Intentional Nonlinearity in the Small Scale with Applications to Multi-Frequency Atomic Force Microscopy and Mass Sensing
Abstract: In recent decades, micro- and nanomechanical resonators have drawn considerable attention due to their high sensitivity, portability, and relatively low cost. They are currently used in a wide variety of applications including precise frequency generation and timekeeping, nanoscale imaging, and sensor technology. This presentation will include results of experimental, numerical, and analytical investigations of microscale mechanical resonators with applications in atomic force microscopy (AFM) and mass sensing. The focus of this research effort is to exploit nonlinear phenomena to enhance existing measurement techniques in AFM and mass sensing.
In the first part of the talk, a summary of my work in the area of AFM will be presented in which I consider a new design of the AFM cantilever. The new probe design uses internal resonance to passively amplify higher harmonics for use in multi-harmonic AFM. In contrast to other multi-frequency AFM techniques, this approach provides multiple channels with strong signal to noise ratios while maintaining the simplicity of a single excitation frequency. I studied the capability of this cantilever to characterize material properties of polymers, bacteria, and viruses and found that the internal resonance-based design results in enhanced sensitivity to Young’s modulus.
In the second part of the talk, I will present results from a study of a new micromechanical mass sensor design that utilizes amplitude shifts within ultra-wide broadband resonances. The sensor consists of a clamped-clamped beam under harmonic base excitation having a concentrated mass at its center. Interestingly, because of geometric nonlinearity, for sufficiently large base excitation amplitudes, there is no theoretically predicted jump-down bifurcation point in the primary resonance curve. Further, the critical excitation level above which there is no theoretical jump-down event is significantly lowered by the presence of the concentrated mass, hence its critical role in the beam design. In practice, a jump-down bifurcation point may occur because of the excitation of higher resonances, perturbations in the initial conditions, and/or excitation amplitude caused by noise, or the basin of attraction for the upper branch solution may become impractically small. However, I believe it may be possible to physically realize a critical excitation amplitude above which the bandwidth of the resonance increases substantially. By operating at an excitation amplitude above this critical threshold, the ultrawide resonant bandwidth can be exploited in a mass-sensing technique based on amplitude tracking.