Free vibration analysis of functionally graded annular plates under thermal environment by the spectro-geometric method

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Journal of Vibration and Shock ›› 2022, Vol. 41 ›› Issue (10) : 1-7.

SHI Xianjie1，ZUO Peng1,2

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Abstract

A free vibration analysis model of functionally graded annular plates under thermal environment is established with the spectro-geometric method. Firstly, the model assumes that the material properties are temperature-dependent and show a continuous gradient along the thickness of the structure. Secondly, arbitrary boundary conditions are simulated by setting various type boundary restraining springs along boundary edge. Based on the first-order shear deformation theory, the vibration energy equation of the functionally graded annular plate is deduced. Thirdly, the displacement admissible functions are expressed with spectro-geometric method and Fourier series function. Then the Rayleigh-Ritz method is employed to derive the vibration analysis model for functionally graded annular plate under thermal environment. The numerical example gives a comparative analysis of the frequency characteristics of functionally graded annular plates considering thermal environment factors. The results show that the current model has good calculation accuracy. Also, it is suitable for analyzing the thermal vibration characteristics of functionally graded annular plates. Through the parameterization study of the FGM annular plate, it is found that the changes of the environmental temperature, boundary conditions, and gradient index will have an impact effect on the thermal vibration characteristics of the functionally graded annular plate.

Key words

functionally graded annular plate / thermal environment / free vibration / spectro-geometric method

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SHI Xianjie1，ZUO Peng1,2. Free vibration analysis of functionally graded annular plates under thermal environment by the spectro-geometric method[J]. Journal of Vibration and Shock, 2022, 41(10): 1-7

