Fig. 5: Parametric study of the 1:2 IR The left column shows the ERM amplitude, while the right column shows the IRM amplitude.
From: Strong internal resonance in a nonlinear, asymmetric microbeam resonator
The effect of the excitation level is shown in (a) for \(\omega _1 = 1,\,\omega _2 = 2,\,\zeta _1 = \zeta _2 = 0.001,\,\left| {\alpha _1} \right| = 0.87,\,\left| {\alpha _2} \right| = 1.75,\,\lambda = 0.1,\,{\mathrm{and}}\,\sigma _1 = 0.01\). When the driving force increases, the IR activation range expands, and the oscillation amplitudes increase. A change in the internal frequency mismatch shown in (b) for \(\omega _1 = 1,\,\omega _2 = 2,\,\zeta _1 = \zeta _2 = 0.001,\,\left| {\alpha _1} \right| = 0.87,\,\left| {\alpha _2} \right| = 1.75,\,\lambda = 0.1,\,{\mathrm{and}}\,w_F = 5 \times 10^{ - 4}\), alters the overall resonance line shape from a symmetric M-shape to asymmetric ones. The effect of nonlinear coupling constants is shown in (c) for \(\omega _1 = 1,\,\omega _2 = 2,\,\zeta _1 = \zeta _2 = 0.001,\lambda = 0.1,\,\sigma _1 = 0.01,\,{\mathrm{and}}\,w_F = 5 \times 10^{ - 4}\). A larger nonlinear coefficient enhances the energy transfer between the ERM and IRM as the ERM amplitude decreases and the IRM amplitude increases. The same sets of data plotted in the 2-D graphs can be found in the Supplementary Information
