TY - JOUR
T1 - Subcritical parametric dynamics of microbeams
AU - Ghayesh, Mergen H.
AU - Farokhi, Hamed
AU - Alici, Gursel
PY - 2015/10/1
Y1 - 2015/10/1
N2 - The aim of this paper is to analyse the size-dependent nonlinear parametric dynamics of microbeams; the source of parametric excitation is a time-dependent longitudinal excitation load. Taking into account small-size effects, via the modified couple stress theory, the expressions for the potential and kinetic energies of the system are developed. A multi-degree-of-freedom discretised system is obtained by transforming the continuous model into a reduced-order one via the Galerkin scheme. For the system in the subcritical mean axial load regime, the parametric response is obtained via two different numerical techniques; first one is based on a continuation technique and the second one is via a direct time-integration method. A stability analysis is also conducted via the Floquet theory. Results for the nonlinear parametric response are illustrated in the form of parametric frequency-response diagrams, parametric force-response curves, time histories, phase-plane portraits, fast Fourier transforms (FFTs), and Poincaré maps. The effect of taking into account the length-scale parameter on the parametric response of the system is also highlighted.
AB - The aim of this paper is to analyse the size-dependent nonlinear parametric dynamics of microbeams; the source of parametric excitation is a time-dependent longitudinal excitation load. Taking into account small-size effects, via the modified couple stress theory, the expressions for the potential and kinetic energies of the system are developed. A multi-degree-of-freedom discretised system is obtained by transforming the continuous model into a reduced-order one via the Galerkin scheme. For the system in the subcritical mean axial load regime, the parametric response is obtained via two different numerical techniques; first one is based on a continuation technique and the second one is via a direct time-integration method. A stability analysis is also conducted via the Floquet theory. Results for the nonlinear parametric response are illustrated in the form of parametric frequency-response diagrams, parametric force-response curves, time histories, phase-plane portraits, fast Fourier transforms (FFTs), and Poincaré maps. The effect of taking into account the length-scale parameter on the parametric response of the system is also highlighted.
KW - Microbeam
KW - Modified couple stress theory
KW - Parametric excitation
KW - Subcritical
U2 - 10.1016/j.ijengsci.2015.06.001
DO - 10.1016/j.ijengsci.2015.06.001
M3 - Article
AN - SCOPUS:84936806405
VL - 95
SP - 36
EP - 48
JO - International Journal of Engineering Science
JF - International Journal of Engineering Science
SN - 0020-7225
M1 - 2664
ER -