References

[1]. 边祖光. 功能梯度材料板壳结构的耦合问题研究[D]. 杭州：浙江大学，2005.
BIAN Zu-guang. On coupled problems of functionally graded materials plates and shells [D]. Hangzhou: Zhejiang University, 2005.
[2]. 毛贻齐. 低速冲击下损伤层合/功能梯度板壳的非线性动力学研究[D]. 长沙：湖南大学，2011.
MAO Yi-qi. Nonlinear dynamic analysis for laminated/FGM plates and shells with damage under low velocity impact [D]. Changsha: Hunan University, 2011.
[3]. 盛国刚. 压电与功能梯度圆柱壳的力学特性研究[D]. 上海：上海交通大学，2009.
SHENG Guo-gang. Research on the property of mechanics of piezoelectric and functionally graded cylindrical shell [D]. Shanghai: Shanghai Jiao Tong University, 2009.
[4]. SU Z, JIN G, SHI S, etc. A unified solution for vibration analysis of functionally graded cylindrical, conical shells and annular plates with general boundary conditions[J]. International Journal of Mechanical Sciences,2014,80:62-80.
[5]. 王青山. 任意边界条件下复合材料回转类中厚板壳及耦合结构振动特性研究[D]. 哈尔滨：哈尔滨工程大学，2016.
WANG Qing-shan. Study of vibration characteristics for moderately thick plates and shells of revolution and coupled structures subjected to general boundary conditions [D]. Harbin: Harbin Engineering University, 2016.
[6]. ZHAO J, XIE F, WANG A, etc. Dynamics analysis of functionally graded porous (FGP) circular, annular and sector plates with general elastic restraints[J]. Composites Part B: Engineering,2019,159:20-43.
[7]. 滕兆春，蒲育，房晓林. FGM圆环板面内自由振动的DQM求解[J]. 北京理工大学学报，2014, 34(12):1211-1216.
TENG Zhao-chun, PU Yu, FANG Xiao-lin. In-plane free vibration analysis for FGM annular plates by differential quadrature method [J]. Transaction of Beijing Institute of Technology, 2014, 34(12):1211-1216.
[8]. Kumar Y. Free vibration of two-directional functionally graded annular plates using chebyshev collocation technique and differential quadrature method[J]. International Journal of Structural Stability and Dynamics,2015,15(06):1450086.
[9]. Mohammadimehr M, Afshari H, Salemi M, etc. Free vibration and buckling analyses of functionally graded annular thin sector plate in-plane loads using GDQM[J]. Structural engineering and Mechanics,2019,71(5):525-44.
[10]. Jodaei A, Jalal M, Yas M H. Free vibration analysis of functionally graded annular plates by state-space based differential quadrature method and comparative modeling by ANN[J]. Composite Part B: Engineering,2021,43(2):340-353.
[11]. Żur K K. Free vibration analysis of elastically supported functionally graded annular plates via quasi-Green's function method[J]. Composites Part B: Engineering,2018,144:37-55.
[12]. WU C P, YU L T. Free vibration analysis of bi-directional functionally graded annular plates using finite annular prism methods[J]. Journal of Mechanical Science and Technology,2019,33(5):2267-2279.
[13]. Haddadpour H, Mahmoudkhani S, Navazi H M. Free vibration analysis of functionally graded cylindrical shells including thermal effects[J]. Thin-Walled Structures,2007,45(6):591-599.
[14]. Mirtalaie S H. Differential quadrature free vibration analysis of functionally graded thin annular sector plates in thermal environments[J]. Journal of Dynamic Systems, Measurement and Control,2018,140(10):101006.
[15]. YANG Y F, CHEN D, YANG B. 3D thermally induced analysis of annular plates of functionally graded materials[J]. Theoretical and Applied Mechanics Letters,2019,9(5):297-301.
[16]. Malekzadeh P, Heydarpour Y. Free vibration analysis of rotating functionally graded cylindrical shells in thermal environment[J]. Composite Structures,2012,94(9):2971-2981.
[17]. Malekzadeh P, Haghighi M R G, Atashi M M. Free vibration analysis of elastically supported functionally graded annular plates subjected to thermal environment[J]. Meccanica,2011,46(5): 893-913.
[18]. ZHOU K, HUANG X, TIAN J, etc. Vibration and flutter analysis of supersonic porous functionally graded material plates with temperature gradient and resting on elastic foundation[J]. Composite Structures,2018,204:63-79.
[19]. LI Z, ZHONG R, WANG Q S, etc. The thermal vibration characteristics of the functionally graded porous stepped cylindrical shell by using characteristic orthogonal polynomials[J]. International Journal of Mechanical Sciences,2020,182:105779.
[20]. 蒲育. 热环境中功能梯度圆环板的面内自由振动分析[D]. 兰州：兰州理工大学，2013.
PU Yu. In-plane free vibration analysis of functionally graded annual plates under thermal environment [D]. Lanzhou: Lanzhou University of Technology, 2013.
[21]. 滕兆春，蒲育. 温度影响下FGM圆环板的面内自由振动分析[J]. 振动与冲击，2015, 34(09):210-217.
TENG Zhao-chun, PU Yu. In-plane free vibration of FGM annual plates considering temperature effect [J]. Journal of Vibration and Shock, 2015, 34(09): 210-217.
[22]. 吕朋，杜敬涛，邢雪, 等. 热环境下弹性边界约束FGM圆环板面内振动特性分析[J]. 振动工程学报，2017, 5(30):713-723.
LÜ Peng, DU Jing-tao, XING Xue, et al. Study on in-plane vibration characteristics of elastically restrained FGM annual panel in thermal environment [J]. Journal of Vibration Engineering, 2017, 30(5):713-723.
[23]. 石鹏，董春迎. 具有混合边界条件的功能梯度材料圆环版在热环境中的自由振动[C]// 北京力学会第18届学术年会.北京：北京力学会，2012.
SHI Peng, DONG Chun-ying. Free vibration of functionally graded material annular plates with mixed boundary conditions in thermal environment [C]. Annual Conference of Beijing Society of Mechanics, 2012.
[24]. 石先杰. 复杂边界条件下旋转结构统一动力学模型的构建与研究[D]. 哈尔滨：哈尔滨工程大学，2014.
SHI Xian-jie. The construction and analysis on unified dynamical model of revolve structures subjected to complex boundary conditions [D]. Harbin: Harbin Engineering University, 2014.
[25]. Barati M R, Zenkour A M. Electro-thermoelastic vibration of plates made of porous functionally graded piezoelectric materials under various boundary conditions[J]. Journal of Vibration and Control,2018,24(10):1910-1926.
[26]. Ebrahimi F, Barati M R. Electromechanical buckling behavior of smart piezoelectrically actuated higher-order size-dependent graded nanoscale beams in thermal environment[J]. International Journal of Smart and Nano Materials,2016,7(2):69-90.