Table 1 Values for k 1 and k 3 for different deformation shapes

From: Nonlinear dynamic characterization of two-dimensional materials

 

k 1

k 3

Def. shape

AFM

πn 0

\(\frac{1}{{{{(1.05 - 0.15\nu - 0.16{\nu ^2})}^3}}}\frac{{Eh}}{{{R^2}}}\)

ΔP

4πn 0

\(\frac{{8\pi }}{{3(1 - \nu )}}\frac{{Eh}}{{{R^2}}}\)

This work

1.56πn 0

\(\frac{\pi }{{1.27 - 0.97\nu - 0.27{\nu ^2}}}\frac{{Eh}}{{{R^2}}}\)

  1. k 1 and k 3 for AFM nanoindentation (AFM), bulge testing of membranes (ΔP) and the nonlinear dynamics method (this work) for the fundamental resonance mode. The corresponding deformation shape, which determines the functional dependence of k 1 and k 3, is shown on the right
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