M.Sc Student | Slavkin Iliya |
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Subject | High Frequency Nonlinear Micro Mass Sensor of Enhanced Performance and Sensitivity |

Department | Department of Mechanical Engineering |

Supervisor | Professor Oleg Gendelman |

Full Thesis text |

Microfabricated cantilever beams are ubiquitous in MEMS systems, in particular, they are used as high sensitivity sensing elements of force and deformation (AFM e.g.). Current sensors and devices based on microfabricated beams are operated mostly in linear resonance mode. However, the narrow bandwidth limits the ability of such beams to sense higher frequency components. In this work, we focus on studying a microfabricated beam resonator with an intentional geometric nonlinearity. The latter is introduced through the integration of a nanotube coupling element that is capable of effectively channeling excitation energy from the basic excitation mode to a mode with triple frequency. We will demonstrate that such an innovative nonlinear beam resonator can significantly improve the mass sensing sensitivity.

A two degrees of freedom lumped mass mathematical model with an essential cubic nonlinearity is examined. The parameters of the unforced Hamiltonian system are intentionally chosen to set the eigenfrequencies of the linear system to be at 1:3 ratio and a harmonic forcing at the first natural frequency of the system is applied in order to enable an internal resonance mechanism that amplifies the reaction of the system at a triple frequency.

The different attractors of the system are explored numerically and analytically. Numerical continuation is used in order to explore the bifurcations and stability of the internal resonance mechanism. In addition, a stability analysis is carried out using analytical methods. The analytical results are compared to the numerical ones.

The sensitivity of mass sensing is examined through the addition of a small mass to the second DOF. Several dynamical effects occur upon the addition of mass to the second DOF, on the one hand the internal resonance mechanism may undergo different types of bifurcations. On the other hand, when the internal resonance mechanism stays structurally stable, a slight addition of mass to the second DOF can cause a significant change in the amplitudes of the motion harmonics. This phenomenon may be utilized in order to attain high sensitivity of mass sensing.