不同模量铁木辛柯梁的自由振动特性分析

doi:10.12066/j.issn.1007-2861.1976

Abstract

Abstract:

Free vibration of a beam with different modulus in tension and compression was studied. Unit body under a pure shear condition with different modulus in tension and compression was used to derivean expression of shear elasticity modulus with variational elasticity modulus. Based on elastic mechanics, structural mechanics, and the theory of different modulus, a vibration differential equation of Timoshenko Beam and Euler-Bernoulli beam is established, and the free vibration frequency of a simply supported Timoshenko Beam calculated. Considering different modulus, the position of neutral axis have a step change in the period of vibration, making the principle mode function piecewise. The results indicate that different modulus of a material has a great influence on the natural frequency of beam, which induces decrease in then at ural frequencies and therefore is worth consideration in structural vibration.

Key words: Timoshenko beam, Euler-Bernoulli beam, free vibration, vibration mode function, natural frequency

CLC Number:

TU323.3

Yang YANG, Wenjuan YAO. Analytical solution for free vibration of Timoshenko beam with different modulus[J]. Journal of Shanghai University（Natural Science Edition）, 2019, 25(6): 978-989.

Figures/Tables 7

Fig.1

Fig.2

Table 1

Table 2

Fig.3

Table 3

Fig.4

References 19

[1]	Barak M M, Currey J D, Weiner S , et al. Are tensile and compressive Young's moduli of compact bone different[J]. Journal of the Mechanical Behavior of Biomedical Materials, 2009,2(1):51-60.
[2]	Tsoukleri G, Parthenios J, Papagelis K , et al. Subjecting a graphene monolayer to tension and compression[J]. Small, 2009,5(21):2397-2402.
[3]	杨海天, 朱应利 . 光滑函数法求解拉压不同弹性模量问题[J]. 计算力学学报, 2006,23(1):19-23.
[4]	Yao W J, Ye Z M . Analytical solution for bending beam subject to lateral force with different modulus[J]. Applied Mathematics and Mechanics, 2004,25(10):1107-1117.
[5]	Yao W J, Ye Z M . Analytical solution of bending-compression column using different tension-compression modulus[J]. Applied Mathematics and Mechanics, 2004,25(9):983-993.
[6]	Yao W J, Ye Z M . Internal forces for statically indeterminate structures having different moduli[J]. Journal of Engineering Mechanics, 2006,132(7):739-746.
[7]	Yao W J, Zhang C H, Jiang X F . Nonlinear mechanical behavior of combined members with different moduli[J]. International Journal of Nonlinear Sciences and Numerical Simulation, 2006,7(2):233-238.
[8]	Yao W J, Liu J K . Temperature stress for bending beam with different modulus under different constraints[J]. International Journal of Multidiscipline Modeling in Materials and Structures, 2014,10(2):163-175.
[9]	Leal A A, Deitzel J M, Gillespie J W . Compressive strength analysis for high performance fibers with different modulus in tension and compression[J]. Journal of Composite Materials, 2009,43(6):661-674.
[10]	He X T, Zheng Z L, Sun J Y . Convergence analysis of a finite element method based on different moduli in tension and compression[J]. International Journal of Solids & Structures, 2009,46(20):3734-3740.
[11]	He X T . Application of the Kirchhoff hypojournal to bending thin plates with different moduli in tension and compression[J]. Journal of Mechanics of Materials & Structures, 2010,5(5):755-769.
[12]	黄翀, 吴晓, 杨立军 . 线性分布载荷作用下双模量圆板的计算分析[J]. 机械强度, 2012,34(1):64-68.
[13]	吴晓, 赵均海, 黄志刚 . 双模量材料圆板热弯曲及热屈曲的研究[J]. 应用力学学报, 2015,32(4):549-555.
[14]	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.
[15]	吴晓, 杨立军, 黄翀 . 不同模量面板夹心泡沫铝板大挠度弯曲[J]. 西安建筑科技大学学报(自然科学版), 2014,46(2):181-186.
[16]	Iwase T, Hirashima K . Dynamic response analysis of thick rectangular beam mode of bimodulus material.[J]. Transactions of the Japan Society of Mechanical Engineers Series A, 1997,63(608):765-773.
[17]	赵荣国, 徐友钜, 陈忠富 , 等. 不同拉压特性结构振动分析的双线性近似方法[J]. 振动与冲击, 2005,24(1):4-7.
[18]	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.
[19]	王铭慧, 赵永刚, 王康建 , 等. 拉压弹性模量不等材料简支梁的线性振动问题[J]. 甘肃科学学报, 2014,26(5):10-13.

Analytical solution for free vibration of Timoshenko beam with different modulus

RichHTML

PDF

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 7

References 19

Related Articles 6

Recommended Articles

Metrics

Comments

[1]	Yuan DAI, Tianyu WANG, Xiao YANG. Vibration analysis of cracked beam based on crack's equivalent rotational spring model [J]. Journal of Shanghai University（Natural Science Edition）, 2019, 25(6): 965-977.
[2]	Xiao YANG, Cheng QIAN, Xuewei QIAN. Bending of Timoshenko beam with arbitrary stepped cross-section [J]. Journal of Shanghai University（Natural Science Edition）, 2019, 25(5): 786-795.
[3]	ZHU Weiping, ZHOU Chujian, DI Qinfeng. Effect of lateral stimuli on vibration of clamped-hinged pipeline with fluid-structure interaction [J]. Journal of Shanghai University（Natural Science Edition）, 2016, 22(5): 597-605.
[4]	YANG Xiao, ZHANG Min, LIU Hui. Bending of Simple-Supported Composite Beam Considering Effect of Adhesive Layer Slip [J]. Journal of Shanghai University（Natural Science Edition）, 2013, 13(5): 501-507.
[5]	YANG Xiao1,JIN Pan1,XU Xiao-hui2. Dynamic Characteristics of Timoshenko Beam Partly Immersed in Water on Coupled Elastic Foundation [J]. Journal of Shanghai University（Natural Science Edition）, 2009, 15(6): 566-575.
[6]	LI Ying;CHENG Chang jun . Application of Differential Quadrature Method to Space Axial Symmetry Problems in Elasticity [J]. Journal of Shanghai University（Natural Science Edition）, 2007, 13(1): 55-61 .