摘要
Background, Motivation and Objective Periodic multilayered magnetoelectric composites, whose unit cell consists of alternately stacked piezoelectric and piezomagnetic material layers, have potential applications in fast-response sensors, transducers and filters. Due to the elastic wave bands in periodic multilayered magnetoelectric composites, these acoustic wave devices can usually entail superior performance. Consequently, it is essential to investigate the elastic wave bands in periodic multilayered magnetoelectric composites. Through comprehensive literature survey about this topic, it is found that although the SH wave bands in periodic multilayered magnetoelectric composites have been studied, few attention has been paid on P-SV wave bands. Therefore, in this paper we focus on the analysis of P-SV wave bands in periodic multilayered magnetoelectric composites made of transversely isotropic piezoelectric and piezomagnetic materials, in which the SH waves and P-SV waves are uncoupled. This paper has two objectives. First, an alternative analytical method, i.e. the method of reverberation-ray matrix(MRRM) is extended to the analysis of the P-SV wave bands in periodic multilayered transversely-isotropic magnetoelectric composites. Second, comprehensive dispersion curves of P-SV waves in periodic transversely-isotropic magnetoelectric composites are calculated, from which the general dispersion properties of P-SV waves in this kind of material are summarized. Statement of Contribution/Methods As an alternative analytical method, the method of reverberation-ray matrix(MRRM) for the analysis of the P-SV wave bands in periodic multilayered transversely-isotropic magnetoelectric composites, are formulated based on the state space formalism and two-dimensional elasticity of transversely isotropic piezoelectric and piezomagnetic materials. The state equations of any transversely isotropic piezoelectric or piezomagnetic layer are derived in dual local coordinates, which are solved to obtain the traveling wave solutions with unknown wave amplitudes. The compatibility conditions of state variables in the dual local coordinates within all layers and the coupling conditions of state variables in layers at all joints lead to the phase and scattering relations. These two kinds of relations are combined to give the system equations. Then the vanishing of the determinant of system matrix(coefficient matrix of the system equations) results to dispersion equation, which can be solved numerically by a root searching method to give the band properties. Results Take periodic transversely-isotropic magnetoelectric composites with the unit cell consisting of Ba Ti O3 and Co Fe2O4 layers as example. Comprehensive dispersion curves of P-SV waves, which include the frequency-wavenumber curve, the frequency-wavelength curve, the frequency-phase velocity curve, the wavenumber-phase velocity curve and the wavelength-phase velocity curve, are calculated by searching the roots of the dispersion equation numerically. Some results are compared with the corresponding ones in reference to validate the proposed method. General dispersion properties of P-SV waves in periodic transversely-isotropic magnetoelectric composites are then summarized. Discussion and Conclusions From the derivation of the proposed MRRM, it is noticed that the formulation is free from exponentially growing function and has uniformity for any complicated unit cell. Numerical examples indicate that the proposed MRRM is numerically stable and gives accurate results. Some general dispersion properties of P-SV waves in periodic transversely-isotropic magnetoelectric composites are noticed. For examples: Only the frequency-related dispersion curves reflect the band properties; The pass-bands and the stop-bands usually appear alternately within boundary frequencies.
Background, Motivation and Objective Periodic multilayered magnetoelectric composites, whose unit cell consists of alternately stacked piezoelectric and piezomagnetic material layers, have potential applications in fast-response sensors, transducers and filters. Due to the elastic wave bands in periodic multilayered magnetoelectric composites, these acoustic wave devices can usually entail superior performance. Consequently, it is essential to investigate the elastic wave bands in periodic multilayered magnetoelectric composites. Through comprehensive literature survey about this topic, it is found that although the SH wave bands in periodic multilayered magnetoelectric composites have been studied, few attention has been paid on P-SV wave bands. Therefore, in this paper we focus on the analysis of P-SV wave bands in periodic multilayered magnetoelectric composites made of transversely isotropic piezoelectric and piezomagnetic materials, in which the SH waves and P-SV waves are uncoupled. This paper has two objectives. First, an alternative analytical method, i.e. the method of reverberation-ray matrix(MRRM) is extended to the analysis of the P-SV wave bands in periodic multilayered transversely-isotropic magnetoelectric composites. Second, comprehensive dispersion curves of P-SV waves in periodic transversely-isotropic magnetoelectric composites are calculated, from which the general dispersion properties of P-SV waves in this kind of material are summarized. Statement of Contribution/Methods As an alternative analytical method, the method of reverberation-ray matrix(MRRM) for the analysis of the P-SV wave bands in periodic multilayered transversely-isotropic magnetoelectric composites, are formulated based on the state space formalism and two-dimensional elasticity of transversely isotropic piezoelectric and piezomagnetic materials. The state equations of any transversely isotropic piezoelectric or piezomagnetic layer are derived in dual local coordinates, which are solved to obtain the traveling wave solutions with unknown wave amplitudes. The compatibility conditions of state variables in the dual local coordinates within all layers and the coupling conditions of state variables in layers at all joints lead to the phase and scattering relations. These two kinds of relations are combined to give the system equations. Then the vanishing of the determinant of system matrix(coefficient matrix of the system equations) results to dispersion equation, which can be solved numerically by a root searching method to give the band properties. Results Take periodic transversely-isotropic magnetoelectric composites with the unit cell consisting of Ba Ti O3 and Co Fe2O4 layers as example. Comprehensive dispersion curves of P-SV waves, which include the frequency-wavenumber curve, the frequency-wavelength curve, the frequency-phase velocity curve, the wavenumber-phase velocity curve and the wavelength-phase velocity curve, are calculated by searching the roots of the dispersion equation numerically. Some results are compared with the corresponding ones in reference to validate the proposed method. General dispersion properties of P-SV waves in periodic transversely-isotropic magnetoelectric composites are then summarized. Discussion and Conclusions From the derivation of the proposed MRRM, it is noticed that the formulation is free from exponentially growing function and has uniformity for any complicated unit cell. Numerical examples indicate that the proposed MRRM is numerically stable and gives accurate results. Some general dispersion properties of P-SV waves in periodic transversely-isotropic magnetoelectric composites are noticed. For examples: Only the frequency-related dispersion curves reflect the band properties; The pass-bands and the stop-bands usually appear alternately within boundary frequencies.
引文