Abstract

In this paper, the nonlinear vibration control of sandwich shallow doubly-curved nanoshells with functionally graded piezoelectric (FGP) nanocomposite sensors and actuators is investigated based on surface/interface piezoelectric theory and nonlocal piezoelectric theory. The FGP sandwich shallow doubly-curved nanoshell is supposed to rest on the visco-Pasternak foundation. To get a desired vibration response for the present system, the velocity feedback control strategy is employed in this paper. Within the framework of the first-order shear deformation theory, the nonlinear equations of motion are obtained by using Hamilton’s principle and solved by utilizing harmonic balance method. The main novelty of this paper is that an analytical solution is achieved for the nonlinear vibration control of the system with surface/interface effect and nonlocal effect under the nonuniform external electric field model. Through numerical examples, it is found that an excellent control effect can be achieved for the present system by optimizing the geometric parameters of FGP sandwich shallow doubly-curved nanoshells. The uniform external electric field model overestimates the damping characteristic of FGP sandwich shallow doubly-curved nanoshells, especially for the system with a great thickness. In addition, surface/interface density may play a dominant role in the surface/interface energy.

摘要

在本文中，基于表面/界面压电理论和非局部压电理论研究了具有功能梯度压电（FGP）纳米复合传感器和致动器的夹层浅双弯曲纳米壳的非线性振动控制。FGP 夹层浅双弯曲纳米壳应该位于粘胶-帕斯捷尔纳克基础上。为了获得当前系统所需的振动响应，本文采用速度反馈控制策略。在一阶剪切变形理论的框架内，利用Hamilton原理得到非线性运动方程组，并利用调和平衡法求解。本文的主要创新之处在于，在非均匀外电场模型下，实现了具有表面/界面效应和非局部效应的系统非线性振动控制的解析解。通过数值算例发现，通过优化FGP夹层浅双曲纳米壳的几何参数，可以对本系统实现良好的控制效果。均匀的外部电场模型高估了 FGP 夹层浅双弯曲纳米壳的阻尼特性，特别是对于厚度较大的系统。此外，表面/界面密度可能在表面/界面能量中起主导作用。发现通过优化FGP夹层浅双曲纳米壳的几何参数，可以对本系统实现良好的控制效果。均匀的外部电场模型高估了 FGP 夹层浅双弯曲纳米壳的阻尼特性，特别是对于厚度较大的系统。此外，表面/界面密度可能在表面/界面能量中起主导作用。发现通过优化FGP夹层浅双曲纳米壳的几何参数，可以对本系统实现良好的控制效果。均匀的外部电场模型高估了 FGP 夹层浅双弯曲纳米壳的阻尼特性，特别是对于厚度较大的系统。此外，表面/界面密度可能在表面/界面能量中起主导作用。