Models for thermoelastic attenuation of waves in heterogeneous solids

Geophysics ◽  
1984 ◽  
Vol 49 (7) ◽  
pp. 1032-1040 ◽  
Author(s):  
Baxter H. Armstrong
Keyword(s):  
Temperature Variation ◽  
Wave Attenuation ◽  
Homogeneous Equation ◽  
Low Frequency ◽  
Temperature Wave ◽  
Heterogeneous Solids ◽  
One Dimensional ◽  
Thermal Current ◽  
Periodic Arrangement ◽  
Heterogeneous Solid

Some one‐dimensional models of a heterogeneous solid are presented consisting of a succession of slabs with different anharmonic properties. The equation for the temperature variation in these models due to passage of a longitudinal elastic wave can be solved exactly in the approximation of weak attenuation. The solutions are given in terms of the forced oscillation plus the temperature wave solutions to the homogeneous equation needed to match the boundary conditions of continuity of temperature and thermal current. Thermoelastic attenuation due to this temperature variation is compared to that of Zener’s classical approach. For periodic arrangement of slab properties or upon use of Zener’s boundary condition of vanishing thermal current, the temperature‐wave approach reproduces Zener‐type attenuation. However, a succession of slabs with a random, uncorrelated distribution of the Gruneisen constant leads to a new result with attenuation proportional to the three‐halves power of the wave frequency in the low‐frequency limit. The results are discussed in the context of seismoacoustic wave attenuation.

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.

A Novel Fault-location Method for HVDC Transmission Lines Based on Concentric Relaxation Principle and Wavelet Packet

2020 ◽  
Vol 13 (5) ◽  
pp. 705-716
Author(s):  
Congshan Li ◽  
Ping He ◽  
Feng Wang ◽  
Cunxiang Yang ◽  
Yukun Tao ◽  
...  
Keyword(s):  
Transmission Lines ◽  
Traveling Wave ◽  
Fault Location ◽  
Wave Attenuation ◽  
Wavelet Packet ◽  
Low Frequency ◽  
Evaluation Process ◽  
Location Method ◽  
Hvdc Transmission ◽  
Instantaneous Energy

Background: A novel fault location method of HVDC transmission line based on a concentric relaxation principle is proposed in this paper. Methods: Due to the different position of fault, the instantaneous energy measured from rectifier and inverter are different, and the ratio k between them is the relationship to the fault location d. Through the analysis of amplitude-frequency characteristics, we found that the wave attenuation characteristic of low frequency in the traveling wave is stable, and the amplitude of energy is larger, so we get the instantaneous energy ratio by using the low-frequency data. By using the method of wavelet packet decomposition, the voltage traveling wave signal was decomposed. Results: Finally, calculate the value k. By using the data fitting, the relative function of k and d can be got, that is the fault location function. Conclusion: After an exhaustive evaluation process considering different fault locations, fault resistances, and noise on the unipolar DC transmission system, four-machine two-area AC/DC parallel system, and an actual complex grid, the method presented here showed a very accurate and robust behavior.

scholarly journals Numerical Modelling and Optimization of Two-Dimensional Phononic Band Gaps in Elastic Metamaterials with Square Inclusions

2021 ◽  
Vol 11 (7) ◽  
pp. 3124
Author(s):  
Alya Alhammadi ◽  
Jin-You Lu ◽  
Mahra Almheiri ◽  
Fatima Alzaabi ◽  
Zineb Matouk ◽  
...  
Keyword(s):  
Elastic Wave ◽  
Tungsten Carbide ◽  
Composite Structure ◽  
Elastic Waves ◽  
Wave Attenuation ◽  
Low Frequency ◽  
Filling Fraction ◽  
Carbide Composite ◽  
Elastic Metamaterials ◽  
Tungsten Carbide Composite

