217 / 2021-04-04 00:28:41

Transverse Vibration of Axially Moving Functionally Graded Nanoplates in a Hygrothermal Environment based on the Nonlocal Strain Gradient Theory

Nonlocal Strain Gradient,Functionally Graded Nanoplate,Hygrothermal,Axially Moving

Vibration of continuous systems

A functionally graded nanoplate subjected to elastic vibration and rigid body motion is considered. From the simplified differential nonlocal strain gradient constitutive relation and Kirchhoff plate model, the strain potential, external potential and kinetic energy are obtained with the aid of defining physical neutral layer of the functionally graded nanoplate in a hygrothermal environment. The governing equation of motion is derived in which the traditional nonlocality of strains and strain gradients, and higher-order gradients of nonlocal stresses are involved. The composite beam function method and complex modal method are utilized to determine the vibration frequency. The numerical results show that vibration frequencies of the axially moving functionally graded nanoplate decrease with an increase in the nonlocal parameter, temperature changing, moisture concentration and axial speed, while they increase with the increase of the material characteristic scale parameter and aspect ratio. There is an interaction between the nonlocal parameter and material characteristic scale parameter, influencing and restricting each other. The larger of the nonlocal and material characteristic scale parameters is dominant in the stiffness softening or hardening behavior of nanostructures.