线性分布荷载作用下梯度功能压电悬臂梁的解

PIEZOELECTRIC CANTILEVER ACTUATOR SUBJECTED TO A LINEARLY DISTRIBUTED LOADING

采用逆解法求解了上表面受线性分布荷载作用的压电悬臂梁执行器,其中体积力Fz呈非线性分布.首先确定了应力函数和电位移函数的多项式表达式,进而研究了该问题的通解,以及体积力的不同分布对解答的影响.常体积力和无体力情况下的解可以由上述解直接得到.本文为研究其它类型的压电梯度微观结构提供了一种可行的方法.

The inverse method is traditionally used to solve elastic problems. In the present paper this method is applied for a piezoelectric cantilever actuator subjected to a linear distributed loading on the upper surface. Nonlinear body force Fz is also considered. The stress function and induction function in the form of polynomials are obtained. The general solutions as well as the influence of the distribution profile of body force on this solution are discovered. From this conclusion the solutions of the cantilever actuator with constant body force and without body force can be easily found. This work provides a feasible method to study other kinds of functionally gradient piezoelectric microstructures.