The emergence of dissipation dilution

in doubly clamped nanomechanical resonators

Bachelor thesis (2019)

Authors

J.C. van der Zalm Applied Sciences

Contributors

G.A. Steele QN/Steele Lab - (mentor)

P.G. Steeneken Dynamics of Micro and Nano Systems - Mechanical, Maritime and Materials Engineering (mentor)

Faculty

Applied Sciences, Applied Sciences

Model Stress Strain Deformation Quality factor Damping Nano Mechanical Nanomechanical Resonator Resonators Dissipation dilution Doubly Clamped Loss tangent Loss angle Structural damping Torsion Elongation Stretching Transverse motion Mass Spring Springs Beam Euler Bernoulli Euler Bernoulli Beam Engineering Spring constant

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Published Date

22-07-2019

Language

English

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Faculty

Applied Sciences

Abstract

The goal of the research described in this thesis was to investigate the basis of dissipation dilution as well as make it comprehensible. In the written literature we could find that the kinetic energy of an oscillating beam is stored into two types of potential energy~\cite{Kippenberg, Kotthaus}. A dissipative bending component and a conservative component due to elongation.

After this the different types of damping were introduced. Of which structural damping was most important, it is experimentally found to be approximately constant for many materials over a large band of frequencies. The loss tangent and quality factor for this type of damping are both constant. The physical origin of this behaviour isn't really understood. But there have been ideas hinted that it is due to surface imperfections~\cite{Kippenberg}.

To simulate dissipation dilution a spring system has been developed. In this system part of the energy is stored in torsion springs and another part in elongation springs. From this model it is observed that the effective spring constant of the total system depends on the initial strain. At low amounts of strain the spring constant is similar to that of torsion springs while at higher strains it becomes more like the elongation spring model. The quality factor of the beam is found to increase linearly with the strain.

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