scholarly journals Continuum limit of amorphous elastic bodies: A finite-size study of low-frequency harmonic vibrations

2002 ◽  
Vol 66 (17) ◽  
Author(s):  
A. Tanguy ◽  
J. P. Wittmer ◽  
F. Leonforte ◽  
J.-L. Barrat
Keyword(s):  
Continuum Limit ◽  
Finite Size ◽  
Low Frequency ◽  
Harmonic Vibrations ◽  
Elastic Bodies ◽  
Frequency Harmonic

A meter of the double-amplitude peak and frequency of low-frequency harmonic vibrations

2010 ◽  
Vol 53 (2) ◽  
pp. 296-297
Author(s):  
S. P. Pronin ◽  
E. A. Zryumov ◽  
A. V. Yudenkov ◽  
P. A. Zryumov
Keyword(s):  
Low Frequency ◽  
Harmonic Vibrations ◽  
Frequency Harmonic

A waveform inversion technique for measuring elastic wave attenuation in cylindrical bars

Geophysics ◽  
1992 ◽  
Vol 57 (6) ◽  
pp. 854-859 ◽  
Author(s):  
Xiao Ming Tang
Keyword(s):  
Elastic Wave ◽  
Wave Attenuation ◽  
Waveform Inversion ◽  
Finite Size ◽  
Low Frequency ◽  
Frequency Range ◽  
Multiple Reflections ◽  
Low Frequencies ◽  
The Time Domain ◽  
Attenuation Values

A new technique for measuring elastic wave attenuation in the frequency range of 10–150 kHz consists of measuring low‐frequency waveforms using two cylindrical bars of the same material but of different lengths. The attenuation is obtained through two steps. In the first, the waveform measured within the shorter bar is propagated to the length of the longer bar, and the distortion of the waveform due to the dispersion effect of the cylindrical waveguide is compensated. The second step is the inversion for the attenuation or Q of the bar material by minimizing the difference between the waveform propagated from the shorter bar and the waveform measured within the longer bar. The waveform inversion is performed in the time domain, and the waveforms can be appropriately truncated to avoid multiple reflections due to the finite size of the (shorter) sample, allowing attenuation to be measured at long wavelengths or low frequencies. The frequency range in which this technique operates fills the gap between the resonant bar measurement (∼10 kHz) and ultrasonic measurement (∼100–1000 kHz). By using the technique, attenuation values in a PVC (a highly attenuative) material and in Sierra White granite were measured in the frequency range of 40–140 kHz. The obtained attenuation values for the two materials are found to be reliable and consistent.

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 Continuum limit of the vibrational properties of amorphous solids

2017 ◽  
Vol 114 (46) ◽  
pp. E9767-E9774 ◽  
Author(s):  
Hideyuki Mizuno ◽  
Hayato Shiba ◽  
Atsushi Ikeda
Keyword(s):  
Large Scale ◽  
Continuum Limit ◽  
Scaling Law ◽  
Mean Field ◽  
Low Frequency ◽  
Amorphous Solids ◽  
Mode Analysis ◽  
Vibrational Modes ◽  
Phonon Modes ◽  
The Continuum

The low-frequency vibrational and low-temperature thermal properties of amorphous solids are markedly different from those of crystalline solids. This situation is counterintuitive because all solid materials are expected to behave as a homogeneous elastic body in the continuum limit, in which vibrational modes are phonons that follow the Debye law. A number of phenomenological explanations for this situation have been proposed, which assume elastic heterogeneities, soft localized vibrations, and so on. Microscopic mean-field theories have recently been developed to predict the universal non-Debye scaling law. Considering these theoretical arguments, it is absolutely necessary to directly observe the nature of the low-frequency vibrations of amorphous solids and determine the laws that such vibrations obey. Herein, we perform an extremely large-scale vibrational mode analysis of a model amorphous solid. We find that the scaling law predicted by the mean-field theory is violated at low frequency, and in the continuum limit, the vibrational modes converge to a mixture of phonon modes that follow the Debye law and soft localized modes that follow another universal non-Debye scaling law.

scholarly journals Double Pendulum Induced Stability

2015 ◽  
Vol 07 (06) ◽  
pp. 1550088
Author(s):  
Bezdenejnykh Nikolai ◽  
Andres Mateo Gabin ◽  
Raul Zazo Jimenez
Keyword(s):  
Theoretical Analysis ◽  
Potential Energy ◽  
High Frequency ◽  
Relative Equilibrium ◽  
Double Pendulum ◽  
Harmonic Vibrations ◽  
Hamilton Equations ◽  
High Frequency Harmonic ◽  
Good Agreement ◽  
Frequency Harmonic

