A Nonlocal Strain Gradient Approach for Out-of-Plane Vibration of Axially Moving Functionally Graded Nanoplates in a Hygrothermal Environment

Chengxiu Zhu,Jianwei Yan,Pingyuan Wang,Cheng Li,Fabio Botta

doi:10.1155/2021/8332125

Abstract

Vibration analyses on axially moving functionally graded nanoplates exposed to hygrothermal environments are presented. The theoretical model of the nanoplate is described via the Kirchhoff plate theory in conjunction with the concept of the physical neutral layer. By employing the nonlocal strain gradient theory, the governing equation of motion is derived based on Hamilton’s principle. The composite beam function method, as well as the complex modal approach, is utilized to obtain the vibration frequencies of axially moving functionally graded nanoplates. Some benchmark results related to the effects of temperature changing, moisture concentration, axial speed, aspect ratio, nonlocal parameter, and the material characteristic scale parameter on the stiffness of axially moving functionally graded nanoplates are obtained. The results reveal that with increasing the nonlocal parameter, gradient index, temperature changing, moisture concentration, and axial speed, the vibration frequencies decrease. The frequencies increase while increasing the material characteristic scale parameter and aspect ratio. Moreover, there is an interaction between the nonlocal parameter and material characteristic scale parameter, influencing and restricting each other.

Highlights

With the rise of micro/nanotechnologies, the development and application of micro/nano-electromechanical systems (MEMS/NEMS) have developed rapidly, such as micro/nanosensors, micro/nanoresonators, smart wearable devices, and medical nanorobots [1, 2]. e systematic and in-depth understandings of the mechanical properties of these devices and their key micro/nanocomponents are needed to provide theoretical guidance for the mechanical-based design and regulation [3, 4]
There have been numerous investigations on this topic, especially the studies on the mechanical behavior of uniform nanomaterials and structures based on the molecular dynamic simulation or nonclassical continuum approaches [5,6,7,8,9]. ese results play an important role in perfecting performances and promoting the industrialization of MEMS/NEMS [10] and cellular mechanics [11]
The summary is concluded in Section 4. e results of the present work are of reference significance for the design, optimization, and control of axially moving MEMS/ NEMS based on functionally gradient nanoplates, such as nanorobots and nanosensors subjected to hygrothermal environments

Summary

Introduction

With the rise of micro/nanotechnologies, the development and application of micro/nano-electromechanical systems (MEMS/NEMS) have developed rapidly, such as micro/nanosensors, micro/nanoresonators, smart wearable devices, and medical nanorobots [1, 2]. e systematic and in-depth understandings of the mechanical properties of these devices and their key micro/nanocomponents are needed to provide theoretical guidance for the mechanical-based design and regulation [3, 4]. E novelty of this research is to explore the effects of the axial speed, gradient index, and internal and external characteristic parameters on the vibration of axially moving functionally graded nanoplates exposed to hygrothermal environments. E remaining parts of the present work are arranged as follows: In Section 2, the theoretical model of the axially moving functionally graded nanoplate subjected to hygrothermal loads is established, and the effect of the gradient index on the bending stiffness is demonstrated. E results of the present work are of reference significance for the design, optimization, and control of axially moving MEMS/ NEMS based on functionally gradient nanoplates, such as nanorobots and nanosensors subjected to hygrothermal environments. To analyze the out-of-plane vibration of axially moving functionally graded nanoplates in hygrothermal environments, Hamilton’s principle is utilized to derive the governing equation of motion, which requires t2. The hygrothermal resultant can be expressed by h/2

Metal p

Numerical Results and Discussion

Conclusions