TY - JOUR
T1 - Modal interactions and energy transfers in large-amplitude vibrations of functionally graded microcantilevers
AU - Farokhi, Hamed
AU - Ghayesh, Mergen H.
AU - Gholipour, Alireza
AU - Hussain, Shahid
PY - 2018/9
Y1 - 2018/9
N2 - Modal interactions and internal energy transfers are investigated in the large-amplitude oscillations of a functionally graded microcantilever with an intermediate spring-support. Based on the Mori–Tanaka homogenization technique and the modified couple stress theory, the energy terms of the functionally graded microsystem (kinetic and size-dependent potential energies) are developed and dynamically balanced. Large-amplitude deformations, due to having one end free, are modeled taking into account curvature-related nonlinearities and assuming an inextensibility condition. The continuous model of the functionally graded microsystem is reduced, by means of the Galerkin method, yielding an inertial- and stiffness-wise nonlinear model. Numerical simulations on this highly nonlinear reduced-order model of the functionally graded microcantilever are performed using a continuation method; a possible case of modal interactions is determined by obtaining the natural frequencies of the microsystem. The nonlinear oscillations of the microcantilever are examined, and it is shown how the energy fed to the functionally graded microsystem (from the base excitation) is transferred between different modes of oscillation.
AB - Modal interactions and internal energy transfers are investigated in the large-amplitude oscillations of a functionally graded microcantilever with an intermediate spring-support. Based on the Mori–Tanaka homogenization technique and the modified couple stress theory, the energy terms of the functionally graded microsystem (kinetic and size-dependent potential energies) are developed and dynamically balanced. Large-amplitude deformations, due to having one end free, are modeled taking into account curvature-related nonlinearities and assuming an inextensibility condition. The continuous model of the functionally graded microsystem is reduced, by means of the Galerkin method, yielding an inertial- and stiffness-wise nonlinear model. Numerical simulations on this highly nonlinear reduced-order model of the functionally graded microcantilever are performed using a continuation method; a possible case of modal interactions is determined by obtaining the natural frequencies of the microsystem. The nonlinear oscillations of the microcantilever are examined, and it is shown how the energy fed to the functionally graded microsystem (from the base excitation) is transferred between different modes of oscillation.
KW - energy transfer
KW - Functionally graded microcantilever
KW - material gradient index
KW - modal interaction
KW - natural frequency
KW - size-dependent vibration
UR - http://www.scopus.com/inward/record.url?scp=85029125941&partnerID=8YFLogxK
UR - http://www.mendeley.com/research/modal-interactions-energy-transfers-largeamplitude-vibrations-functionally-graded-microcantilevers
U2 - 10.1177/1077546317714883
DO - 10.1177/1077546317714883
M3 - Article
AN - SCOPUS:85029125941
SN - 1077-5463
VL - 24
SP - 3882
EP - 3893
JO - JVC/Journal of Vibration and Control
JF - JVC/Journal of Vibration and Control
IS - 17
ER -