Theory 18/Nanomechanics

Nonlinearity Onset Is an Amplitude Ratio

The claim

The onset of nonlinear behaviour in a nanoresonator is set by the ratio of vibration amplitude to beam thickness rather than by absolute amplitude.

01The mechanism

Geometric nonlinearity arises when deflection changes the tension appreciably; that depends on the ratio of amplitude to dimension, not on the amplitude itself.

02Predictions

P1Onset should track the ratio.
P2Thicker beams should tolerate larger amplitude.

03Refutation

Onset tracking absolute amplitude would remove the ratio.