A numerical simulation study on elastic wave propagation of a phononic composite structure consisting of epoxy and tungsten carbide is presented for low-frequency elastic wave attenuation applications. The calculated dispersion curves of the epoxy/tungsten carbide composite show that the propagation of elastic waves is prohibited inside the periodic structure over a frequency range. To achieve a wide bandgap, the elastic composite structure can be optimized by changing its dimensions and arrangement, including size, number, and rotation angle of square inclusions. The simulation results show that increasing the number of inclusions and the filling fraction of the unit cell significantly broaden the phononic bandgap compared to other geometric tunings. Additionally, a nonmonotonic relationship between the bandwidth and filling fraction of the composite was found, and this relationship results from spacing among inclusions and inclusion sizes causing different effects on Bragg scatterings and localized resonances of elastic waves. Moreover, the calculated transmission spectra of the epoxy/tungsten carbide composite structure verify its low-frequency bandgap behavior.

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.

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.

scholarly journals MULTIDIMENSIONAL REPRESENTATION OF AUTOMATIC DOSING DEVICE SIGNALS

2018 ◽  
pp. 26-32
Author(s):  
Denis Borisovich Fedosenkov ◽  
Anna Alekseevna Simikova ◽  
Boris Andreevich Fedosenkov ◽  
Stanislav Matveevich Kulakov
Keyword(s):  
Fourier Transform ◽  
Wigner Distribution ◽  
Low Frequency ◽  
Stationary Flow ◽  
Complex Model ◽  
Signal Spectrum ◽  
One Dimensional ◽  
Time Frequency ◽  
Cohen's Class ◽  
Discrete Values

The article describes the development of a special approach based on using multidimensional wavelet distributions principle to monitor and control the feed dozing processes in the mix preparation unit. As a key component, this approach uses the multidimensional time-frequency Wigner-Ville distribution, which is the part of Cohen's class distributions. The research focuses on signals characterizing mass transfer processes in the form of material flow measuring signals in relevant points of the unit. Wigner-Ville distribution has been shown in time terms as Fourier transform of products of multiplied parts of the signal under consideration for past and future time moments; corresponding distribution for the frequency spectrum is shown as Fourier transform of the products of signal parts for high-frequency and low-frequency fragments of the signal spectrum. It has been noted that when using a complex model of a dozing signal, discrete values (samples) of the latter are considered as its real values. The description of the signal parameters (amplitude, phase, frequency) has been carried out with the help of Hilbert transform. In Cohen's class distributions which represent one-dimensional non-stationary flow signals, the concept of ‘instantaneous frequency’ has been introduced. A graphical explanation for the transformation of a process flow signal from a one-dimensional time domain to a time-frequency 2 D/ 3 D -space is presented. The technology of developing a multidimensional image in the form of Wigner distribution for one-dimensional signals of continuous spiral or screw-type feeders has been examined in detail. There have been considered the features to support Wigner distribution, which allow to guess the presence or absence of time-frequency distribution elements in the interval of signal recording. There has been demonstrated how Wigner distribution can be obtained for a continuous-intermittent feeding signal. It has been concluded that for a certain types of the signal for zero fragments of the latter, non-zero time-frequency elements (i.e. virtual, anomalous ones) appear on the distribution. In addition to Wigner distribution, two other distributions - of Rihachek and Page - are considered. They display the same signal and also contain virtual elements, but in different domains of the time-frequency space. A generalized multidimensional compound signal distribution with a so-called distribution kernel available in it is presented, which includes a correction parameter that allows controlling the intensity of the virtual signal energy.

scholarly journals Tunable Omnidirectional Band Gap Properties of 1D Plasma Annular Periodic Multilayer Structure Based on an Improved Fibonacci Topological Structure

2021 ◽  
Author(s):  
Hong-Mei Peng ◽  
Bao-Fei Wan ◽  
Peng-Xiang Wang ◽  
Dan Zhang ◽  
Hai-Feng Zhang
Keyword(s):  
Band Gap ◽  
Plasma Frequency ◽  
Incident Angle ◽  
Low Frequency ◽  
Interesting Phenomenon ◽  
Azimuthal Mode ◽  
One Dimensional ◽  
Theoretical Support ◽  
Omnidirectional Band Gap ◽  
High Reflection

