Size-Dependent Transverse Vibration of Microbeams

  • Ömer CivalekEmail author
  • Bekir Akgöz
Reference work entry


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.


Microbeam Size dependency Vibration Small-scale effect Modified strain gradient theory Higher-order beam theory Shear deformation effect Modified shear correction factor Length-scale parameter Trigonometric beam model 



This study has been supported by The Scientific and Technological Research Council of Turkey (TÜBİTAK) with Project No: 112M879. This support is gratefully acknowledged.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Civil Engineering Department, Division of MechanicsAkdeniz UniversityAntalyaTurkey

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