基于一阶剪切变形理论FGM梁自由振动的改进型GDQ法求解

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振动与冲击 ›› 2018, Vol. 37 ›› Issue (16) : 212-218.

论文

蒲育1，滕兆春2

作者信息 +

Free vibration of FGM beams based on the first-order shear deformation theory by a modified generalized differential quadrature method

PU Yu1， TENG Zhaochun2

Author information +

文章历史 +

摘要

基于一阶剪切变形梁理论(FSBT)，建立了以轴向位移、横向位移及转角为未知函数的FGM梁自由振动的控制微分方程组。引入边界控制参数并采用改进型广义微分求积法(GDQ)数值研究了4种典型边界FGM梁自由振动的频率特性。结果表明本文的分析方法对FGM梁自由振动研究行之有效。刻画并分析了边界条件、梯度指标、跨厚比对FGM梁自振频率的影响规律。

Abstract

Based on the first-order shear deformation beam theory (FSBT), the governing differential equations for free vibration of functionally graded material (FGM) beams were obtained, in which the unknown functions are axial displacement, deflection and rotation angle.By introducing boundary condition coefficients and applying a modified generalized differential quadrature (GDQ) method, we investigated the natural frequencies for free vibration of FGM beams under four boundary conditions.The formulations’ availability and accuracy were demonstrated by comparing them with results available in the existing literature.Then the effects of the boundary conditions, material graded index, and length-to-thickness ratio on the FGM beams’ natural frequency parameters were analyzed.

导出引用

蒲育1，滕兆春2 . 基于一阶剪切变形理论FGM梁自由振动的改进型GDQ法求解[J]. 振动与冲击, 2018, 37(16): 212-218

PU Yu1， TENG Zhaochun2. Free vibration of FGM beams based on the first-order shear deformation theory by a modified generalized differential quadrature method[J]. Journal of Vibration and Shock, 2018, 37(16): 212-218

参考文献

[1] M. Aydogdu, V. Taskin. Free vibration analysis of functionally graded beams with simply supported edges[J]. Materials and Design, 2007, 28(5): 1651-1656.
[2] Li Shi-rong, Wan Ze-qing, Zhang Jing-hua. Free vibration of functionally graded beams based on both classical and first-order shear deformation beam theories[J]. Applied Mathematics and Mechanics, 2014, 35(5): 591-606.
[3] M. Simsek, Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories[J]. Nuclear Engineering and Design, 2010, 240(4): 697-705.
[4] T. P. Vo, H. T. Thai, et al. Static and vibration analysis of functionally graded beams using refined shear deformation theory[J]. Meccanica, 2014, 49(1): 155-168.
[5] H. T. Thai, T. P. Vo. Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories[J]. International Journal of Mechanical Sciences, 2012, 62(1): 57-66.
[6] T. K. Nguyen, T. P. Vo, H. T. Thai. Static and free vibration of axially loaded functionally graded beams based on the first-order shear deformation theory[J]. Composites: Part B, 2013, 55: 147-157.
[7] K. K. Pradhan, S. Chakraverty. Effects of different shear deformation theories on free vibration of functionally graded beams[J]. International Journal of Mechanical Sciences, 2014, 82(5): 149-160.
[8] K. K. Pradhan, S. Chakraverty. Generalized power-law exponent based shear deformation theory for free vibration of functionally graded beams[J]. Applied Mathematics and Computation, 2015, 268: 1240-1258.
[9] 蒲育, 滕兆春. Winkler-Pasternak弹性地基FGM梁自由振动二维弹性解[J], 振动与冲击, 2015, 34(20): 74-79.
PU Yu, TENG Zhao-chun. Two-dimensional elasticity solutions for free vibration of FGM beams resting on Winkler-Pasternak elastic foundation[J]. Journal of Vibration and Shock, 2015, 34(20): 74-79.
[10]V. Kahya, M. Turan. Finite element model for vibration and buckling of functionally graded beams based on the first-order shear deformation theory[J]. Composites: Part B, 2017, 109: 108-115.
[11] M. Simsek, J. N. Reddy. Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory[J]. International Journal of Engineering Science, 2013, 64(1): 37-53.
[12] L. Li, Y. J. Hu. Nonlinear bending and free vibration analyses of nonlocal strain gradient beams made of functionally graded material[J]. International Journal of Engineering Science, 2016, 107: 77-97.
[13] F. Ebrahimi E. Salari. Nonlocal thermo-mechanical vibration analysis of functionally graded nanobeams in thermal environment[J]. Acta Astronautica, 2015, 113(1): 29-50.
[14] C. T. Luan, T. P. Vo, et al. Fundamental frequency analysis of functionally graded sandwich beams based on the state space approach[J]. Composite Structures, 2015, 156: 263-275.
[15] 蒲育, 滕兆春, 赵海英. 四边弹性约束矩形板面内自由振动的DQM求解[J], 振动与冲击, 2016, 35(12): 55-60.
PU Yu, TENG Zhao-chun, ZHAO Hai-ying. In-plane free vibration analysis for rectangular plates with elastically restrained edges by differential quadrature method[J]. Journal of Vibration and Shock, 2016, 35(12): 55-60.
[16] C. Shu, H. Du. Implementation of clamped and simply supported boundary conditions in the GDQ free vibration of beams and plates[J]. International Journal of Solids and Structures, 1997, 34(7): 819-835.