压电/压磁层合纳米梁屈曲及自由振动的研究 1)

针对压电/压磁层合纳米梁屈曲、自由振动问题，基于非局部理论与正弦剪切型变形梁理论，建立了力学模型；利用哈密顿原理推导出层合梁运动方程与边界条件；通过数值解法求得层合梁临界屈曲载荷与自由振动频率。对数值结果分析可知：磁电弹夹层对压电/压磁层合纳米梁屈曲和自由振动的影响不能忽略；磁电弹夹层中压电或压磁材料的体积分数和夹层厚度为主要影响因素；分析得到的影响规律可为此类材料在工程中的应用提供理论参考。

BUCKING AND FREE VIBRATION OF PIEZOELECTRIC/PIEZOMAGNETIC LAMINATED NANO-BEAM 1)

For the problem of buckling and free vibration of piezoelectric/piezomagnetic laminated nano-beams, a mechanical model is established based on the non-local theory and the sinusoidal shear deformation beam theory. The motion equations and the boundary conditions of the laminated beam are derived by the Hamilton's principle. The critical buckling load and the free vibration frequency of the laminated beam are obtained by the numerical method. The numerical results show that the effects of the magneto-electro-elastic interlayer on the buckling and the free vibration of the piezoelectric/piezomagnetic laminated nano-beam cannot be ignored. The volume fraction of the piezoelectric materials or piezomagnetic materials and the thickness of the interlayer are the main influencing factors. The influence analysis can provide a theoretical reference for the application of such materials in engineering.