剪切型压电层合圆柱壳的精确解  

EXACT SOLUTION FOR LAMINATED CYLINDRICAL SHELLS WITH PIEZOELECTRIC SHEAR ACTUATORS

作　　者：李红云[1] 孙雁[1] 刘正兴[1] 

机构地区：[1]上海交通大学工程力学系,上海200030

出　　处：《复合材料学报》2005年第3期162-167,共6页Acta Materiae Compositae Sinica

基　　金：国家自然科学基金资助(10132010)

摘　　要：对剪切型压电层合圆柱壳在电场和机械力作用下的应力场、位移场和电势分布进行了分析。在每层的局部坐标系下对该层的应力场、位移场和电势进行傅立叶展开,然后采用状态空间方法得到变系数的8维一阶常微分方程组,采用Frobenius方法得到应力场、位移场和电势的解。数值算例显示了电场和机械力作用下,壳体厚度对应力场和位移场分布的不同影响。得到的3维精确解为其他剪切型压电弹性层合壳的壳体理论提供理论依据和验证。The exact solution of piezoelastic laminated cylindrical shells embedded with shear piezoelectric actuators was discussed. Under the local surface coordinates, each of the response quantities of every layer of the shell was expanded in a double Fourier series. Eight first-order ordinary homogeneous differential equations with variable coefficients were generated using state-space approach. The solutions of displacement, stress and electric potential of the cylindrical shell were got using the Frobenius method. The numerical results show the different effects of the thickness ratios on the response quantities for mechanical and electric loads: (1) the axial displacement exhibits a zigzag variation for various thickness shells, but approaches linear distribution through the entire shell thickness for thin shells under mechanical loading; (2) transverse stresses σz and τθz show strong nonlinear under electric potentials, but are piecewise linear for thin shells under mechanical loading; (3) the electric potential is piecewise linear for both electric and mechanical loads. The results could help to verify other laminate theories for multilayer cylindrical shells with shear actuators.

关 键 词：压电弹性 剪切作动 圆柱壳 状态空间法 Frobenius方法 

分 类 号：O343.1[理学—固体力学] TB330.1[理学—力学]