The natural vibration of bimodulous beam considering shear effect

WU Xiao HUANG Zhigang YANG Lijun

Journal of Vibration and Shock ›› 2015, Vol. 34 ›› Issue (24) : 160-163.

PDF(1053 KB)
PDF(1053 KB)
Journal of Vibration and Shock ›› 2015, Vol. 34 ›› Issue (24) : 160-163.

The natural vibration of bimodulous beam considering shear effect

  • WU Xiao  HUANG Zhigang  YANG Lijun
Author information +
History +

Abstract

Considering the shear effect, the natural vibration problem of bimodulous beam is studied in this paper. On the basis of considering shear effect, the vibration differential equation of bimodulous beam is established, the mode shape expression of vibration problem of bimodulous beam is derived, and the influence of shear effect on natural vibration frequencies of bimodulous beam is analyzed. The computational results indicate that the influence of shear effect on natural vibration of bimodulous beam can not be ignored in some case. The conclusion that, there are discontinuity points in the odd wave type and wave shape of the natural vibration problem of bimodulous beam, is also got.

Key words

shear effect / bimodulous / beam / natural vibration / frequency

Cite this article

Download Citations
WU Xiao HUANG Zhigang YANG Lijun. The natural vibration of bimodulous beam considering shear effect[J]. Journal of Vibration and Shock, 2015, 34(24): 160-163

References

[1] Medri G. A nonlinear elastic model for isotropic materials with different behavior in tension and compression [J]. Transactions of the ASME, 1982, 26(104): 26-28.
[2] Srinivasan R S, Ramachandra L S. Axisymmetric nonlinear dynamic response of bimodulous annular plates [J]. Journal of Vibration and Acoustics, 1990, 112(2): 202-205.
[3] 阿巴尔楚米扬. 邬瑞锋, 张允真译. 不同模量弹性理论[M]. 北京: 中国铁道出版社, 1986: 274-275.
Ambartsumyan S A. Translated by Wu Ruifeng, Zhang Yunzhen. Elasticity theory of different modulus [M]. Beijing: China Railway Press, 1986: 274-275. (in Chinese)
[4] 蔡来生, 俞焕然. 拉压模量不同弹性物质的本构[J]. 西安科技大学学报, 2009, 29(1): 17-21.
Cai Laisheng, YU Huanran. Constitutive relation of elastic materials with different elastic moduli in tension and compression [J]. Journal of Xi’an University of Science and Technology, 2009, 29(1): 17-21. (in Chinese)
[5]  罗战友, 夏建中, 龚晓南. 不同拉压模量及软化特性材料的柱形孔扩张问题的统一解[J]. 工程力学, 2008, 25(9): 79-84.
Luo Zhanyou, Xia Jianzhong, Gong Xiaonan. Unified solution for expansion of cylindrical cavity in strain-softening materials with different elastic moduli in tension and compression [J]. Engineering Mechanics, 2008, 25(9): 79-84. (in Chinese)
[6]  张晓月. 基于敏度分析的不同模量桁架正反问题求解[D]. 大连: 大连理工大学, 2008.
Zhang Xiaoyue. Sensitivity analysis based numerical solutions of normal and inverse problems of elastic bimodular truss structure [D]. Dalian: Dalian University of Technology, 2008. (in Chinese)
[7]  杨海天, 张晓月, 何宜谦. 基于敏度分析的拉压不同模量桁架问题的数值分析[J]. 计算力学学报, 2011, 28(2): 237-242.
Yang Haitian, Zhang Xiaoyue, He Yiqian. Sensitivity analysis based numerical solution for truss structures with bi-modulus [J]. Chinese Journal of Computational Mechanics, 2011, 28(2): 237-242. (in Chinese)
[8] 吴晓, 杨立军, 黄翀, 等. 用能量法研究双模量大挠度圆板的轴对称弯曲[J]. 计算力学学报, 2011, 28(2): 274-278.
Wu Xiao, Yang Lijun, Huang Chong, etc.. Large deflection axisymmetric bending of bi-modulous circular plate with energy method [J]. Chinese Journal of Computational Mechanics, 2011, 28(2): 274-278. (in Chinese)
[9] 吴晓, 杨立军, 黄翀, 等. 双模量矩形板的大挠度弯曲计算分析[J]. 工程力学, 2010, 27(1): 17-22.
Wu Xiao, Yang Lijun, Huang Chong, etc.. Large deflection bending calculation and analysis of bimodulous rectangular plate [J]. Engineering Mechanics, 2010, 27(1): 17-22. (in Chinese)
[10] 吴晓, 杨立军. 拉压弹性模量不同厚壁球壳的弹性解析解[J]. 湖南科技大学学报(自然科学版), 2012, 27(4): 35-38.
Wu Xiao, Yang Lijun. Elastic solutions for thick wall spherical shell of bimodulous materials under uniform pressure [J]. Journal of Hunan University of Science & Technology (Natural Science Edition), 2012, 27(4): 35-38. (in Chinese)
[11] 吴晓, 杨立军, 黄翀. 双模量圆板中心在冲击荷载作用下的弹性计算[J]. 西安建筑科技大学学报(自然科学版), 2012, 44(5): 614-619.
Wu Xiao, Yang Lijun, Huang Chong. Elastic dynamic calculation for bimodulous circular plate under the condition of impact load [J]. Journal of Xi ’an University of Architecture & Technology (Natural Science Edition), 2012, 44(5): 614-619. (in Chinese)
[12] 吴晓, 黄翀, 孙晋. 双模量悬臂梁在分布荷载作用下的Kantorovich解[J]. 湖南科技大学学报(自然科学版), 2012, 27(2): 55-59.
Wu Xiao, Huang Chong, Sun Jin. The Kantorovich solution for bimodulous cantilever under distributed loads [J]. Journal of Hunan University of Science & Technology (Natural Science Edition), 2012, 27(2): 55-59. (in Chinese)
[13] 吴晓, 黄翀, 杨立军. 双模量平行四边形板弯曲的Kantorovich变分解[J]. 力学季刊, 2010, 31(4): 597-603.
Wu Xiao, Huang Chong, Yang Lijun. Kantorovich variational solution of bending bimodulous parallelogram plate [J]. Chinese Quarterly of Mechanics, 2010, 31(4): 597-603. (in Chinese)
[14] 姚文娟, 叶志明. 不同模量弯压柱的解析解[J]. 应用数学和力学, 2004, 25(9): 901-909.
Yao Wenjuan, Ye Zhiming. Analytical solution of bending- compression column using different tension-compression modulus. Applied Mathematics and Mechanics, 2004, 25(9): 901-909. (in Chinese)
[15] 姚文娟, 叶志明. 不同模量横力弯曲梁的解析解[J]. 应用数学和力学, 2004, 25(10):1014-1022.
Yao Wenjuan, Ye Zhiming. Analytical solution for bending beam subject to lateral force with different modulus. Applied Mathematics and Mechanics, 2004, 25(10): 1014-1022. (in Chinese)
[16] 刘相斌, 宋宏伟. 不同模量弯曲梁的自由振动[J]. 大连民族学院学报, 2007, 40(5): 104-107.
Liu Xiangbin,Song Hongwei. Free vibration of the bending beam about different tensile-compressive modulus. Journal of Dalian Nationalities University,2007, 40(5): 104-107. (in Chinese)
PDF(1053 KB)

Accesses

Citation

Detail

Sections
Recommended

/