Handbook of Mathematics

Bronshtein, I. N.; Semendyayev, K. A.; Musiol, G.; Muehlig, Heiner

doi:10.1007/978-3-662-05382-9

Cited by 235 publications

(185 citation statements)

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“…For any piezoelectric rod in the unit cell, say member j, applying Fourier transform [36] (p. 725) to the time-domain governing equations and constitutive relations, as given in Equations (A12) and (A11), leads to the frequency-domain counterparts as…”

Section: Governing Equations and Wave Solutions Of A Constituent Rodmentioning

confidence: 99%

“…The specified electrical coefficients are external capacitance C and control gain K g for the applied electric capacity and the applied feedback control conditions, respectively, while the electric-open and the electric-short conditions do not have specified electrical coefficient. According to the theory of ordinary differential equations [36] (p. 503), the solution to the spectral axial displacement can be obtained directly from Equation (1). Substituting the above expressions of dφ{dx into the first formula of Equation (2) and then introducing the solution to the spectral axial displacement, one obtains the wave solution to the spectral axial force.…”

Section: Governing Equations and Wave Solutions Of A Constituent Rodmentioning

confidence: 99%

“…The first and the second terms in the two formulas of Equation (4), when combining with the kernel function e iωt of the Fourier transform [36] (p. 725), represent waves traveling along the negative and positive x-axis that are called as the arriving and departing waves, respectively. a 1 and d 1 are the corresponding undetermined wave amplitudes.…”

Section: Governing Equations and Wave Solutions Of A Constituent Rodmentioning

confidence: 99%

“…or any elastic rod (or electrode) in the unit cell, say member h (or i), the frequency-domain governing equation and constitutive relation are obtained by Fourier transform [36] (p. 725) to their time-domain counterparts, as given in Equations (A17) and (A18)…”

Section: Governing Equations and Wave Solutions Of A Constituent Rodmentioning

confidence: 99%

“…which indicates that e iqL " µ is the eigenvalue of the global transfer matrix T with referring to the definition of the eigenvalues of a matrix [36] (pp. 278-279).…”

Section: Dispersion Relation Of Infinite Periodic Structuresmentioning

confidence: 99%

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Analysis of Longitudinal Waves in Rod-Type Piezoelectric Phononic Crystals

Guo

2016

Crystals

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Phononic crystals can be used to control elastic waves due to their frequency bands. This paper analyzes the passive and active control as well as the dispersion properties of longitudinal waves in rod-type piezoelectric phononic crystals over large frequency ranges. Based on the Love rod theory for modeling the longitudinal wave motions in the constituent rods and the method of reverberation-ray matrix (MRRM) for deriving the member transfer matrices of the constituent rods, a modified transfer matrix method (MTMM) is proposed for the analysis of dispersion curves by combining with the Floquet-Bloch principle and for the calculation of transmission spectra. Numerical examples are provided to validate the proposed MTMM for analyzing the band structures in both low and high frequency ranges. The passive control of longitudinal-wave band structures is studied by discussing the influences of the electrode's thickness, the Poisson's effect and the elastic rod inserts in the unit cell. The influences of electrical boundaries (including electric-open, applied electric capacity, electric-short and applied feedback control conditions) on the band structures are investigated to illustrate the active control scheme. From the calculated comprehensive frequency spectra over a large frequency range, the dispersion properties of the characteristic longitudinal waves in rod-type piezoelectric phononic crystals are summarized.

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Section: Governing Equations and Wave Solutions Of A Constituent Rodmentioning

confidence: 99%

Section: Governing Equations and Wave Solutions Of A Constituent Rodmentioning

confidence: 99%

Section: Governing Equations and Wave Solutions Of A Constituent Rodmentioning

confidence: 99%

Section: Governing Equations and Wave Solutions Of A Constituent Rodmentioning

confidence: 99%

“…which indicates that e iqL " µ is the eigenvalue of the global transfer matrix T with referring to the definition of the eigenvalues of a matrix [36] (pp. 278-279).…”

Section: Dispersion Relation Of Infinite Periodic Structuresmentioning

confidence: 99%

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Analysis of Longitudinal Waves in Rod-Type Piezoelectric Phononic Crystals

Guo

2016

Crystals

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Calibrating Dense Spatial Arrays for Amplitude Statics and Orientation Errors

Langston

2018

JGR Solid Earth

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An iterative procedure is designed to calibrate dense arrays of three‐component seismic instruments for station amplitude statics and horizontal component orientation errors. Station amplitude statics refers to differences in sensor and digitizer gains and amplification effects due to local site and installation conditions. Amplitude statics and orientation errors can seriously affect computation of the wavefield gradient tensor that is the basis of seismic strain and rotation computations as well as analysis of wave field attributes through wave gradiometry since wave spatial gradients rely on first‐order differences of the wavefield between sensors in an array. The technique is based on the assumption of a common wave field observed over a small array using teleseismic earthquake observations. In situ calibration of the broad band, 800‐m aperture array at Pinyon Flat, California, achieves relative amplitude precision for vertical components of the array from 0.16% to 0.25% and horizontal components from 0.16% to 0.61%. Relative sensor orientations can be determined to a precision better than 0.35°. Comparison of horizontal strains computed from array observations of a regional M4.9 earthquake and strains from the Gladwin Tensor borehole strain meter at Pinyon Flat shows excellent correspondence over the frequency band of 0.05 to 2 Hz. Agreement of borehole measured strains and seismic array strains for regional/local seismic events gives confidence that a borehole strain meter and single, three‐component, colocated seismometer can be used as a “point array” for deducing wavefield attributes from wave gradiometry.

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Bandwidth Extension of Telephony Speech

Haykin

2010

Adaptive Signal Processing

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Handbook of Mathematics

Cited by 235 publications

References 0 publications

Analysis of Longitudinal Waves in Rod-Type Piezoelectric Phononic Crystals

Analysis of Longitudinal Waves in Rod-Type Piezoelectric Phononic Crystals

Calibrating Dense Spatial Arrays for Amplitude Statics and Orientation Errors

Bandwidth Extension of Telephony Speech

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