Transverse free vibration analysis of a rotating rectangular plate made of viscoelastic material with fractional derivative

SUN Yujian1,WANG Zhongmin1,2

Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (8) : 126-133.

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PDF(994 KB)
Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (8) : 126-133.

Transverse free vibration analysis of a rotating rectangular plate made of viscoelastic material with fractional derivative

  • SUN Yujian1,WANG Zhongmin1,2
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Abstract

The transverse free vibration of a rotating viscoelastic rectangular plate described by fractional derivative constitutive relation is studied. Based on the plane problem of the plate, the Kelvin-Voigt two-dimensional constitutive relation with fractional derivative is obtained from the Kelvin-Voigt three-dimensional constitutive equation with fractional derivative. The differential equation of motion for rotating rectangular plate made of viscoelastic material with fractional derivative is established with Hamilton principle. Differential quadrature method is used to discretize the differential equations of motion and boundary conditions, and the complex eigen-equation of the system is obtained. The effects of fractional derivative order, width to length ratio, radius to length ratio and thickness to length ratio on the imaginary part of dimensionless complex frequency of the system are analyzed. The results show that with the increase of the rotational angular speed, the imaginary part (natural frequency) of the first three order dimensionless complex frequencies increases; with the increase of the fractional derivative order, the imaginary part of dimensionless complex frequency decreases; and the effect of each parameter on the third order imaginary part of the complex frequency is greater than the first and second order.

Key words

rotating rectangular plate / viscoelasticity with fractional derivative / transverse vibration / differential quadrature method

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SUN Yujian1,WANG Zhongmin1,2. Transverse free vibration analysis of a rotating rectangular plate made of viscoelastic material with fractional derivative[J]. Journal of Vibration and Shock, 2023, 42(8): 126-133

