Akademik Veri Yönetim Sistemi
The Third International Conference on Applied Mathematics in Engineering (ICAME’24), Balıkesir, Türkiye, 26 - 28 Haziran 2024, ss.1
This current work presents a new conceptual model to investigate the
hydrodynamic sensitivity of a micro-cantilever with the consideration of driving
force strength. A nonlinear dynamic model of an oscillating micro-cantilever is
constructed based on a forced and damped Duffing-Mathieu oscillator including
the bimodal-frequency excitation scheme. Duffing-Mathieu equations are solved
by using diverse theoretical methods for different applications. In the
present work, the effect of excitation force magnitude on time-domain responses
of the micro-cantilever in sugar solutions with different concentrations is
explored for single- and bimodal-frequency excitations. The simulation result
indicates that the amplitude of 0.55 nm at the first eigenmode is acquired in
55% sugar solution under the driving force strength of 400 nN in the
single-frequency operation. Besides, effective hydrodynamic forces acting on
the one-side area of the vibrating micro-cantilever are determined considering
Sader's hydrodynamic functions. Magnitudes of hydrodynamic forces remarkably
change on the time domain as the excitation force varies for the first two
flexural modes. To illustrate, the viscous loads at the second eigenmode appear
in the range of 20-2000 nN as the driving force strength ranges from 100 nN to
400 nN. Obviously, the Duffing and Mathieu functions in the proposed model have
also significant influences on time-domain responses and effective hydrodynamic
forces. Correspondingly, the displacements of the micro-cantilever and
effective viscous loads at the first two eigenmodes are obtained for different
nonlinearity degrees of mechanical systems. Micro-cantilever responses strongly
depend on excitation frequency and amplitude in Mathieu functions. It is worth
mentioning that as the parameter of excitation amplitude is varied from 1 to
12, the amplitude at the first eigenmode decreases from 600 pm to 500 pm. Therefore,
the multimodal nonlinear dynamic model enables to evaluate the influence of
driving force strength on nonlinear behaviours of the micro-cantilever at
higher mode in a viscous environment.