M.Sc Thesis

M.Sc StudentMintz Tova
SubjectNonlinear Dynamics and Stability of a Microbeam Array
Subject to Parametric Excitation
DepartmentDepartment of Mechanical Engineering
Supervisors PROF. Oded Gottlieb


In the past decade, arrays of micro-resonators have been successfully used as storage devices and for mapping of surfaces via scanning probe microscopy (SPM) and as coupled microbeam arrays which exhibit complex electrically tunable collective response. The performance of both example arrays are governed by nonlinear effects. The SPM array can at specific operating conditions, yield spurious random-like surface maps of periodic structures, whereas the complex response of the tunable array is not yet completely understood.

We have investigated the nonlinear dynamics of a three element microbeam array that is subject to electrodynamic parametric excitation. We derived a theoretical continuum based model for the array which incorporates linear viscoelastic material properties and a geometric nonlinearity truncated to cubic order. Solution of the reduced order nonlinear modal dynamical system near its principle parametric resonance is obtained via multiple scale asymptotics. The theoretical analysis is verified numerically and reveals a complex bifurcation structure which includes coexisting stable periodic in-phase and out of-phase dynamics. We manufactured and tested a three element array of gold microbeams, and present a qualitative comparison between theory and experiments. A relatively good agreement between theory and experiment has been obtained for the case of a single beam, demonstrating the importance of modeling nonlinear damping which is essential for obtaining bounded response for arrays that are excited  arametrically.