References

[1] Du H , Lim M K , Liew K M . A power series solution for vibration of a rotating Timoshenko beam[J]. Journal of Sound and Vibration, 1994, 175(4): 505-523.
[2] Lin S C , Hsiao K M . Vibration analysis of a rotating Timoshenko beam[J]. Journal of Sound and Vibration, 2001, 240(2): 303-322.
[3] Jarrar F , Hamdan M N . Nonlinear vibrations and buckling of a flexible rotating beam: A prescribed torque approach[J]. Mechanism and Machine Theory, 2007, 42(8): 919-939.
[4] 邱志成. 旋转柔性梁系统振动频响特性分析及振动抑制[J]. 振动与冲击, 2008(6): 75-80+122+188.
QIU Zhi-cheng. Vibration frequency response feature analysis and vibration suppression of rotating flexible beam[J]. Journal of Vibration and Shock, 2008(6): 75-80+122+188.
[5] 任勇生, 代其义, 孙丙磊, 等. 旋转几何非线性复合材料薄壁梁的自由振动分析[J]. 振动与冲击, 2013, 32(14): 139-147.
REN Yong-sheng, DAI Qi-yi, SUN Bing-lei, et al. Free vibration of a rotating composite thin-walled beam with large deformation[J]. Journal of Vibration and Shock, 2013, 32(14): 139-147.
[6] Dokainish M A , Rawtani S . Vibration analysis of rotating cantilever plates[J]. International Journal for Numerical Methods in Engineering, 2010, 3(2): 233-248.
[7] Yoo H H , Kim S K . Free vibration analysis of rotating cantilever plates[J]. AIAA Journal, 2012, 40(11): 2188-2196.
[8] Yoo H H , Kim S K . Flapwise bending vibration of rotating plates[J]. International Journal for Numerical Methods in Engineering, 2010, 55(7): 785-802.
[9] Yoo H H, Pierre C . Modal characteristic of a rotating rectangular cantilever plate[J]. Journal of Sound and Vibration, 2003, 259(1): 81-96.
[10] Sun J, Kari L, Arteaga I L. A dynamic rotating blade model at an arbitrary stagger angle based on classical plate theory and the Hamilton's principle[J]. Journal of Sound and Vibration, 2013, 332(5): 1355-1377.
[11] Rostami H, Ranji A R, Bakhtiarinejad F. Free in-plane vibration analysis of rotating rectangular orthotropic cantilever plates[J]. International Journal of Mechanical Sciences, 2016, 115(2): 438-456.
[12] Chen J , Li Q S . Vibration characteristics of a rotating pre-twisted composite laminated blade[J]. Composite Structures, 2019, 208(1): 78-90.
[13] 黎亮, 章定国, 洪嘉振. 作大范围运动FGM矩形薄板的动力学特性研究[J]. 动力学与控制学报, 2013, 11(4): 43-49.
LI Liang, ZHANG Ding-guo, HONG Jia-zhen. Dynamics of rectangular functionally graded thin plates undergoing large overall motion[J]. Journal of Dynamics and Control, 2013,11(4): 43-49.
[14] 寇海江, 袁惠群. 旋转大变形板振动高阶非线性效应的变分法研究[J]. 振动工程学报, 2015, 28(1): 44-51.
KOU Hai-jiang, YUAN Hui-qun. High-order nonlinear vibration analysis of the rotating large deflection plate based on the variational principle[J]. Journal of Vibration Engineering, 2015, 28(1): 44-51.
[15] Gemant A. On fractional differentials. XLV[J]. Philosophical Magazine, 1938, 25(168): 540-549.
[16] 刘林超. 分数导数型粘弹性材料的力学行为及在结构减振中的应用研究[D]. 广州:暨南大学,2005.
LIU Lin-chao. Mechanical properties of viscoelastic materials modeled by fractional derivative and application study on suppressing vibration of structure[D]. Guangzhou: Jinan University, 2005.
[17] 刘林超, 闫启方. 分数导数Kelvin粘弹性圆形薄板的轴对称弯曲分析[J]. 力学季刊, 2010, 31(3): 36-40.
LIU Lin-chao, YAN Qi-fang. Bending analysis of symmetrically viscoelastic thin circular late with fractional derivative kelvin model[J]. Chinese Quarterly of Mechanics, 2010, 31(3): 36-40.
[18] 葛志新, 陈咸奖, 陈松林. 一类含有分数阶导数的参数激励振动问题[J]. 振动与冲击, 2017, 36(4): 88-92.
GE Zhi-xin, CHEN Xian-jiang, CHEN Song-lin. A class of parametric excitation vibration problems with fractional derivative[J]. Journal of Vibration and Shock, 2017, 36(4): 88-92.
[19] 盖盼盼, 徐赵东, 吕令毅, 等. 黏弹性阻尼隔振系统动力分析与优化设计[J]. 振动与冲击, 2019, 38(1): 238-242.
GAI Pan-pan, XU Zhao-dong, LV Ling-yi, et al. Dynamic analysis and parametric optimization for vibration isolation systems with viscoelastic damping[J]. Journal of Vibration and Shock, 2019, 38(1): 238-242.
[20] Rouzegar J, Vazirzadeh M, Heydari M H. A fractional viscoelastic model for vibrational analysis of thin plate excited by supports movement[J]. Mechanics Research Communications, 2020, 110: 103618.
[21] 张亚鹏,高峰.分数导数粘弹性模型的矩形板的振动分析[J]. 噪声与振动控制, 2012, 32(3): 34-36+81.
ZHANG Ya-peng, GAO Feng. Vibration analysis of rectangular plates with fractional derivative viscoelastic model[J]. Noise and Vibration Control, 2012, 32(3): 34-36+81.
[22] 赵永玲, 侯之超, 黄友剑,等. 橡胶材料的一种5参数分数导数模型[J]. 振动与冲击, 2015, 34(23): 37-41.
ZHAO Yong-ling, HOU Zhi-chao, HUANG You-jian, et al. A fractional derivative model with five parameters for rubber materials[J]. Journal of Vibration and Shock, 2015, 34(23): 37-41.
[23] 王忠民, 李会侠. 基于微分求积法分析旋转圆板的横向振动[J]. 振动与冲击, 2014, 33(1): 125-129.
WANG Zhong-min, LI Hui-xia. Transverse vibration analysis of spinning circular plate based on differential quadrature method[J]. Journal of Vibration and Shock, 2014, 33(1): 125-129.
[24] 王永亮. 微分求积法和微分求积单元法——原理与应用[D]. 南京:南京航空航天大学,2001.
 WANG Yong-liang. Differential quadrature method and differential quadrature element method—Theory and application.[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2001.
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