We study the transverse oscillatory modes of nanomechanical silicon nitride strings under high tensilestress as a function of geometry and mode indexm 9. Reproducing all observed resonance frequencieswith classical elastic theory we extract the relevant elastic constants. Based on the oscillatory local strainwe successfully predict the observed mode-dependent damping with a single frequency-independent fitparameter. Our model clarifies the role of tensile stress on damping and hints at the underlying micro-scopic mechanisms.
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