A Numerical Analysis of Single-Frequency Responses of the Resonant Micro-Cantilever to Dynamic Acoustic Forces Based on the Forced Van der Pol-Rayleigh-Mathieu Oscillator

Abstract

In the present work, a nonlinear dynamic model based on the forced Van der Pol-Rayleigh-Mathieu is used to acquire the observable responses of the micro-cantilever to dynamic acoustic forces in the single-frequency excitations. Behaviors of the resonant micro-cantilever under external forces are strongly dependent on the simulation parameters. The start time, the time interval, and the initial boundary conditions considerably affect the flexural deflections on the particular time domains. Additionally, amplitude and phase shift can be simply extracted from the oscillatory motions to explore the micro-cantilever sensitivity to acoustic forces for different start times and time intervals. For instance, the amplitude at the second eigenmode fluctuates in the 0–500 pm region on the start time domain of 0–20 ms for the time interval range of 0.0001–0.1 ms. It is remarkably vital to observe the changes in the observables in response to different values of numerical simulation parameters for better sensitivity analysis. Furthermore, dynamic responses including displacements and velocities are demonstrated for the first two flexural eigenmodes considering different initial displacements. Therefore, the single-frequency responses of the resonant micro-cantilever can be investigated to quantify the sensitivity to periodic acoustic forces considering the effects of numerical simulation parameters.