An analytical solution for nonlinear vibration control of sandwich shallow doubly-curved nanoshells with functionally graded piezoelectric nanocomposite sensors and actuators

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.

Keywords:

• FGP sandwich shallow doubly-curved nanoshells
• nonlinear vibration control
• harmonic balance method
• analytical solution
• size-dependent effect

Additional information

Funding

This work is supported by the projects of National Natural Science Foundations of China (Nos. 11790282, 11872041), National Natural Science Foundations of Hebei, China (A2019210037), and the funded project for Innovative Graduates in Hebei, China (No. CXZZBS2019146).