【摘要】 基于修正的应变梯度理论，研究横向和纵向磁场下导电矩形微板的固有振动。利用Kirchhoff板理论建立力学模型，采用修正的应变梯度理论描述尺寸效应，借助Maxwell电磁理论计算涡流产生的洛伦兹力。在Hamilton’s原理框架下，建立磁弹性耦合的尺寸相关动力学方程。利用Galerkin法对控制方程进行时空离散，通过状态空间法解析获得系统固有频率。结果表明：修正的应变梯度理论比修正的偶应力理论、经典理论更能精确刻画微板的动力学行为；板厚接近材料尺度参数或板形状趋近正方形时，系统固有频率明显增加；纵向磁场对固有频率的影响较横向磁场更为明显。更多还原

【Abstract】 Based on the modified strain gradient theory, the natural vibration of conductive rectangular microplates in transverse and longitudinal magnetic fields was studied. A mechanical model was established using the Kirchhoff plate theory; the MSGT was used to describe the size effect, and the Lorentz force generated by eddy currents was calculated using the Maxwell electromagnetic theory. By virtue of the Hamilton’s principle, the size-dependent dynamic equations considering magnetoelastic coupling were established. The governing equations were discretized in time and space by the Galerkin method, and the frequency of the system was obtained analytically through the state space method. The results show that the MSGT can more accurately describe the dynamic behavior of the microplate than the modified couple stress theory and the classical theory; when the plate thickness approaches the material scale parameter or the plate shape approaches square, the frequency increases significantly; the longitudinal magnetic field affects the frequency more obviously than the transverse magnetic field.更多还原