复合材料层合板自由振动的谱切比雪夫解法

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (11) : 285-290.

论文

复合材料层合板自由振动的谱切比雪夫解法

郭琛琛1，刘涛1，王青山2，秦斌3

作者信息 +

Spectral Tchebychev method for free vibration of composite laminated plates

GUO Chenchen1, LIU Tao1, WANG Qingshan2, QIN Bin3

Author information +

文章历史 +

摘要

采用二维谱切比雪夫法(2D-ST)，对一般边界条件下复合材料层合板的自由振动进行了分析。基于一阶剪切变形理论(FSDT)，采用边界弹簧技术模拟任意边界条件，推导了复合材料层合板的能量方程表达式。利用二维谱切比雪夫法求解能量方程，得到了任意边界条件下复合材料层合板的自由振动特征方程。在数值算例中，通过与其它方法的计算结果进行对比，验证了所提出方法的收敛性和准确性，并在此基础上研究了弹性模量比和铺设角对复合材料层合板振动特性的影响。

Abstract

The two-dimensional spectral-Tchebychev (2D-ST) technique is used to analyze the free vibration of composite laminated plates under general boundary conditions. Based on the first-order shear deformation theory (FSDT), the boundary spring technique is used to simulate arbitrary boundary conditions, and the energy equation expression of composite laminated plates is derived. The energy equation is solved by the two-dimensional spectral-Tchebychev technique, and the free vibration characteristic equation of the composite laminated plates under arbitrary boundary conditions is obtained. In the numerical example, by comparing the calculation results with other methods, the convergence and accuracy of the proposed technique are verified. On this basis, the effect of elastic modulus ratio and laying angle on the vibration characteristics of composite laminated plates is studied.

导出引用

郭琛琛1，刘涛1，王青山2，秦斌3. 复合材料层合板自由振动的谱切比雪夫解法[J]. 振动与冲击, 2022, 41(11): 285-290

GUO Chenchen1, LIU Tao1, WANG Qingshan2, QIN Bin3. Spectral Tchebychev method for free vibration of composite laminated plates[J]. Journal of Vibration and Shock, 2022, 41(11): 285-290

