多鐵纖維複合材料反平面剪力波之散射

Abstract

磁電耦合效應為材料在外加磁場作用下產生電極化，或在外加電場作用下產生磁極化的現象，常應用於感測器、致動器與能量轉換器上。因多數單相多鐵性材料的磁電耦合效應過於微弱，無法實際應用於工程，故發展出多鐵性複合材料以提升磁電耦合效應。 本研究探討具非完美交界面壓電壓磁複合材料，在反平面剪力波(SH wave)的作用下之彈性位移、電勢能與磁勢能收斂性、方向場型(directivity pattern)、勢能場分佈(potential field distribution)與散射截面(scattering cross-section)。本文使用之壓電材料為鈦酸鋇(BaTiO3)，壓磁材料為鈷鐵氧(CoFe2O4)。當壓電置入壓磁母材，強非完美交界面(Mechanically stiff and highly electromagnetic conducting interface)條件對彈性位移、電勢能與磁勢能收斂性、方向場型和散射截面影響顯著；而弱非完美交界面(Mechanically compliant and weakly electromagnetic conducting interface)條件則僅對磁勢能收斂性有影響。相對地，當壓磁置入壓電母材，強非完美交界面條件對電勢能與磁勢能收斂性、勢能場分佈與散射截面有影響；而弱非完美交界面條件則對彈性位移、電勢能與磁勢能收斂性及勢能場分佈有顯著影響。方向場型在內含物 處對高頻率入射波敏感。散射截面則受彈性非完美界面影響，在低頻剪力波入射時，會使其先被激發至一極值，其後再進行較緩和地變化。

Magnetoelectricity refers to the magnetization induced by an electric field, or conversely the polarization induced by a magnetic field. The coupling between the electric and magnetic fields provides opportunities for technological applications in sensing, actuation, and data storage. However, this coupling is limited to monolithic or single-phase materials, and is often observed only at very low temperatures. Therefore, researchers have turned to composite media consisting of piezoelectric (PE) and piezomagnetic (PM) phases. In this thesis, we consider the scattering of an anti-plane shear wave by a PE (PM) circular cylinder in a PM (PE) matrix. Two kinds of imperfect contact cases are investigated: (I) mechanically stiff and highly electromagnetic conducting interfaces, and (II) mechanically compliant and weakly electromagnetic conducting interfaces. Numerical results show that for the mechanical imperfection interface, the directivity pattern of shadow side (θ= 0) is more sensitive than that of the incident side (θ=π) as the frequency increases. For the PE in PM composite, case (I) has great influence on the convergence of potentials, directivity pattern and scattering cross-section, while case (II) has only influence on the convergence of magnetic potential. For the PM in PE composite, case (I) has influence on the convergence of electromagnetic potential, potential field distribution, scattering cross-section, while case (II) has influence on the convergence of potentials, and the potential field distribution.