Linear Piezoelectric Plate Vibrations

Tiersten, H. F.

doi:10.1007/978-1-4899-6453-3

Cited by 768 publications

(363 citation statements)

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“…139-142), [30], which considers the Poisson's effect, the time-domain equations governing the longitudinal wave motions in any of the constituent rods described in its dual local coordinates can be derived by Hamilton principle [29] (pp. 126-131), [34]. The assumptions of the Love rod with considering the Poisson's effect include: (1) The axial displacement (electric potential) is uniformly distributed on any cross-section of the rod.…”

Section: Governing Equations and Wave Solutions Of A Constituent Rodmentioning

confidence: 99%

“…The proportional coefficients are the multiplication of the corresponding Poisson's ratios with the axial strain of that cross-section. Apply these assumptions and the three-dimensional elasticity [33,34], [35] (pp. 57-60), the derivation for a piezoelectric rod is detailed in Appendix A, and that for an elastic rod which representing any of the elastic rods and the electrodes is briefed in Appendix B.…”

Section: Governing Equations and Wave Solutions Of A Constituent Rodmentioning

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%

Analysis of Longitudinal Waves in Rod-Type Piezoelectric Phononic Crystals

Guo

2016

Crystals

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“…The geometric parameters are c = 20 mm, c 1 = 4.5 mm, c 2 = 9.5 mm, c 3 = 10.5 mm, c 4 = 15.5 mm, and 2h = 0.3 mm. The material constants needed can be found in [11]. The structure is symmetric about x 3 = c/2.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…For AT-cut quartz plates, c 55 = 68.81, c 56 = 2.53 and c 66 = 29.01 Â 10 9 N/m 2 [11]. c 56 is very small compared to c 55 and c 66 .…”

Section: Fig 2 Antisymmetric Trapped Modes (Identical Electrodes)mentioning

confidence: 93%

“…There exist systematic theoretical results from the 2D plate equations for TSh modes with in-plane variation in one direction only, i.e., in the direction parallel to the TSh particle velocity. Free vibration modes of finite plates with free edges and their frequency spectra [8][9][10], energy trapping in partially electroded plates and Bechmann's number regarding electrode dimension [4], monolithic filters with two pairs of electrodes [11], arrays of multiple resonators [12,13], and resonator capacitance from forced vibration analyses [14] have been obtained.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of a monolithic crystal plate acoustic wave filter

Liu

Yang

2011

Ultrasonics

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a b s t r a c tWe study thickness-shear and thickness-twist vibrations of a finite, monolithic, AT-cut quartz plate crystal filter with two pairs of electrodes. The equations of anisotropic elasticity are used with the omission of the small elastic constant c 56 . An analytical solution is obtained using Fourier series from which the resonant frequencies, mode shapes, and the vibration confinement due to the electrode inertia are calculated and examined.

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Reflection and Transmission of Shear Waves in Monoclinic Media

Chattopadhyay

Saha

Chakraborty

1997

Int. J. Numer. Anal. Meth. Geomech.

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This paper deals with the propagation, reflection and transmission of shear waves in monoclinic media. The dispersion equation for a monoclinic layer overlying a monoclinic half-space has been obtained and curves are plotted. The amplitude ratios for both the reflected and transmitted waves due to reflection of shear waves at the interface of two monoclinic half-spaces have also been computed and the numerical results are presented graphically. The results are compared with the isotropic case. It has been observed that, in monoclinic media, the amplitude ratios for reflected and transmitted wave increases approximately by 25 and 50 per cent respectively, in comparison to the isotropic case.

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Linear Piezoelectric Plate Vibrations

Cited by 768 publications

References 0 publications

Analysis of Longitudinal Waves in Rod-Type Piezoelectric Phononic Crystals

Analysis of Longitudinal Waves in Rod-Type Piezoelectric Phononic Crystals

Analysis of a monolithic crystal plate acoustic wave filter

Reflection and Transmission of Shear Waves in Monoclinic Media

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