1st IFToMM Young Faculty Group Symposium on Emerging Fields in Mechanism and Machine Science, Duisburg, Almanya, 19 - 21 Kasım 2024, ss.1-2
Numerical and analytical methods are widely used to
reflect the vibrational dynamics of the resonant micro-cantilevers under
external forces for diverse Micro-Electro-Mechanical-System (MEMS) applications.
Variations in free oscillation observables such as amplitude, phase shift, and
frequency shift responses strongly depend on the patterns of external forces.
The micro-cantilevers can be resonated periodically with the driving forces in
the absence of other external forces, thereby oscillating with the free
amplitudes. Tip-sample interaction force such as Casimir force determines
the oscillation characteristics of the Atomic Force Microscopy (AFM)
micro-cantilevers in single- and multi-frequency excitations. Dynamic and
static acoustic forces can act on the one-side surface of the periodically
actuated micro-cantilever in various operating environments. The effects of
acoustic forces on the responses of the micro- and nano-systems are to be
considered for different technological applications in biophysics and microrheology
fields. Thus, sensitivity to target external forces can be explored by
isolating the acoustic force effects on the behaviors of micro-structures. In
the present work, three AFM micro-cantilevers are driven using single- and
bimodal-frequency excitation schemes to improve sensitivity to acoustic
forces. The Laplace transformation approach is utilized to obtain analytical
expressions of the out-of-plane deflections for the first flexural eigenmode. The
fourth-order Runge-Kutta method, the modified Rosenbrock formula,
Adams-Bashforth-Moulton formula, and the numerical differentiation formula are
applied to the second-order linear differential equations to obtain periodic
oscillations. Therefore, the performances of different numerical methods for
calculating micro-cantilever deflections are demonstrated considering the
analytical results in the current work.