In this work, a study of the relative equilibrium of a double pendulum whose point of suspension performs high frequency harmonic vibrations is presented. In order to determine the induced positions of equilibrium of the double pendulum at different gravity and vibration configurations, a set of experiments has been conducted. The theoretical analysis of the problem has been developed using Kapitsa’s method and numerical method. The method of Kapitsa allows to analyze the potential energy of a system in general and to find the values of the parameters of the problem that correspond to the relative extreme of energy — positions of stable or unstable equilibrium. The results of numerical and theoretical analysis of Hamilton equations are in good agreement with the results of the experiments.

Filter for testing low-frequency harmonic analyzers S5-2 and S5-3

1974 ◽  
Vol 17 (4) ◽  
pp. 616-617
Author(s):  
A. S. Karavaev ◽  
L. V. Mishin
Keyword(s):  
Low Frequency ◽  
Frequency Harmonic

Vibration of otolithlike scatterers due to low frequency harmonic wave excitation in water.

2011 ◽  
Vol 129 (4) ◽  
pp. 2472-2472 ◽  
Author(s):  
Carl R. Schilt ◽  
Ted W. Cranford ◽  
Petr Krysl ◽  
Anthony D. Hawkins
Keyword(s):  
Harmonic Wave ◽  
Low Frequency ◽  
Wave Excitation ◽  
Frequency Harmonic

scholarly journals Continuum limit in numerical simulations of the $\mathcal{N}=2$ Landau–Ginzburg model

2019 ◽  
Vol 2019 (10) ◽  
Author(s):  
Okuto Morikawa
Keyword(s):  
Field Theory ◽  
Continuum Limit ◽  
Central Charge ◽  
Finite Size ◽  
Scaling Analysis ◽  
Finite Size Scaling ◽  
Superconformal Field Theory ◽  
Lattice Field ◽  
Scaling Dimension ◽  
The Continuum

Abstract The $\mathcal{N}=2$ Landau–Ginzburg description provides a strongly interacting Lagrangian realization of an $\mathcal{N}=2$ superconformal field theory. It is conjectured that one such example is given by the two-dimensional $\mathcal{N}=2$ Wess–Zumino model. Recently, the conjectured correspondence has been studied by using numerical techniques based on lattice field theory; the scaling dimension and the central charge have been directly measured. We study a single superfield with a cubic superpotential, and give an extrapolation method to the continuum limit. Then, on the basis of a supersymmetric-invariant numerical algorithm, we perform a precision measurement of the scaling dimension through a finite-size scaling analysis.

scholarly journals Theoretical and experimental study on a finite size vector sensor array with a cylindrically symmetric carrier

2019 ◽  
Vol 283 ◽  
pp. 07008
Author(s):  
Junyuan Guo ◽  
Shi-e Yang ◽  
Hongjuan Chen ◽  
Shengchun Piao ◽  
Longhao Qiu
Keyword(s):  
Finite Size ◽  
Low Frequency ◽  
Doa Estimation ◽  
Radial Component ◽  
Tangential Component ◽  
Low Frequencies ◽  
Cylindrically Symmetric ◽  
Noise Characteristics ◽  
Vector Sensor ◽  
Array Gain

In this work, a finite size acoustic vector sensor (AVS) array is designed and its performance is theoretically and experimentally studied. The two-dimensional AVS array is comprised of five vector sensors and configured as a cross, and the array carrier is a cylindrically symmetric structure. Theoretical analysis and simulation indicate that the proposed method considering structure scattering can widen the working bandwidth. Furthermore, the utilization of vector sensor enables a significant white noise gain improvement at low frequencies, which makes the array more robust and easier to realize. Experiments have been done to study the array performance from several aspects including sensor noise characteristics, the beampattern, the direction-of-arrival (DOA) estimation ability and the array gain. From the change of the sensor directivity patterns or the amplitude distortion of the noise field, we can clearly observe the scattering field intensity. Moreover, it shows that the influence of the structure scattering on the tangential component of the vector field is symmetric, while that of the radial component is asymmetric. Experimental results also demonstrate that, with the proposed method, the 2nd and the 3rd order beamformers can be obtained which could be further used for the estimation of target DOA. In addition, an array gain of at least 6 dB is obtained capable of detection of weak signals. Our results indicate that the proposed array with a physical size less than one meter, although affected by nearby scatterers, can effectively break the Rayleigh limit and realize the remote detection in low-frequency regime.

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