参考文献

[1] Kant T, Swaminathan K.Free vibration of isotropic, orthotropic, and multilayer plates based on higher order refined theories[J].Journal of Sound and Vibration,2001, 241 (2): 319-327.
[2] Reddy J N. Mechanics of laminated composite plates and shells: theory and analysis[M]. CRC press,2003.
[3] Shi J W, Nakatani A, Kitagawa H.Vibration analysis of fully clamped arbitrarily laminated plate[J].Composite Structures,2004, 63 (1): 115-122.
[4] Liew K M.Solving the vibration of thick symmetric laminates by Reissner/Mindlin plate theory and the p-Ritz method[J].Journal of Sound and Vibration,1996, 198 (3): 343-360.
[5] Ye T, Jin G, Su Z, et al.A modified Fourier solution for vibration analysis of moderately thick laminated plates with general boundary restraints and internal line supports[J].International Journal of Mechanical Sciences,2014, 80: 29-46.
[6] Qin B, Zhong R, Wu Q, et al.A unified formulation for free vibration of laminated plate through Jacobi-Ritz method[J].Thin-Walled Structures,2019, 144: 106354.
[7] Shi D, Zhang H, Wang Q, et al.Free and forced vibration of the moderately thick laminated composite rectangular plate on various elastic winkler and pasternak foundations[J].Shock and Vibration,2017, 2017.
[8] Roque C M C, Ferreira A J M, Jorge R M N.Free vibration analysis of composite and sandwich plates by a trigonometric layerwise deformation theory and radial basis functions[J].Journal of Sandwich Structures & Materials,2006, 8 (6): 497-515.
[9] Xiang S, Shi H, Wang K-M, et al.Thin plate spline radial basis functions for vibration analysis of clamped laminated composite plates[J].European Journal of Mechanics-A/Solids,2010, 29 (5): 844-850.
[10] Bui T Q, Nguyen M N, Zhang C.An efficient meshfree method for vibration analysis of laminated composite plates[J].Computational Mechanics,2011, 48 (2): 175-193.
[11] 陈富军, 魏春志, 姚林泉.基于局部移动Kriging无网格方法的层合板自由振动分析[J].计算力学学报,2013, 000 (004): 559-564.
CHEN F J,WEI C Z,YAO L Q. Free vibration analysis of laminated composite plates by local moving Kriging meshless method[J]. Chinese Journal of Computational Mechanics, 2013, 000 (004): 559-564.
[12] 张科. 层合板结构振动分析的无网格方法[D]. 苏州市: 苏州大学,2015.
Zhang K. Vibration analysis of composite laminates using meshless method[D]. Suzhou: Soochow University. 2015.
[13] 郭向群, 杨康, 项松, et al.复合材料层合板自由振动的薄板样条无网格解[J].材料导报,2016 (S2): 179-182.
GUO X Q, YANG K, XIANG S,et al. Meshless Solutions Based on the Thin Plate Spline for Free Vibration of Laminated Composite Plates[J].Materiaols Reports, 2016 (S2): 179-182.
[14] 陈莘莘, 李鹤.复合材料层合板自由振动分析的无网格自然邻接点Petrov-Galerkin法[J].计算力学学报,2018, 35 (06): 79-84.
CHEN S S, LI H. Free vibration analysis of laminated composite plates bythe meshless natural neighbour Petrov-Galerkin method[J]. Chinese Journal of Computational Mechanics, 2018, 35 (06): 79-84.
[15] 李情, 陈莘莘.复合材料层合板自由振动的插值型重构核粒子法[J].应用力学学报,2020, v.37;No.163 (03): 442-446+497.
Li Q, Chen S S. Composite plates based on interpolating reproducing kernel particle method[J]. Chinese Journal of Applied Mechanics, 2020, v.37;No.163 (03): 442-446+497.
[16] Gottlieb D, Orszag S A. Numerical analysis of spectral methods: theory and applications[M]. SIAM,1977.
[17] Zhou D, Au F T K, Cheung Y K, et al.Three-dimensional vibration analysis of circular and annular plates via the Chebyshev–Ritz method[J].International Journal of Solids and Structures,2003, 40 (12): 3089-3105.
[18] Yagci B, Filiz S, Romero L L, et al.A spectral-Tchebychev technique for solving linear and nonlinear beam equations[J].Journal of Sound and Vibration,2009, 321 (1-2): 375-404.
[19] 黄意新. 一种基于Chebyshev多项式理论的结构力学计算方法[D]. 哈尔滨市: 哈尔滨工业大学,2017.
Huang Y X. A novel numerical method for structural mechanics based on chebyshev polynomials theory[D]. Harbin: Harbin Institute of Technology, 2017.
[20] Pasquetti R, Rapetti F.Spectral element methods on triangles and quadrilaterals: comparisons and applications[J].Journal of Computational Physics,2004, 198 (1): 349-362.
[21] Filiz S, Bediz B, Romero L A, et al.A spectral-Tchebychev solution for three-dimensional vibrations of parallelepipeds under mixed boundary conditions[J].Journal of applied mechanics,2012, 79 (5).
[22] Filiz S, Bediz B, Romero L A, et al.Three dimensional dynamics of pretwisted beams: A spectral-Tchebychev solution[J].Journal of Sound and Vibration,2014, 333 (10): 2823-2839.
[23] Bediz B, Romero L A, Ozdoganlar O B.Three dimensional dynamics of rotating structures under mixed boundary conditions[J].Journal of Sound and Vibration,2015, 358: 176-191.
[24] Bediz B.Three-dimensional vibration behavior of bi-directional functionally graded curved parallelepipeds using spectral Tchebychev approach[J].Composite Structures,2018, 191: 100-112.
[25] Bediz B.A spectral-Tchebychev solution technique for determining vibrational behavior of thick plates having arbitrary geometry[J].Journal of Sound and Vibration,2018, 432: 272-289.
[26] Bediz B, Aksoy S.A spectral-Tchebychev solution for three-dimensional dynamics of curved beams under mixed boundary conditions[J].Journal of Sound and Vibration,2018, 413: