TY - JOUR
T1 - On the nonlinear mechanics of layered microcantilevers
AU - Ghayesh, Mergen H.
AU - Farokhi, Hamed
AU - Gholipour, Alireza
AU - Hussain, Shahid
PY - 2017/11/1
Y1 - 2017/11/1
N2 - The nonlinear mechanics of three-layered microcantilevers under base excitation is investigated numerically. Employing the modified version of the couple stress-based theory, together with the Bernoulli-Euler beam theory, the potential energy of the three-layered microsystem is derived, while accounting for size effects. Obtaining the kinetic energy, the equations of motion in the longitudinal and transverse directions are derived via Hamilton's principle. Application of the inextensibility condition reduces the two equations of motion to one nonlinear integro-partial differential equation for the transverse oscillation, consisting of geometrical and inertial nonlinearities. The nonlinear equation of partial-differential type is reduced to set of equations of ordinary-differential type through use of a weighted-residual method. Solving the resultant set of discretised equations via a continuation technique gives the frequency-amplitude and force-amplitude responses of the microsystem. The nonlinear response is investigated for different layer composition and different layer thicknesses. The effect of small-scale parameter, as well as base excitation amplitude, is also examined.
AB - The nonlinear mechanics of three-layered microcantilevers under base excitation is investigated numerically. Employing the modified version of the couple stress-based theory, together with the Bernoulli-Euler beam theory, the potential energy of the three-layered microsystem is derived, while accounting for size effects. Obtaining the kinetic energy, the equations of motion in the longitudinal and transverse directions are derived via Hamilton's principle. Application of the inextensibility condition reduces the two equations of motion to one nonlinear integro-partial differential equation for the transverse oscillation, consisting of geometrical and inertial nonlinearities. The nonlinear equation of partial-differential type is reduced to set of equations of ordinary-differential type through use of a weighted-residual method. Solving the resultant set of discretised equations via a continuation technique gives the frequency-amplitude and force-amplitude responses of the microsystem. The nonlinear response is investigated for different layer composition and different layer thicknesses. The effect of small-scale parameter, as well as base excitation amplitude, is also examined.
KW - Layered microcantilever
KW - Microsystem
KW - Nonlinear resonance
KW - Numerical simulation
KW - Size effects
UR - http://www.scopus.com/inward/record.url?scp=85021125518&partnerID=8YFLogxK
U2 - 10.1016/j.ijengsci.2017.06.012
DO - 10.1016/j.ijengsci.2017.06.012
M3 - Article
AN - SCOPUS:85021125518
SN - 0020-7225
VL - 120
SP - 1
EP - 14
JO - International Journal of Engineering Science
JF - International Journal of Engineering Science
ER -