Free and forced vibration nonlinear analysis of a microbeam using finite strain and velocity gradients theory

Ralston Fernandes, S. Mahmoud Mousavi, Sami El-Borgi

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8 Citations (Scopus)


A nonlinear finite strain and velocity gradient framework is formulated for the Euler–Bernoulli beam theory. This formulation includes finite strain and the strain gradient within the strain energy generalization as well as velocity and its gradient within the kinetic energy generalization. Consequently, static and kinetic internal length scales are developed to capture size effects. The governing equation with initial and boundary conditions is obtained using the variational approach. Free and forced vibration of a simply supported nanobeam is studied for different values of static and kinetic length scales using the method of multiple scales.

Original languageEnglish
Pages (from-to)2657-2670
Number of pages14
JournalActa Mechanica
Issue number9
Publication statusPublished - 1 Sep 2016


ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanical Engineering

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