Theoretical study on the sensitivity of dynamic acoustic force measurement through monomodal and bimodal excitations of rectangular micro-cantilever

We present a detailed analysis on measurement sensitivity of dynamic acoustic forces via numerical simulation of the micro-cantilever responses. The rectangular micro-cantilever is regarded as a point mass in the dynamic model of forced and damped harmonic oscillator. We use single- and bimodal-frequency excitation schemes for actuation of the micro-cantilever in the presence of dynamic acoustic forces. In bimodal-frequency excitation scheme, the micro-cantilever is excited at its first two eigenmode frequencies simultaneously as opposed to single-frequency excitation. First, we numerically obtain micro-cantilever deflections by solving the equations of Motions (EOMs) constructed for the first two eigenmodes. Then, we determine oscillation amplitude and phase shift as a function of acoustic force strength within different frequency regions. Moreover, we relate amplitude and phase shift to virial and energy dissipation in order to explore the interaction between flexural modes in multifrequency excitation. The simulation results point out that bimodal-frequency excitation improves the measurement sensitivity of dynamic acoustic forces at particular frequencies. Herein, simultaneous application of driving forces enables higher sensitivities of observables and energy quantities as acoustic force frequencies become around the eigenmode frequencies. For our case, we obtain the highest phase shift (similar to 178 degrees) for the acoustic force strength of 100 pN at the frequency of around 307.2 kHz. Therefore, this method can be easily adapted to improve measurement sensitivity of dynamic acoustic forces in a wider frequency window.