کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
825040 | 1470006 | 2013 | 9 صفحه PDF | دانلود رایگان |
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.
Journal: International Journal of Engineering Science - Volume 63, February 2013, Pages 52–60