Study of Free Vibration of Porous Functionally Graded Rectangular Plates With Initial Deformation

WANG Yucheng; GAO Fangqing; DENG Hexuan; GU Dingao

doi:10.21656/1000-0887.450227

Volume 46 Issue 11

Nov. 2025

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2025 > 46(11): 1429-1439

WANG Yucheng, GAO Fangqing, DENG Hexuan, GU Dingao. Study of Free Vibration of Porous Functionally Graded Rectangular Plates With Initial Deformation[J]. Applied Mathematics and Mechanics, 2025, 46(11): 1429-1439. doi: 10.21656/1000-0887.450227

Citation:

PDF( 2467 KB)

Study of Free Vibration of Porous Functionally Graded Rectangular Plates With Initial Deformation

doi: 10.21656/1000-0887.450227

School of Mechanics and Aerospace Engineering, Southwest Jiaotong University,Chengdu 610031, P.R.China

Received Date: 2024-08-06
Rev Recd Date: 2024-12-02

Available Online: 2025-12-05

Abstract

Abstract

To meet the efficient design optimization requirements of functionally graded plates under multi-parameter dynamic effects, a unified theoretical framework and model for dynamic analysis was established, under the coupled influences of initial deformation, pore distribution, and gradient effects. The displacement field was described with the 1st-order shear deformation theory to account for the transverse shear effects caused by the graded material variation in the thickness direction. The displacement was discretized with the Chebyshev-Ritz method, and the energy functional expression of the porous functionally graded plate with initial deformation was derived. The characteristic equation of the vibration system was derived based on the principle of minimum energy, and the free vibration properties of the multi-functional graded plate were analyzed through numerical solutions. The convergence and accuracy of this method were validated by comparison with results from previous literatures and finite element analysis. The results show that, the introduction of initial deformation will significantly affect the natural vibration frequencies of porous functional gradient rectangular plates, in addition to the porosity, gradient indexes and other parameters will also affect the natural vibration frequency of the plate.
- initial deformation,
- free vibration,
- functional gradient,
- porosity,
- Chebyshev-Ritz method

FullText(HTML)

References(25)

References

滕兆春, 马铃权, 付小华. 多孔功能梯度材料Timoshenko梁的非线性自由振动分析[J]. 西北工业大学学报, 2022,40(5): 1145-1154.

(TENG Zhaochun, MA Lingquan, FU Xiaohua. Nonlinear free vibration analysis of Timoshenko beams with porous functionally graded materials[J].Journal of Northwestern Polytechnical University,2022,40(5): 1145-1154. (in Chinese))

[2]LI C, SHEN H S, WANG H. Nonlinear vibration of sandwich beams with functionally graded negative Poisson’s ratio honeycomb core[J].International Journal of Structural Stability and Dynamics,2019,19(3): 1950034.

[3]李双鹏. 多孔功能梯度板的等几何分析[D]. 南京: 南京航空航天大学, 2021.(LI Shuangpeng. Porosity-dependent isogeometric analysis of functionally graded plates[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2021. (in Chinese))

[4]THAI H T, KIM S E. A review of theories for the modeling and analysis of functionally graded plates and shells[J].Composite Structures,2015,128: 70-86.

[5]李华东, 朱锡, 梅志远, 等. 功能梯度板壳的力学研究进展[J]. 材料导报, 2012,26(1): 110-118.(LI Huadong, ZHU Xi, MEI Zhiyuan, et al. The development of the mechanical behaviour researches on functionally graded plates and shells[J].Materials Reports,2012,26(1): 110-118. (in Chinese))

[6]CHEN M F, JIN G Y, YE T G, et al. An isogeometric finite element method for the in-plane vibration analysis of orthotropic quadrilateral plates with general boundary restraints[J].International Journal of Mechanical Sciences,2017,133: 846-862.

[7]PINGULKAR P,BHEEMAPPA S. Free vibration analysis of laminated composite plates using finite element method[J].Polymers and Polymer Composites,2016,24(7): 529-538.

[8]VINYAS M. A higher-order free vibration analysis of carbon nanotube-reinforced magneto-electro-elastic plates using finite element methods[J].Composites (Part B):Engineering,2019,158: 286-301.

[9]李情, 陈莘莘. 基于重构边界光滑离散剪切间隙法的复合材料层合板自由振动分析[J]. 应用数学和力学, 2022,43(10): 1123-1132.(LI Qing, CHEN Shenshen. Free vibration analysis of laminated composite plates based on the reconstructed edge-based smoothing DSG method[J].Applied Mathematics and Mechanics,2022,43(10): 1123-1132. (in Chinese))

[10]CHEN S S, XU C J, TONG G S, et al. Free vibration of moderately thick functionally graded plates by a meshless local natural neighbor interpolation method[J].Engineering Analysis With Boundary Elements,2015,61: 114-126.

[11]WANG J F, YANG J P, LAI S K, et al. Stochastic meshless method for nonlinear vibration analysis of composite plate reinforced with carbon fibers[J].Aerospace Science and Technology,2020,105: 105919.

