Timoshenko beam model is applied to study the flexomagnetic effect in a cantilever beam. The size-effect phenomenon in a piezomagnetic body is considered by the strain-gradients in the constitutive equation for the magnetic induction. The principle of virtual work is applied to derive general governing equations. The effect of flexomagneticity on the Timoshenko piezomagnetic beam is analytically investigated. The developed general beam model recovers to the classical Timoshenko beam model with vanishing flexomagnecity. The numerical results reveal that both the deflection and rotation are reduced with respect to the classical Timoshenko beam model. The reduction of deflection and rotation is more intensive if the beam thickness is decreasing.

Timoshenko 梁模型用于研究悬臂梁中的挠磁效应。压电体中的尺寸效应现象通过磁感应的本构方程中的应变梯度来考虑。应用虚功原理推导出一般控制方程。分析研究了挠曲磁性对 Timoshenko 压电梁的影响。开发的通用梁模型恢复到经典的 Timoshenko 梁模型，具有消失的柔韧性。数值结果表明，相对于经典的 Timoshenko 梁模型，偏转和旋转都减少了。如果梁厚度减小，偏转和旋转的减少会更加强烈。