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

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.

System Identification using Self-Adaptive Filtering Applied to Second-Order Gradient Materials

“…However, in various fields modern continuum mechanics is also driven by applications that include higher gradients [2]. This is particular true for materials with micro-structure, functionally graded materials, and metamaterials [3][4][5][6][7][8]. Furthermore, finite gradient plasticity [8][9] and theories for gradient fluids [10][11][12] became blossoming fields of research in the last decades.…”

“…This is particular true for materials with micro-structure, functionally graded materials, and metamaterials [3][4][5][6][7][8]. Furthermore, finite gradient plasticity [8][9] and theories for gradient fluids [10][11][12] became blossoming fields of research in the last decades. Because of the broad range of research in this field, the list of references is restricted to recent publications.…”

Effect of non‐local modified couple stress theory on the responses of axially moving thermoelastic nano‐beams

“…Nonlocal effects are taken into account to account for strain gradients, and the traditional normal strain is replaced with a gradient normal strain. Zhu et al [26] demonstrated a vibration study of hygrothermal exposed, axially moving, functionally graded nanoplates. They used Kirchhoff's plate theory and the idea of a physical neutral layer to describe a nanoplate in a theoretical way.…”

“…Zhu et al. [26] demonstrated a vibration study of hygrothermal exposed, axially moving, functionally graded nanoplates. They used Kirchhoff's plate theory and the idea of a physical neutral layer to describe a nanoplate in a theoretical way.…”

Boundary stabilization for axially moving Kirchhoff string under fractional PI control

“…The boundary stabilization is also available for two kinds of nonlinear axially moving beam systems in [27,28]. In addition to vibration control, the dynamics or vibration behavior of the axially moving structures also becomes an important topic and we refer this to [29][30][31][32][33][34].…”