摘要
Based on the new modified couple stress theory and considering the flexoelectric effect of the piezoelectric layers,the Euler Bernoulli nano-beam model of composite laminated materials driven by electrostatically fixed supports at both ends is established. The nonlinear differential governing equations and boundary conditions are derived by the Hamilton principle. The generalized differential quadrature method(GDQM) and the Newton Raphson method are used to numerically solve the differential governing equations. The influence of flexoelectric effect on the static and the dynamic pull-in characteristics of laminated nano-beams is analyzed. The results of the numerical calculation are in a good agreement with those in the literature when the model degenerated into a nanobeam model without flexoelectric effect. The stacking sequence,length scale parameter l and piezoelectric layer applied voltage V_(p) of the composite will affect the pull-in voltage,frequency and time-domain response of the structure. Given that the flexoelectric effect will reduce the pull-in voltage and dimensionless natural frequency of the structure,the maximum dimensionless displacement at the midpoint of the beam and the period of time-domain response should be increased.
基于新修正偶应力理论,在考虑挠曲电效应的情况下,建立了两端固支静电驱动复合材料层合Euler-Bernoulli纳米梁模型,通过Hamilton原理导出其非线性微分控制方程以及边界条件,选用广义微分求积法(Generalized differential quadrature method,GDQM)和Newton-Raphson法对微分控制方程进行数值求解,分析了挠曲电效应对层合纳米梁静态和动态吸合特性产生的影响。结果表明:考虑挠曲电效应的复合材料层合纳米梁模型退化为不考虑挠曲效应的纳米梁模型后的数值计算结果与已有文献中数据相吻合。复合材料的铺层顺序、长度尺度参数l以及压电层施加电压V_(p)等参数对结构的吸合电压、频率以及时域响应都会产生影响。同时,考虑挠曲电效应会使得结构的吸合电压和量纲化为一的固有频率减小,梁中点最大量纲化为一的位移和时域响应的周期增大。
