TY - JOUR
T1 - Size-dependent large-amplitude oscillations of microcantilevers
AU - Ghayesh, Mergen H.
AU - Farokhi, Hamed
PY - 2017/8/1
Y1 - 2017/8/1
N2 - The size-dependent oscillations of a microcantilever with a tip (end) mass and a spring support undergoing a large-amplitude motion is analysed theoretically, taking into account curvature-related nonlinearities. Modelling small-size effects via use of the modified couple stress theory, the size-dependent potential and kinetic energies of the system are obtained. The continuous models for the motion behaviour of the microcantilever are developed via use of an energy method on the basis of Hamilton’s principle. Application of the centreline-inextensibility in oscillation course of the microcantilever results in a continuous model of the system with nonlinear inertial terms, which when coupled with curvature nonlinearities produces a highly nonlinear system. A weighted-residual method is then employed to truncate the continuous model, yielding the reduced-order model of the microcantilever motion with a generalised-coordinate-dependent mass matrix (due to inertial nonlinearities); a coupled continuation-time-integration method is then employed for the numerical simulations. The large-amplitude oscillation behaviour of the system is examined by constructing the frequency–responses and force-responses. The effect of the size of the end-mass on the nonlinear oscillation behaviour of the microcantilever is analysed. The importance of taking into account different nonlinearity sources is discussed. It is shown that the modified couple stress theory results in a stronger softening behaviour when compared to the classical continuum mechanics.
AB - The size-dependent oscillations of a microcantilever with a tip (end) mass and a spring support undergoing a large-amplitude motion is analysed theoretically, taking into account curvature-related nonlinearities. Modelling small-size effects via use of the modified couple stress theory, the size-dependent potential and kinetic energies of the system are obtained. The continuous models for the motion behaviour of the microcantilever are developed via use of an energy method on the basis of Hamilton’s principle. Application of the centreline-inextensibility in oscillation course of the microcantilever results in a continuous model of the system with nonlinear inertial terms, which when coupled with curvature nonlinearities produces a highly nonlinear system. A weighted-residual method is then employed to truncate the continuous model, yielding the reduced-order model of the microcantilever motion with a generalised-coordinate-dependent mass matrix (due to inertial nonlinearities); a coupled continuation-time-integration method is then employed for the numerical simulations. The large-amplitude oscillation behaviour of the system is examined by constructing the frequency–responses and force-responses. The effect of the size of the end-mass on the nonlinear oscillation behaviour of the microcantilever is analysed. The importance of taking into account different nonlinearity sources is discussed. It is shown that the modified couple stress theory results in a stronger softening behaviour when compared to the classical continuum mechanics.
KW - Modify Couple Stress Theory
KW - Resonant Region
KW - Timoshenko Microbeam
KW - Symmetric Curvature Tensor
KW - Small Excitation Frequency
U2 - 10.1007/s00542-016-3203-x
DO - 10.1007/s00542-016-3203-x
M3 - Article
AN - SCOPUS:85000785435
VL - 23
SP - 3477
EP - 3488
JO - Microsystem Technologies
JF - Microsystem Technologies
SN - 0946-7076
IS - 8
ER -