Akademik Veri Yönetim Sistemi
9th IFS and Contemporary Mathematics and Engineering Conference, Mersin, Türkiye, 8 - 11 Temmuz 2023, ss.1-4
In this current work, a forced Van der Pol oscillator based dynamic model is introduced to demonstrate the time-domain sensitivities of the micro-cantilever to the micro-rheological properties of the surrounding fluids. Effects of diverse multi-frequency excitations on hydrodynamically forced displacements are investigated for the glycerol-water solutions with different concentrations. It is demonstrated that the frequency of the displacements under hydrodynamic loads decreases with increasing dynamic viscosity and density of the fluids (among 55\% and 85\% Glycerol-water solutions) in bimodal- and trimodal-frequency excitations. In addition, steady-state observables are achieved at only particular eigenmodes in single- and multi-frequency operations depending on the nonlinearity level of the dynamic systems. It is highlighted that hydrodynamically forced periodic oscillations are obtained for the first and second eigenmodes by utilizing a nonlinear oscillator with the highest selected value of forced Van der Pol parameter ($\mu$ =10$^{30}$) for all excitation schemes. Clearly, higher eigenmodes require different ultra-high values for the nonlinearity parameter to acquire periodic vibrations in multi-modal operations. In general, achieving the steady-state observables at the eigenmodes is substantially critical in quantifying the dynamic responses to fluid properties. Under tetramodal-frequency excitation, the vibration frequency of around 7.33 MHz and amplitude of around 0.03 pm are achieved at the first eigenmode for 75\% Glycerol-water solution. Therefore, the micro-cantilever nonlinear sensitivity to micro-rheological properties at the fundamental and higher eigenmodes could be improved by utilizing multi-frequency excitation schemes.