Performance comparisons of different numerical methods for obtaining out-of-plane deflections of a resonant AFM micro-cantilever under acoustic emissions

Yılmaz Ç.

1st IFToMM Young Faculty Group Symposium on Emerging Fields in Mechanism and Machine Science, Duisburg, Almanya, 19 - 21 Kasım 2024, ss.1-2

  • Yayın Türü: Bildiri / Özet Bildiri
  • Basıldığı Şehir: Duisburg
  • Basıldığı Ülke: Almanya
  • Sayfa Sayıları: ss.1-2
  • Akdeniz Üniversitesi Adresli: Evet

Özet

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.