Vibration and wave propagation analysis of twisted micro-beam using strain gradient theory

doi:10.1007/s10483-016-2138-9

Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (10): 1375-1392.doi: https://doi.org/10.1007/s10483-016-2138-9

Vibration and wave propagation analysis of twisted micro-beam using strain gradient theory

M. MOHAMMADIMEHR, M. J. FARAHI, S. ALIMIRZAEI

Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan 87317-53153, Iran

收稿日期:2016-01-26 修回日期:2016-05-10 出版日期:2016-10-01 发布日期:2016-10-01
通讯作者: M. MOHAMMADIMEHR E-mail:mmohammadimehr@kashanu.ac.ir
基金资助:
Project supported by the Iranian Nanotechnology Development Committee and the University of Kashan (No.463855/11)

Vibration and wave propagation analysis of twisted micro-beam using strain gradient theory

M. MOHAMMADIMEHR, M. J. FARAHI, S. ALIMIRZAEI

Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan 87317-53153, Iran

Received:2016-01-26 Revised:2016-05-10 Online:2016-10-01 Published:2016-10-01
Supported by:
Project supported by the Iranian Nanotechnology Development Committee and the University of Kashan (No.463855/11)

摘要/Abstract

摘要：

In this research, vibration and wave propagation analysis of a twisted microbeam on Pasternak foundation is investigated. The strain-displacement relations (kinematic equations) are calculated by the displacement fields of the twisted micro-beam. The strain gradient theory (SGT) is used to implement the size dependent effect at microscale. Finally, using an energy method and Hamilton’s principle, the governing equations of motion for the twisted micro-beam are derived. Natural frequencies and the wave propagation speed of the twisted micro-beam are calculated with an analytical method. Also, the natural frequency, the phase speed, the cut-off frequency, and the wave number of the twisted micro-beam are obtained by considering three material length scale parameters, the rate of twist angle, the thickness, the length of twisted micro-beam, and the elastic medium. The results of this work indicate that the phase speed in a twisted micro-beam increases with an increase in the rate of twist angle. Moreover, the wave number is inversely related with the thickness of micro-beam. Meanwhile, it is directly related to the wave propagation frequency. Increasing the rate of twist angle causes the increase in the natural frequency especially with higher thickness. The effect of the twist angle rate on the group velocity is observed at a lower wave propagation frequency.

关键词: twisted micro-beam, vibration and wave propagation analysis, strain gradient theory (SGT), rate of twist angle

Abstract:

Key words: strain gradient theory (SGT), vibration and wave propagation analysis, rate of twist angle, twisted micro-beam

中图分类号:

M. MOHAMMADIMEHR, M. J. FARAHI, S. ALIMIRZAEI. Vibration and wave propagation analysis of twisted micro-beam using strain gradient theory[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(10): 1375-1392.

