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Research Papers

# Modal Analysis of a Rotating Thin Plate via Absolute Nodal Coordinate Formulation

[+] Author and Article Information
Jiang Zhao

MOE Key Laboratory of Mechanics and Control for Aerospace Structures, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing, Chinazhaojiang@nuaa.edu.cn

Qiang Tian1

Key Laboratory of Dynamics and Control of Flight Vehicle, Ministry of Education, School of Aerospace Engineering, Beijing Institute of Technology, 100081 Beijing, Chinatianqiang_hust@yahoo.com.cn

Haiyan Hu

MOE Key Laboratory of Mechanics and Control for Aerospace Structures, Nanjing University of Aeronautics and Astronautics, 210016 Nanjing, China; Key Laboratory of Dynamics and Control of Flight Vehicle, Ministry of Education, School of Aerospace Engineering, Beijing Institute of Technology, 100081 Beijing, Chinahhyae@nuaa.edu.cn

1

Corresponding author.

J. Comput. Nonlinear Dynam 6(4), 041013 (May 20, 2011) (8 pages) doi:10.1115/1.4003975 History: Received November 10, 2010; Revised March 30, 2011; Published May 20, 2011; Online May 20, 2011

## Abstract

Modal analysis of a rotating thin plate is made in this paper through the use of the thin plate elements described by the absolute nodal coordinate formulation (ANCF). The analytical expressions of elastic forces and their Jacobian matrices of the thin plate elements are derived and expressed in a computationally efficient way. The static analysis of a cantilever thin plate and the modal analysis of a square thin plate with completely free boundaries are made to validate the derived formulations. The modal analysis of a rotating cantilever thin plate based on the ANCF is studied. The effect of rotating angular velocity on the natural frequencies is investigated. The eigenvalue loci veering and crossing phenomena along with the corresponding modeshape variations are observed and carefully discussed. Finally, the effects of dimensional parameters on the dimensionless natural frequencies of the thin plate are studied.

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## Figures

Figure 1

Three-dimensional thin plate element of ANCF

Figure 2

A cantilever thin plate

Figure 3

A rotating rectangular thin plate

Figure 4

Lowest five natural frequencies versus angular velocity (δ=1, σ=0)

Figure 5

Lowest five natural frequencies versus angular velocity (δ=1, σ=1)

Figure 6

Nodal lines of the lowest five mode shapes of a nonrotating cantilever square thin plate

Figure 7

Nodal lines of the lowest five mode shapes of a rotating cantilever square thin plate (σ=0, γ=10)

Figure 8

Variation of the nodal line of the third mode shape (σ=0) with an increase of angular velocity

Figure 9

Variation of the nodal line of the fourth mode shape (σ=0) with an increase of angular velocity

Figure 10

Variation of the nodal lines of the third and fourth mode shapes (σ=0) with an increase of angular velocity

Figure 11

Lowest five natural frequencies versus angular velocity (δ=5, σ=1)

Figure 12

Nodal lines of the lowest five mode shapes of a nonrotating cantilever thin plate

Figure 13

Nodal lines of the lowest five mode shapes of a rotating cantilever thin plate (δ=5, σ=1)

Figure 14

Effect of dimensional parameters on dimensionless natural frequency

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