Stiffening of higher modes in doubly-clamped beam resonators depending on ground state amplitude

Doubly-clamped beams offer an ideal structure for studying nonlinear mechanical coupling between different vibrational modes. Until now, there is lack of experimental data concerning the stiffening of higher modes induced by the ground mode. In this paper, we construct virtual experimental data for the nonlinear mechanical coupling of in- and out-of-plane modes of a doubly-clamped beam resonator using full transient FEM simulations. We find a very good agreement of the simulation results with a formula derived for in-plane modes by Owers-Bradley, Lulla et al. Finally, we generalize the formula to include out-of-plane modes, and show that also this case can be correctly described.