[12]QIN B, ZHONG R, WU Q Y, et al. A unified formulation for free vibration of laminated plate through Jacobi-Ritz method[J].Thin-Walled Structures,2019,144: 106354.

[13]鲍四元, 邓子辰. 薄板弯曲自由振动问题的高精度近似解析解及改进研究[J]. 应用数学和力学, 2016,37(11): 1169-1180.(BAO Siyuan, DENG Zichen. High-precision approximate analytical solutions for free bending vibrations of thin plates and an improvement[J].Applied Mathematics and Mechanics,2016,37(11): 1169-1180. (in Chinese))

[14]王永福, 漆文凯, 沈承, 等. 弹性约束边界条件下矩形蜂窝夹芯板的自由振动分析[J]. 应用数学和力学, 2019,40(6): 583-594.(WANG Yongfu, QI Wenkai, SHEN Cheng, et al. Free vibration analysis of rectangular honeycomb-cored plates under elastically constrained boundary conditions[J].Applied Mathematics and Mechanics,2019,40(6): 583-594. (in Chinese))

[15]TORNABENE F, LIVERANI A, CALIGIANA G. FGM and laminated doubly curved shells and panels of revolution with a free-form meridian: a 2-D GDQ solution for free vibrations[J].International Journal of Mechanical Sciences,2011,53(6): 446-470.

[16]WANG Y, FENG C, YANG J, et al. Nonlinear vibration of FG-GPLRC dielectric plate with active tuning using differential quadrature method[J].Computer Methods in Applied Mechanics and Engineering,2021,379: 113761.

[17]滕兆春, 丁树声, 郑鹏君. 弹性地基上变厚度矩形板自由振动的GDQ法求解[J]. 应用力学学报, 2014,31(2): 236-241.(TENG Zhaochun, DING Shusheng, ZHENG Pengjun. Free vibration analysis of rectangular plates with variable thickness on elastic foundation by using GDQ method[J].Chinese Journal of Applied Mechanics,2014,31(2): 236-241. (in Chinese))

[18]张继超, 钟心雨, 陈一鸣, 等. 基于Hamilton体系的功能梯度矩形板自由振动问题的解析解[J]. 应用数学和力学, 2024,45(9): 1157-1171.(ZHANG Jichao, ZHONG Xinyu, CHEN Yiming, et al. Hamiltonian system-based analytical solutions to free vibration problems of functionally graded rectangular plates[J]. Applied Mathematics and Mechanics,2024,45(9): 1157-1171. (in Chinese))

[19]梁斌, 李戎, 张伟, 等. 功能梯度材料圆柱壳的振动特性研究[J]. 船舶力学, 2011,15(1/2): 109-117.(LIANG Bin, LI Rong, ZHANG Wei, et al. Vibration characteristics of functionally graded materials cylindrical shells[J].Journal of Ship Mechanics,2011,15(1/2): 109-117. (in Chinese))

[20]王青山, 史冬岩, 罗祥程. 任意边界条件下矩形板的面内自由振动特性[J]. 华南理工大学学报(自然科学版), 2015,43(6): 127-134.(WANG Qingshan, SHI Dongyan, LUO Xiangcheng. In-plane free vibration of rectangular plates in arbitrary boundary conditions[J].Journal of South China University of Technology (Natural Science Edition), 2015,43(6): 127-134. (in Chinese))

[21]陈莘莘, 童谷生, 魏星. 基于自然单元法的功能梯度中厚板自由振动分析[J]. 力学季刊, 2016,37(2): 345-353.(CHEN Shenshen, TONG Gusheng, WEI Xing. Free vibration analysis of moderately thick functionally graded plates using the natural element method[J].Chinese Quarterly of Mechanics,2016,37(2): 345-353. (in Chinese))

[22]滕兆春, 席鹏飞. 弹性地基上多孔功能梯度材料矩形板的自由振动与临界屈曲载荷分析[J]. 计算力学学报, 2022,39(5): 582-590.(TENG Zhaochun, XI Pengfei. Analysis of free vibrations and critical buckling loads of a porous functionally graded materials rectangular plate resting on elastic foundation[J].Chinese Journal of Computational Mechanics,2022,39(5): 582-590. (in Chinese))

[23]KIRAN M C, KATTIMANI S C, VINYAS M. Porosity influence on structuralbehaviour of skew functionally graded magneto-electro-elastic plate[J].Composite Structures,2018,191: 36-77.

[24]GUPTA A, TALHA M. An assessment of a non-polynomial based higher order shear and normal deformation theory for vibration response of gradient plates with initial geometric imperfections[J].Composites (Part B):Engineering,2016,107: 141-161.

[25]ZHU P, LIEW K M. Free vibration analysis of moderately thick functionally graded plates by local Kriging meshless method[J].Composite Structures,2011,93(11): 2925-2944.

Relative Articles

Supplements(0)

Cited By

Proportional views