional (1D) non-uniform waveguide featuring multiple modulations of parameters with different, arbitrarily related, spatial periods. The considered quasi-periodic waveguide, in particular, can be viewed as a model of pure periodic structures with imperfections. Effects of such imperfections on the waveguide frequency bandgaps are revealed and described by means of the method of varying amplitudes and the method of direct separation of motions. It is shown that imperfections cannot considerably degrade wave attenuation properties of 1D periodic structures, e.g. reduce widths of their frequency bandgaps. Attenuation levels and frequency bandgaps featured by the quasi-periodic waveguide are studied without imposing any restrictions on the periods of the modulations, e.g. for their ratio to be rational. For the waveguide featuring relatively small modulations with periods that are not close to each other, each of the frequency bandgaps, to the leading order of smallness, is controlled only by one of the modulations. It is shown that introducing additional spatial modulations to a pure periodic structure can enhance its wave attenuation properties, e.g. a relatively low-frequency bandgap can be induced providing vibration attenuation in frequency ranges where damping is less effective.

Multicell Homogenization of One-Dimensional Periodic Structures

2010 ◽  
Vol 132 (1) ◽  
Author(s):  
Stefano Gonella ◽  
Massimo Ruzzene
Keyword(s):  
Dynamic Behavior ◽  
Periodic Structures ◽  
Low Frequency ◽  
Structural Response ◽  
Fourier Series Expansion ◽  
Low Frequencies ◽  
One Dimensional ◽  
Physical Constraints ◽  
Unit Cells ◽  
Taylor Series Expansions

Much attention has been recently devoted to the application of homogenization methods for the prediction of the dynamic behavior of periodic domains. One of the most popular techniques employs the Fourier transform in space in conjunction with Taylor series expansions to approximate the behavior of structures in the low frequency/long wavelength regime. The technique is quite effective, but suffers from two major drawbacks. First, the order of the Taylor expansion, and the corresponding frequency range of approximation, is limited by the resulting order of the continuum equations and by the number of boundary conditions, which may be imposed in accordance with the physical constraints on the system. Second, the approximation at low frequencies does not allow capturing bandgap characteristics of the periodic domain. An attempt at overcoming the latter can be made by applying the Fourier series expansion to a macrocell spanning two (or more) irreducible unit cells of the periodic medium. This multicell approach allows the simultaneous approximation of low frequency and high frequency dynamic behavior and provides the capability of analyzing the structural response in the vicinity of the lowest bandgap. The method is illustrated through examples on simple one-dimensional structures to demonstrate its effectiveness and its potentials for application to complex one-dimensional and two-dimensional configurations.

Asymptotic derivation of a refined equation for an elastic beam resting on a Winkler foundation

2021 ◽  
pp. 108128652110238
Author(s):  
Barış Erbaş ◽  
Julius Kaplunov ◽  
Isaac Elishakoff
Keyword(s):  
Ad Hoc ◽  
Moving Load ◽  
Low Frequency ◽  
Elastic Beam ◽  
Winkler Foundation ◽  
One Dimensional ◽  
Beam Equations ◽  
Dimensional Equation ◽  
Phase And Group Velocities ◽  
Group Velocities

A two-dimensional mixed problem for a thin elastic strip resting on a Winkler foundation is considered within the framework of plane stress setup. The relative stiffness of the foundation is supposed to be small to ensure low-frequency vibrations. Asymptotic analysis at a higher order results in a one-dimensional equation of bending motion refining numerous ad hoc developments starting from Timoshenko-type beam equations. Two-term expansions through the foundation stiffness are presented for phase and group velocities, as well as for the critical velocity of a moving load. In addition, the formula for the longitudinal displacements of the beam due to its transverse compression is derived.