Abstract In this paper, the characteristics of the omnidirectional band gap (OBG) for one-dimensional (1D) plasma cylindrical photonic crystals (PCPCs) are based on an improved Fibonacci topological (IFT) structure are studied. The influences of the azimuthal mode number, incident angle, plasma thickness, and plasma frequency on the OBG are discussed. It is concluded that increasing the azimuth modulus can significantly expand the bandwidth of the OBG, and the OBG can be moved to the low-frequency direction by increasing the plasma frequency. In addition, an interesting phenomenon can be found that when the number of azimuthal modes is equal to 2, the TM wave can produce an extra high reflection zone. It provides a theoretical support for designing the narrowband filters without introducing any physical defect layers in the structure.

Dimensional tailoring of nitrogen-doped graphene for high performance supercapacitors

RSC Advances ◽  
2016 ◽  
Vol 6 (60) ◽  
pp. 55577-55583 ◽  
Author(s):  
Seung Yong Lee ◽  
Chang Hyuck Choi ◽  
Min Wook Chung ◽  
Jae Hoon Chung ◽  
Seong Ihl Woo
Keyword(s):  
High Performance ◽  
Low Frequency ◽  
Frequency Region ◽  
Transfer Resistance ◽  
One Dimensional ◽  
Nitrogen Doped ◽  
Efficient Charge ◽  
Nitrogen Doped Graphene ◽  
Doped Graphene ◽  
Low Mass

In supercapacitors, one dimensional graphene ribbons which form net-like porous structure demonstrate low mass transfer resistance at low frequency region and a consequent efficient charge transferability.

Tunable Nonlinear Band Gaps in a Sandwich-Like Meta-Plate

2021 ◽  
Author(s):  
Yu Xue ◽  
Jinqiang Li ◽  
Yu Wang ◽  
Fengming Li
Keyword(s):  
Band Gap ◽  
Vibration Suppression ◽  
Wave Attenuation ◽  
Structural Parameters ◽  
Low Frequency ◽  
Dispersion Analysis ◽  
Response Analysis ◽  
Working Mechanism ◽  
Frequency Wave ◽  
The Galerkin Method

Abstract This paper aims to explore the actual working mechanism of sandwich-like meta-plates by periodically attaching nonlinear mass-beam-spring (MBS) resonators for low-frequency wave absorption. The nonlinear MBS resonator consists of a mass, a cantilever beam and a spring that can provide negative stiffness in the transverse vibration of the resonator, and its stiffness is tunable by changing the parameters of the spring. Considering the nonlinear stiffness of the resonator, the energy method is applied to obtain the dispersion relation of the sandwich-like meta-plate and the band-gap bounds related to the amplitude of resonator is derived by dispersion analysis. For the finite sized sandwich-like meta-plate with the fully free boundary condition subjected to external excitations, its dynamic equation is also established by the Galerkin method. The frequency response analysis of the meta-plate is carried out by the numerical simulation, whose band-gap range demonstrates good agreement with the theoretical one. Results show that the band-gap range of the present meta-plate is tunable by the design of the structural parameters of the MBS resonator. Furthermore, by analyzing the vibration suppression of the finite sized meta-plate, it can be observed that the nonlinearity of resonators can widen the wave attenuation range of meta-plate.

Detection of Underwater Low-frequency Acoustic Signal and Wave Attenuation

2013 ◽  
Vol 42 (4) ◽  
pp. 432-436
Author(s):  
苗润才 MIAO Run-cai ◽  
王玉明 WANG Yu-ming ◽  
孟峰 MENG Feng ◽  
马静 MA Jing
Keyword(s):  
Acoustic Signal ◽  
Wave Attenuation ◽  
Low Frequency
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