Investigating the buckling and vibration of a Mindlin rectangular nanoplate using modified couple stress theory

Document Type : Original Article

Authors

1 Ph.D Student of Aerospace Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

2 Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran.

3 Department of Mechaniacl Engineering, Ferdowsi University of Mashhad, Mashhad, Iran.

4 Faculty of Materials and Manufacturing Technologies, Malek Ashtar University of Technology, Tehran, Iran

10.22034/asm.2022.13805.1001

Abstract

This paper presents the buckling and vibration characteristics of a Mindlin rectangular nanoplate with simply supported boundary conditions and Navier approach. In order to consider the small scale effects, the modified couple stress theory, with one length scale parameter, is used. In modified couple stress theory, strain energy density is a function of strain tensor, curvature tensor, stress tensor and symmetric part of couple stress tensor. The critical buckling load values and vibration frequencies of different modes are separately solved. The governing equations are numerically solved and results are verified with literature. The effect of material length scale, length, width and thickness of the nanoplate on the buckling loads and vibration frequencies are investigated and the results are presented and discussed in details.

This paper presents the buckling and vibration characteristics of a Mindlin rectangular nanoplate with simply supported boundary conditions and Navier approach. In order to consider the small scale effects, the modified couple stress theory, with one length scale parameter, is used. In modified couple stress theory, strain energy density is a function of strain tensor, curvature tensor, stress tensor and symmetric part of couple stress tensor. The critical buckling load values and vibration frequencies of different modes are separately solved. The governing equations are numerically solved and results are verified with literature. The effect of material length scale, length, width and thickness of the nanoplate on the buckling loads and vibration frequencies are investigated and the results are presented and discussed in details.

Keywords