剪切型压电层合圆柱壳的精确解

EXACT SOLUTION FOR LAMINATED CYLINDRICAL SHELLSWITH PIEZOELECTRIC SHEAR ACTUATORS

  • 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。

     

    Abstract: The exact solution of piezoelastic laminated cylindrical shells embedded with shear piezoelect ric actuators was discussed1Under the local surface coordinates, each of the response quantities of every layer of the shellwas expanded in a double Fourier series1 Eight first-order ordinary homogeneous differential equations with variablecoefficient s were generated using state-space approach. The solutions of displacement, st ress and elect ric potentialof the cylindrical shell were got using the Frobenius method1 The numerical result s show the different effect s of thethickness ratios on the response quantities for mechanical and elect ric loads : (1) the axial displacement exhibit s azigzag variation for various thickness shells, but approaches linear dist ribution through the entire shell thickness forthin shells under mechanical loading ; ( 2 ) t ransverse st resses σz and τθz show st rong nonlinear under elect ricpotentials, but are piecewise linear for thin shells under mechanical loading ; (3) the elect ric potential is piecewiselinear for both elect ric and mechanical loads1 The result s could help to verify other laminate theories for multilayercylindrical shells with shear actuators.

     

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