Band-gap and pass-band classification for oblique waves propagating in a three-dimensional layered functionally graded piezoelectric phononic crystal

Fomenko, Sergey I.; Golub, Mikhail V.; Chen, A‐Li; Wang, Yue‐Sheng; Zhang, Chuanzeng

doi:10.1016/j.jsv.2018.09.059

Cited by 29 publications

(9 citation statements)

References 39 publications

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“…where q and H are the wavenumber of the characteristic coupled elastic waves in and the height of the unit cell, respectively, as can be seen in Figure 1. Combining Equation (28) with Equation (27) and eliminating the state vectorv (m) (h (m) ), one gets…”

Section: Dispersion Relation Of the Laminated Arbitrarily Anisotropicmentioning

confidence: 99%

“…Golub et al [25] and Fomenko et al [26] analyzed by TMM the dispersion properties (such as dispersion curves and transmission/reflection coefficients), the localization factor and the classification of pass-bands and band gaps in phononic crystals composed of a specific number of periodically arranged unit cells with homogenous or functionally-graded interlayers and elastic half-spaces on both sides, whose dependences on the incident angle and the gradation and geometrical properties of interlayers were also discussed. Very recently, this functionally-graded model was extended by Fomenko et al [27] to two cases, i.e., the infinite layered phononic crystals and finite counterparts between two isotropic half-spaces. The unit cell of both cases was composed of four piezoelectric sublayers with two being homogeneous and two being functionally graded.…”

Section: Introductionmentioning

confidence: 99%

“…As far as only the coupled P-SV waves are concerned, Geng and Zhang [36] analyzed the dispersion curves of parallelly propagating coupled P-SV waves in periodic piezoceramic-polymer composites by the method of partial wave expansion with special attention on the effects of the volume fraction and the polymer properties, which are partially validated through the experimentally measured thickness resonance (with polarization parallel to interface) and lateral resonance (with polarization along periodic direction) spectra. Regarding the three-dimensional (3D) coupled waves, besides some occasional discussions in Fomenko et al [27], Podlipenets [37] presented without validation a Hamiltonian system formalism to analyze the dispersion equations of bulk, surface, and plate waves in respectively the infinite, semi-infinite, and finite phononic crystals with constituent materials of mm2 or higher symmetry crystal. With respect to the surface/interface and guided waves, the laminated semi-infinite and finite transversely isotropic piezoelectric phononic crystals, respectively, with bounding plane either parallel or perpendicular to the layering plane have all been considered.…”

Section: Introductionmentioning

confidence: 99%

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Band Tunability of Coupled Elastic Waves along Thickness in Laminated Anisotropic Piezoelectric Phononic Crystals

Guo

Wang

et al. 2019

Crystals

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Although the passively adjusting and actively tuning of pure longitudinal (primary (P-)) and pure transverse (secondary or shear (S-)) waves band structures in periodically laminated piezoelectric composites have been studied, the actively tuning of coupled elastic waves (such as P-SV, P-SH, SV-SH, and P-SV-SH waves), particularly as the coupling of wave modes is attributed to the material anisotropy, in these phononic crystals remains an untouched topic. This paper presents the analytical matrix method for solving the dispersion characteristics of coupled elastic waves along the thickness direction in periodically multilayered piezoelectric composites consisting of arbitrarily anisotropic materials and applied by four kinds of electrical boundaries. By switching among these four electrical boundaries—the electric-open, the external capacitance, the electric-short, and the external feedback control—and by altering the capacitance/gain coefficient in cases of the external capacitance/feedback-voltage boundaries, the tunability of the band properties of the coupled elastic waves along layering thickness in the concerned phononic multilayered crystals are investigated. First, the state space formalism is introduced to describe the three-dimensional elastodynamics of arbitrarily anisotropic elastic and piezoelectric layers. Second, based on the traveling wave solutions to the state vectors of all constituent layers in the unit cell, the transfer matrix method is used to derive the dispersion equation of characteristic coupled elastic waves in the whole periodically laminated anisotropic piezoelectric composites. Finally, the numerical examples are provided to demonstrate the dispersion properties of the coupled elastic waves, with their dependence on the anisotropy of piezoelectric constituent layers being emphasized. The influences of the electrical boundaries and the electrode thickness on the band structures of various kinds of coupled elastic waves are also studied through numerical examples. One main finding is that the frequencies corresponding to (with the dimensionless characteristic wavenumber) are not always the demarcation between pass-bands and stop-bands for coupled elastic waves, although they are definitely the demarcation for pure P- and S-waves. The other main finding is that the coupled elastic waves are more sensitive to, if they are affected by, the electrical boundaries than the pure P- and S-wave modes, so that higher tunability efficiency should be achieved if coupled elastic waves instead of pure waves are exploited.

