Dynamic Analysis of Multi-Stepped Functionally Graded Carbon Nanotube Reinforced Composite Plate with General Boundary Condition

Author:

Kim Kwanghun1ORCID,Kwak Songhun2,Ri Yonguk1,Paek Yongsong1,Han Wonjin3,Ri Kumchol3

Affiliation:

1. Department of Engineering Machine, Pyongyang University of Mechanical Engineering, Pyongyang 999093, Democratic People’s Republic of Korea

2. College of Mechanical Science and Technology, Kim Chaek University of Technology, Pyongyang 950003, Democratic People’s Republic of Korea

3. Department of Life Science, Pyongyang University of Science, Pyongyang 999093, Democratic People’s Republic of Korea

Abstract

This study presents the multi-stepped functionally graded carbon nanotube reinforced composite (FG-CNTRC) plate model for the first time, and its free and forced vibration is analyzed by employing the domain decomposition method. The segmentation technique is employed to discretize the structure along the length direction. The artificial spring technique is applied to the structural boundary and piecewise interface for satisfying the boundary conditions and the combined conditions between subplates. Based on this, the boundary conditions of subdomains could be considered as a free boundary constraint, reducing the difficulty in constructing the allowable displacement function. Since all the structures of subdomains are identical, the allowable displacement functions of them can be uniformly constructed using the two-dimensional ultraspherical polynomial expansion. The potential energy function of the plate is derived from the first-order shear deformation theory (FSDT). The allowable displacement function is substituted into the potential energy function, and then the natural frequencies and mode shapes of the multi-stepped FG-CNTRC plate are decided by using the Rayleigh–Ritz method. The accuracy and reliability of the proposed method are confirmed by the results of the previous literature and finite element method (FEM). On this basis, the influences of the geometric and material parameters on free and forced vibration of the multi-stepped FG-CNTRC plate are also studied.

Funder

Pyongyang University of Mechanical Engineering of DPRK

Publisher

Hindawi Limited

Subject

Mechanical Engineering,Mechanics of Materials,Geotechnical Engineering and Engineering Geology,Condensed Matter Physics,Civil and Structural Engineering

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