具有翻转层的铌酸锂梁弯曲振动研究

Study on Flexural Vibration of Lithium Niobate Beam with an Inversion Layer

研究了一种具有翻转层的新型铌酸锂梁,其翻转层与常规层的压电系数具有相反的符号,在厚度方向上施加电场可激发铌酸锂梁做弯曲振动。将位移和电势表达为梁的厚度和宽度方向的幂级数形式,推导了该种铌酸锂梁弯曲运动的一维方程。利用此一维方程分析了波沿梁长度方向传播的色散关系,以验证其精确程度。结果表明,所推导的一维方程在小波数范围内的色散曲线与三维精确解结果吻合良好;再用所得一维方程分析了梁式压电俘能器的输出功率密度和输出效率,将所得结果与由二维理论、三维理论所得结果进行对比。结果表明,一维方程所得结果与三维方程的结果接近,说明其在压电器件领域极具应用潜力。

A new type of lithium niobate beam with an inversion layer was investigated in this study.The symbols for the piezoelectric constants of this inversion layer were the opposite of those of a regular layer.Thus,the bending vibration of the lithium niobate beam could be excited by an electric field in the thickness direction.The displacement and potential were expressed in a power series form along the thickness and width directions of the beam,and one-dimensional equations of the bending motion of the lithium niobate beam were derived.These one-dimensional equations were used to analyze the dispersion relationship of the wave propagating along the length direction of the beam in order to verify its accuracy.The dispersion curves obtained from these one-dimensional equations coincided with those obtained using the three-dimensional theory in a small wavenumber range.The output power density and output efficiency of a beam-type piezoelectric energy harvester were analyzed using the one-dimensional equations.The results were compared with those derived using the two-dimensional and three-dimensional theories.The results indicated that the results obtained from the one-dimensional equations were very close to those obtained using the three-dimensional equations,suggesting their great application potential in the field of piezoelectric devices.