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Section: Dispersion Relation Of the Laminated Arbitrarily Anisotropicmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Band Tunability of Coupled Elastic Waves along Thickness in Laminated Anisotropic Piezoelectric Phononic Crystals

Guo

Wang

et al. 2019

Crystals

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“…However, the above-mentioned studies mainly focused on scalar waves with only one displacement component. In recent years, the propagation of three-dimensional (3D) harmonic waves in layered structures have been reported [31][32][33][34] . In our previous work, the nonreciprocal transmission in 3D cases in a layered nonlinear elastic wave metamaterial was discussed [35] .…”

Section: Introductionmentioning

confidence: 99%

Tunable three-dimensional nonreciprocal transmission in a layered nonlinear elastic wave metamaterial by initial stresses

Wang

2022

Appl. Math. Mech.-Engl. Ed.

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In this work, the three-dimensional (3D) propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses are investigated. The analytical solutions of the fundamental wave and second harmonic with the quasi-longitudinal (qP) and quasi-shear (qS1 and qS2) modes are derived. Based on the transfer and stiffness matrices, band gaps with initial stresses are obtained by the Bloch theorem. The transmission coefficients are calculated to support the band gap property, and the tunability of the nonreciprocal transmission by the initial stress is discussed. This work is expected to provide a way to tune the nonreciprocal transmission with vector characteristics.

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“…14 Aside from the extensive applications of periodic lattices in solid mechanics, one of the most interesting properties of these structures is their ability to manipulate the propagation of waves. Periodic lattices can stop the propagation of waves in certain frequency ranges [15][16][17][18] or tune their directionality. 19,20 Hence, the application of such structures can be expanded to dynamic and phononic fields such as vibration mitigation, [21][22][23] acoustic and elastic filtering, 24 bio-sensing, 25 and acoustic cloaking.…”

Section: Introductionmentioning

confidence: 99%

Wave propagation and directionality in two-dimensional periodic lattices considering shear deformations

Sepehri

Mashhadi

Fakhrabadi

2022

Proceedings of the Institution of Mechanical Engineers, Part N:

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The effects of shear deformation on analysis of the wave propagation in periodic lattices are often assumed negligible. However, this assumption is not always true, especially for the lattices made of beams with smaller aspect ratios. Therefore, in the present paper, the effect of shear deformation on wave propagation in periodic lattices with different topologies is studied and their wave attenuation and directionality performances are compared. Current experimental limitations make the researchers focus more on the wave propagation in the direction perpendicular to the plane of periodicity in micro/nanoscale lattice materials while for their macro/mesoscale counterparts, in-plane modes can also be analyzed as well as the out-of-plane ones. Four well-known topologies of hexagonal, triangular, square, and Kagomé are considered in the current paper and their wave propagation is investigated both in the plane of periodicity and in the out-of-plane direction. The finite element method is used to formulate the governing equations and Bloch’s theorem is used to solve the dispersion relations. To investigate the effect of shear deformation, both the Timoshenko and Euler-Bernoulli beam theories are implemented. The results indicate that including shear deformation in wave propagation has a softening effect on the band diagrams of wave propagation and moves the dispersion branches to lower frequencies. It can also reveal some bandgaps that are not predicted without considering the shear deformation.

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Band-gap and pass-band classification for oblique waves propagating in a three-dimensional layered functionally graded piezoelectric phononic crystal

Cited by 29 publications

References 39 publications

Band Tunability of Coupled Elastic Waves along Thickness in Laminated Anisotropic Piezoelectric Phononic Crystals

Band Tunability of Coupled Elastic Waves along Thickness in Laminated Anisotropic Piezoelectric Phononic Crystals

Tunable three-dimensional nonreciprocal transmission in a layered nonlinear elastic wave metamaterial by initial stresses

Wave propagation and directionality in two-dimensional periodic lattices considering shear deformations

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