粘贴压电层功能梯度材料Euler梁热屈曲前自由振动的半解析数值法

Semi-Analytic Numerical Method for Free Vibration before Thermal Post-Buckling of Functionally Graded Material Euler Beams with Surface-Bonded Piezoelectric Layers

研究上下表面粘贴压电层的功能梯度材料Euler梁在升温及电场作用下的振动行为。在精确考虑轴线伸长基础上,建立压电功能梯度Euler层合梁在热-电-机械载荷作用下的几何非线性动力学控制方程。其中,假设功能梯度的材料性质沿厚度方向按照幂函数连续变化,压电层为各向同性均匀材料。把问题线性化,利用打靶法,获得在均匀电场和横向非均匀升温场内两端固定和两端简支Euler梁在热屈曲前自由振动特性的半解析数值解。由于材料在横向的非均匀性,即使在均匀升温和均匀电场作用下,梁内仍然会产生拉-弯耦合效应,对梁的自振频率也有一定的影响。

Free vibration before thermal buckling of functionally graded material Euler beams with surface-bonded piezoelectric layers subjected to temperature rise and electric field were studied.By accurately considering the axial extension in the sense of theory of Euler beam,geometrically nonlinear governing equations,for functionally graded beams subjected to thermo-electro-mechanical loadings,were formulated.In the analysis,it was assumed that the material properties of the beam vary continuously as a power function of the thickness coordinate and that the piezoelectric layers are isotropic and homogenous.By using a shooting method to solve the linearized equations,a semi-analytic numerical method is proposed to predict the free vibration behavior of the beams with the fixed and simply supported edges subjected to transversely non-uniform heating and uniform electric field.Due to being transversely non-uniform in the material properties,there exists tension-bending coupling effects on the beam even in uniform temperature and electric rise in the thickness direction,which could impact the natural frequencies to some extent.