Anomalous phase in one-dimensional, multilayer, periodic structures with birefringent materials

2004 ◽  
Vol 70 (16) ◽  
Author(s):  
A. Mandatori ◽  
C. Sibilia ◽  
M. Bertolotti ◽  
S. Zhukovsky ◽  
J. W. Haus ◽  
...  
Keyword(s):  
Periodic Structures ◽  
One Dimensional

Locally resonant periodic structures with low-frequency band gaps

2013 ◽  
Vol 114 (3) ◽  
pp. 033532 ◽  
Author(s):  
Zhibao Cheng ◽  
Zhifei Shi ◽  
Y. L. Mo ◽  
Hongjun Xiang
Keyword(s):  
Frequency Band ◽  
Periodic Structures ◽  
Low Frequency ◽  
Band Gaps

A periodic seismic isolation foundation with an extremely broad low-frequency attenuation zone: Theoretical analysis and experimental verification

2021 ◽  
pp. 136943322110646
Author(s):  
Peng Zhou ◽  
Shui Wan ◽  
Xiao Wang ◽  
Yingbo Zhu ◽  
Muyun Huang
Keyword(s):  
Seismic Isolation ◽  
Seismic Waves ◽  
Periodic Structures ◽  
Finite Size ◽  
Low Frequency ◽  
Bridge Structure ◽  
Engineering Structures ◽  
P Waves ◽  
New Type ◽  
Dominant Frequencies

The attenuation zones (AZs) of periodic structures can be used for seismic isolation design. To cover the dominant frequencies of more seismic waves, this paper proposes a new type of periodic isolation foundation (PIF) with an extremely wide low-frequency AZ of 3.31 Hz–17.01 Hz composed of optimized unit A with a wide AZ and optimized unit B with a low-frequency AZ. The two kinds of optimized units are obtained by topology optimization on the smallest periodic unit with the coupled finite element-genetic algorithm (GA) methodology. The transmission spectra of shear waves and P-waves through the proposed PIF of finite size are calculated, and the results show that the AZ of the PIF is approximately the superposition of the AZs of the two kinds of optimized units. Additionally, shake tests on a scale PIF specimen are performed to verify the attenuation performance for elastic waves within the designed AZs. Furthermore, numerical simulations show that the acceleration responses of the bridge structure with the proposed PIF are attenuated significantly compared to those with a concrete foundation under the action of different seismic waves. Therefore, the newly proposed PIF is a promising option for the reduction of seismic effects in engineering structures.

scholarly journals A Parameter Study of Localization

1996 ◽  
Vol 3 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Sandor Stephen Mester ◽  
Haym Benaroya
Keyword(s):  
Periodic Structures ◽  
Numerical Study ◽  
Vibration Characteristics ◽  
Periodic Pattern ◽  
Parameter Study ◽  
Structural Damping ◽  
One Dimensional

Extensive work has been done on the vibration characteristics of perfectly periodic structures. Disorder in the periodic pattern has been found to lead to localization in one-dimensional periodic structures. It is important to understand localization because it causes energy to be concentrated near the disorder and may cause an overestimation of structural damping. A numerical study is conducted to obtain a better understanding of localization. It is found that any mode, even the first, can localize due to the presence of small imperfections.

scholarly journals Periodic and Near-Periodic Structures

1995 ◽  
Vol 2 (1) ◽  
pp. 69-95 ◽  
Author(s):  
S. S. Mester ◽  
H. Benaroya
Keyword(s):  
State Physics ◽  
Solid State ◽  
Periodic Structures ◽  
Vibration Characteristics ◽  
Aerospace Engineering ◽  
Structural Damping ◽  
Solid State Physics ◽  
One Dimensional ◽  
Fields Of Study ◽  
Effects Of Disorder

Extensive work has been done on the vibration characteristics of perfectly periodic structures. This article reviews the different methods of analysis from several fields of study, for example solid-state physics and civil, mechanical, and aerospace engineering, used to determine the effects of disorder in one-dimensional (1-D) and 2-D periodic structures. In the work examined, disorder has been found to lead to localization in 1-D periodic structures. It is important to understand localization because it causes energy to be concentrated near the disorder and may cause an overestimation of structural damping. The implications of localization for control are also examined.

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