M.Sc Thesis

M.Sc StudentArie Elka
SubjectOn the Dynamics Simulation and Experiments of a Vibrating
MEMS Device
DepartmentDepartment of Mechanical Engineering
Supervisors Full Professors Bucher Izhak
Dr. Seter Dan


Micro Electro Mechanical Systems (MEMS) are mechanical devices having typical dimensions in the micron scale range.

Such systems are constructed on silicon wafers that consist of electrical and mechanical elements.

This work presents a theoretical analysis of the dynamical movement in a vibrating rate gyroscope accompanied by a numerical and an experimental study.

 The micro mechanical device that is the subject of this work is excited by an external electrostatic field -  a common way to stimulate such devices. The sensing of the device output motion is by optical sensing means.

 The dynamical behavior of micro mechanical vibrating devices is affected by the mechanical and electrical coupled domains as well as by the damping mechanism.

Although many works deal with MEMS, the dynamical aspects of such devices did not receive much attention.

Part one of this work describes the investigation of two theoretical models. The first model refers to the motion of a rigid mass connected to a massless cantilever beam having two degrees of freedom. The second model is a Multi Degrees of Freedom (MDOF) - Finite Element (FE) model that describes the flexible 3D mechanical structure upon which the distributed electrostatic force is acting.

   In part two of this work a laboratory set-up was constructed for characterization of the micro mechanical device. This set-up was used to measure the displacement and velocity of the micro mechanical structure under external excitation and while having various environmental conditions. The independent parameters to be investigated are: vacuum level in the enclosure, excitation signal (DC and AC voltage levels) and the actuation frequency. A comparison of the measured response with the two models was conducted.

Realistic damping estimations were extracted by experimental measurements and were used for calibration of the damping ratio in the numerical model.

The measured response shows an additional ‘spike’ that corresponds to a cross coupling between the actuation and sensing modes due to a nonlinear coupling effects. The electrostatic force should not have excited this orthogonal mode according to the commonly used model. This phenomenon is typical for micro mechanical devices with electrostatic actuation and was investigated in this work. An important conclusion of this research is that cross-coupling between lateral and transverse motions cannot be neglected in general.