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# Free Vibration Analysis of Rectangular Plate with Cutouts under Elastic Boundary Conditions in Independent Coordinate Coupling Method

Qiuhong Li1, Wenhao Huang1,*, Joey Sanchez2, Ping Wang1, Qiang Ding3, Jiufa Wang4
1 College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin, 150001, China
2 SAE Concepts, East Brunswick, NJ, 08816, USA
3 No.709 & Institute, China Shipbuilding Industry Corporation (CSIC), Wuhan, 430205, China
4 No.710 & Institute, China Shipbuilding Industry Corporation (CSIC), Yichang, 443003, China
* Corresponding Author: Wenhao Huang. Email:
(This article belongs to this Special Issue: Computer Modeling in Ocean Engineering Structure and Mechanical Equipment)

Computer Modeling in Engineering & Sciences 2023, 134(3), 2093-2121. https://doi.org/10.32604/cmes.2022.021340

Received 09 January 2022; Accepted 09 May 2022; Issue published 20 September 2022

### Abstract

Based on Kirchhoff plate theory and the Rayleigh-Ritz method, the model for free vibration of rectangular plate with rectangular cutouts under arbitrary elastic boundary conditions is established by using the improved Fourier series in combination with the independent coordinate coupling method (ICCM). The effect of the cutout is taken into account by subtracting the energies of the cutouts from the total energies of the whole plate. The vibration displacement function of the hole domain is based on the coordinate system of the hole domain in this method. From the continuity condition of the vibration displacement function at the cutout, the transition matrix between the two coordinate systems is constructed, and the mass and stiffness matrices are completely obtained. As a result, the calculation is simplified and the computational efficiency of the solution is improved. In this paper, numerical examples and modal experiments are presented to validate the effectiveness of the modeling methods, and parameters related to influencing factors of the rectangular plate are analyzed to study the vibration characteristics.

### Keywords

Rectangular plate with cutouts; the independent coordinate coupling method; elastic boundary conditions; free vibration analysis

Li, Q., Huang, W., Sanchez, J., Wang, P., Ding, Q. et al. (2023). Free Vibration Analysis of Rectangular Plate with Cutouts under Elastic Boundary Conditions in Independent Coordinate Coupling Method. CMES-Computer Modeling in Engineering & Sciences, 134(3), 2093–2121.

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