Abstract
The nonlinear forced vibrations of a microbeam are investigated in this paper, employing the strain gradient elasticity theory. The geometrically nonlinear equation of motion of the microbeam, taking into account the size effect, is obtained employing a variational approach. Specifically, Hamilton's principle is used to derive the nonlinear partial differential equation governing the motion of the system which is then discretized into a set of second-order nonlinear ordinary differential equations (ODEs) by means of the Galerkin technique. A change of variables is then introduced to this set of second-order ODEs, and a new set of ODEs is obtained consisting of first-order nonlinear ordinary differential equations. This new set is solved numerically employing the pseudo-arclength continuation technique which results in the frequency-response curves of the system. The advantage of this method lies in its capability of continuing both stable and unstable solution branches.
Original language | English |
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Pages (from-to) | 52-60 |
Number of pages | 9 |
Journal | International Journal of Engineering Science |
Volume | 63 |
Early online date | 26 Dec 2012 |
DOIs | |
Publication status | Published - Feb 2013 |
Keywords
- Microbeam
- Nonlinear dynamics
- Stability
- Strain gradient elasticity