参考文献

[1] Giannakopoulos, A. W., Aravas, N., and Vardoulakis, P. A. A structural gradient theory of torsion, the effects of pretwist, and the tension of pre-twisted DNA. International Journal of Solids and Structures, 50, 3922-3933(2013)
[2] Ho, S. H. and Chen, C. K. Free transverse vibration of an axially loaded non-uniform spinning twisted Timoshenko beam using differential transform. International Journal of Mechanical Sciences, 48, 1323-1331(2006)
[3] Leung, A. Y. T. and Fan, J. Natural vibration of pre-twisted shear deformable beam systems subject to multiple kinds of initial stresses. Journal of Sound and Vibration, 329, 1901-1923(2010)
[4] Yu, A. M., Yang, X. G., and Nie, G. H. Generalized coordinate for warping of naturally curved and twisted beams with general cross-sectional shapes. International Journal of Solids and Structures, 43, 2853-2876(2006)
[5] Wang, Q. and Yu, W. A refined model for thermo elastic analysis of initially curved and twisted composite beams. Engineering Structures, 48, 233-244(2013)
[6] Mustapha, K. B. and Zhong, Z. W. Wave propagation characteristics of a twisted micro scale beam. International Journal of Engineering Science, 53, 46-57(2012)
[7] Cšarek, P., Saje, M., and Zupan, D. Kinematically exact curved and twisted strain-based beam. International Journal of Solids and Structures, 49, 1802-1817(2012)
[8] Chen, W. R. Effect of local Kelvin-Voigt damping on eigen frequencies of cantilevered twisted Timoshenko beams. Procedia Engineering, 79, 160-165(2014)
[9] Subrahmanyam, K. B. and Rao, J. S. Coupled bending-bending vibrations of pre-twisted tapered cantilever beams treated by the Reissner method. Journal of Sound and Vibration, 82, 577-592(1982)
[10] Chen, W. R. On the vibration and stability of spinning axially loaded pre-twisted Timoshenko beams. Finite Elements in Analysis and Design, 46, 1037-1047(2010)
[11] Sinha, S. K. and Turner, K. E. Natural frequencies of a pre-twisted blade in a centrifugal force field. Journal of Sound and Vibration, 330, 2655-2681(2011)
[12] Chen, W. R., Hsin, S. W., and Chu, T. H. Vibration analysis of twisted Timoshenko beams with internal Kelvin-Voigt damping. Procedia Engineering, 67, 525-532(2013)
[13] Banerjee, J. R. Free vibration analysis of a twisted beam using the dynamic stiffness method. International Journal of Solids Structures, 38, 6703-6722(2001)
[14] Sabuncu, M. and Evran, K. The dynamic stability of a rotating pre-twisted asymmetric crosssection Timoshenko beam subjected to lateral parametric excitation. International Journal of Mechanical Sciences, 48, 878-888(2006)
[15] Mohammadimehr, M., Rousta-Navi, B., and Ghorbanpour-Arani, A. Free vibration of viscoelastic double-bonded polymeric nanocomposite plates reinforced by FG-SWCNTs using MSGT, sinusoidal shear deformation theory and meshless method. Composite Structures, 131, 654-671(2015)
[16] Wang, C. M., Zhang, Y. Y., and He, X. Q. Vibration of nonlocal Timoshenko beams. Nanotechnology, 18, 9-18(2007)
[17] Mohammadimehr, M., Rousta-Navi, B., and Ghorbanpour-Arani, A. Modified strain gradient Reddy rectangular plate model for biaxial buckling and bending analysis of double-coupled piezoelectric polymeric nanocomposite reinforced by FG-SWNT. Composite Part B:Engineering, 87, 132-148(2016)
[18] Ghorbanpour-Arani, A., Kolahchi, R., and Vossough, H. Nonlocal wave propagation in an embedded DWBNNT conveying fluid via strain gradient theory. Physica B, 407, 4281-4286(2012)
[19] Narendar, S., Gupta, S. S., and Gopalakrishnan, S. Wave propagation in single-walled carbon nanotube under longitudinal magnetic field using nonlocal Euler-Bernoulli beam theory. Applied Mathematical Modelling, 36, 4529-4538(2012)
[20] Aydogdu, M. Longitudinal wave propagation in multi-walled carbon nanotubes. Composite Structures, 107, 578-584(2014)
[21] Wang, L. Wave propagation of fluid-conveying single-walled carbon nanotubes via gradient elasticity theory. Computational Materials Science, 49, 761-766(2010)
[22] Liew, K. M. and Wang, Q. Analysis of wave propagation in carbon nanotubes via elastic shell theories. International Journal of Engineering Science, 45, 227-241(2007)
[23] Mohammadimehr, M., Mohammadimehr, M. A., and Dashti, P. Size-dependent effect on biaxial and shear nonlinear buckling analysis of nonlocal isotropic and orthotropic micro-plate based on surface stress and modified couple stress theories using differential quadrature method (DQM). Applied Mathematics and Mechanics (English Edition), 37(4), 529-554(2016) DOI 10.1007/s10483-016-2045-9
[24] Wang, B., Zhou, S. H., Zhao, J., and Chen, X. A size-dependent Kirchhoff micro-plate model based on strain gradient elasticity theory. European Journal of Mechanics A/Solids, 30, 517-524(2011)
[25] Paliwal, D. N., Pendey, R. K., and Nath, T. Free vibrations of circular cylindrical shell on Winkler and Pasternak foundations. International Journal of Pressure Vessels and Piping, 69, 79-89(1996)
[26] Reddy J. N. Energy Principles and Variational Methods in Applied Mechanic, John Wiley and Sons, New York (2002)
[27] Li, X. Y., Zhao, X., and Li, Y. H. Green's functions of the forced vibration of Timoshenko beams with damping effect. Journal of Sound and Vibration, 333, 1781-1795(2014)

Vibration and wave propagation analysis of twisted micro-beam using strain gradient theory

Vibration and wave propagation analysis of twisted micro-beam using strain gradient theory

PDF

可视化

被引次数

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 7

编辑推荐

Metrics

本文评价

[1]	Hu DING, J. C. JI. Vibration control of fluid-conveying pipes: a state-of-the-art review[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(9): 1423-1456.
[2]	Bo DOU, Hu DING, Xiaoye MAO, Sha WEI, Liqun CHEN. Dynamic modeling of fluid-conveying pipes restrained by a retaining clip[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(8): 1225-1240.
[3]	Lingkang ZHAO, Peijun WEI, Yueqiu LI. Free vibration of thermo-elastic microplate based on spatiotemporal fractional-order derivatives with nonlocal characteristic length and time[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(1): 109-124.
[4]	Pengcheng ZHAO, Kai ZHANG, Cheng ZHAO, Zichen DENG. Multi-resonator coupled metamaterials for broadband vibration suppression[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(1): 53-64.
[5]	Yanqing WANG, Han WU, Fengliu YANG, Quan WANG. An efficient method for vibration and stability analysis of rectangular plates axially moving in fluid[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(2): 291-308.
[6]	M. KOHANSAL-VAJARGAH, R. ANSARI, M. FARAJI-OSKOUIE, M. BAZDID-VAHDATI. Vibration analysis of two-dimensional structures using micropolar elements[J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(7): 999-1012.
[7]	Qingdong CHAI, Yanqing WANG, Meiwen TENG. Nonlinear free vibration of spinning cylindrical shells with arbitrary boundary conditions[J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(8): 1203-1218.