Abstract
In this chapter, a new microstructure-dependent higher-order shear deformation beam model is introduced to investigate the vibrational characteristics of microbeams. This model captures both the size and shear deformation effects without the need for any shear correction factors. The governing differential equations and related boundary conditions are derived by implementing Hamilton’s principle on the basis of modified strain gradient theory in conjunction with trigonometric shear deformation beam theory. The free vibration problem for simply supported microbeams is analytically solved by employing the Navier solution procedure. Moreover, a new modified shear correction factor is firstly proposed for Timoshenko (first-order shear deformation) microbeam model. Several comparative results are presented to indicate the effects of material length-scale parameter ratio, slenderness ratio, and shear correction factor on the natural frequencies of microbeams. It is observed that effect of shear deformation becomes more considerable for both smaller slenderness ratios and higher modes.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
B. Akgöz, Ö. Civalek, Arch. Appl. Mech. 82, 423 (2012)
B. Akgöz, Ö. Civalek, Acta Mech. 224, 2185 (2013a)
B. Akgöz, Ö. Civalek, Int. J. Eng. Sci. 70, 1 (2013b)
B. Akgöz, Ö. Civalek, Compos. Struct. 112, 214 (2014a)
B. Akgöz, Ö. Civalek, Int. J. Mech. Sci. 81, 88 (2014b)
B. Akgöz, Ö. Civalek, Int. J. Eng. Sci. 85, 90 (2014c)
B. Akgöz, Ö. Civalek, Int. J. Mech. Sci. 99, 10 (2015)
B.S. Altan, H. Evensen, E.C. Aifantis, Mech. Res. Commun. 23, 35 (1996)
R. Ansari, R. Gholami, S. Sahmani, Compos. Struct. 94, 221 (2011)
R. Artan, R.C. Batra, Acta Mech. 223, 2393 (2012)
M. Aydogdu, Compos. Struct. 89, 94 (2009a)
M. Aydogdu, Phys. E. 41, 1651 (2009b)
A.C. Eringen, Z. Angew. Math. Phys. 18, 12 (1967)
A.C. Eringen, Int. J. Eng. Sci. 10, 1 (1972)
A.C. Eringen, J. Appl. Phys. 54, 4703 (1983)
N.A. Fleck, J.W. Hutchinson, J. Mech. Phys. Solids 41, 1825 (1993)
N.A. Fleck, J.W. Hutchinson, J. Mech. Phys. Solids 49, 2245 (2001)
E.S. Hung, S.D. Senturia, J. Microelectromech. Syst. 8, 497 (1999)
M.H. Kahrobaiyan, M. Asghari, M.T. Ahmadian, Finite Elem. Anal. Des. 68, 63 (2013)
M.H. Kahrobaiyan, M. Rahaeifard, S.A. Tajalli, M.T. Ahmadian, Int. J. Eng. Sci. 52, 65 (2012)
M. Karama, K.S. Afaq, S. Mistou, Int. J. Solids Struct. 40, 1525 (2003)
W.T. Koiter, Proc. K. Ned. Akad. Wet. B 67, 17 (1964)
S. Kong, S. Zhou, Z. Nie, K. Wang, Int. J. Eng. Sci. 47, 487 (2009)
D.C.C. Lam, F. Yang, A.C.M. Chong, J. Wang, P. Tong, J. Mech. Phys. Solids 51, 1477 (2003)
M. Levinson, A new rectangular beam theory. J. Sound Vib. 74, 81 (1981)
P. Li, Y. Fang, J. Micromech. Microeng. 20, 035005 (2010)
A.W. McFarland, J.S. Colton, J. Micromech. Microeng. 15, 1060 (2005)
R.D. Mindlin, Int. J. Solids Struct. 1, 417 (1965)
R.D. Mindlin, H.F. Tiersten, Arch. Ration. Mech. Anal. 11, 415 (1962)
W.J. Poole, M.F. Ashby, N.A. Fleck, Scr. Mater. 34, 559 (1996)
J.N. Reddy, J. Appl. Mech. 51, 745 (1984)
J.N. Reddy, J. Mech. Phys. Solids 59, 2382 (2011)
M. Salamat-talab, A. Nateghi, J. Torabi, Int. J. Mech. Sci. 57, 63 (2012)
M. Şimşek, J.N. Reddy, Int. J. Eng. Sci. 64, 37 (2013a)
M. Şimşek, J.N. Reddy, Compos. Struct. 101, 47 (2013b)
K.P. Soldatos, Acta Mech. 94, 195 (1992)
H.T. Thai, T.P. Vo, Int. J. Eng. Sci. 54, 58 (2012)
H.T. Thai, T.P. Vo, Compos. Struct. 96, 376 (2013)
S.P. Timoshenko, Philos. Mag. 41, 744 (1921)
A. Torii, M. Sasaki, K. Hane, S. Okuma, Sensors Actuators A Phys. 44, 153 (1994)
R.A. Toupin, Arch. Ration. Mech. Anal. 17, 85 (1964)
M. Touratier, Int. J. Eng. Sci. 29, 901 (1991)
I. Vardoulakis, J. Sulem, Bifurcation Analysis in Geomechanics (Blackie/Chapman and Hall, London, 1995)
B. Wang, J. Zhao, S. Zhou, Eur. J. Mech. A/Solids 29, 591 (2010)
Z.Y. Wu, H. Yang, X.X. Li, Y.L. Wang, J. Micromech. Microeng. 20, 115014 (2010)
W.C. Xie, H.P. Lee, S.P. Lim, Nonlinear Dyn. 31, 243 (2003)
M.I. Younis, E.M. Abdel-Rahman, A.H. Nayfeh, J. Microelectromech. Syst. 12, 672 (2003)
B. Zhang, Y. He, D. Liu, Z. Gan, L. Shen, Finite Elem. Anal. Des. 79, 22 (2014a)
B. Zhang, Y. He, D. Liu, Z. Gan, L. Shen, Eur J Mech A/Solids 47, 211 (2014b)
J.D. Zook, D.W. Burns, H. Guckel, J.J. Sniegowski, R.L. Engelstad, Z. Feng, Sensors Actuators A Phys. 35, 51 (1992)
Acknowledgments
This study has been supported by The Scientific and Technological Research Council of Turkey (TÜBİTAK) with Project No: 112M879. This support is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this entry
Cite this entry
Civalek, Ö., Akgöz, B. (2019). Size-Dependent Transverse Vibration of Microbeams. In: Voyiadjis, G. (eds) Handbook of Nonlocal Continuum Mechanics for Materials and Structures. Springer, Cham. https://doi.org/10.1007/978-3-319-58729-5_8
Download citation
DOI: https://doi.org/10.1007/978-3-319-58729-5_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-58727-1
Online ISBN: 978-3-319-58729-5
eBook Packages: EngineeringReference Module Computer Science and Engineering