Parametric resonance of intrinsic localized modes in coupled cantilever arrays

• Destabilization of intrinsic localized modes (ILMs) by parametric excitation is investigated for FPU, NKG, and mixed lattices.
• Frequency and amplitude of parametric excitation is determined based on characteristic multipliers of ILMs.
• Unstable regions for the mixed lattice case show very similar shape to those of the Mathieu equation.
• ILMs become unstable by causing parametric resonance.

In this study, the parametric resonances of pinned intrinsic localized modes (ILMs) were investigated by computing the unstable regions in parameter space consisting of parametric excitation amplitude and frequency. In the unstable regions, the pinned ILMs were observed to lose stability and begin to fluctuate. A nonlinear Klein–Gordon, Fermi–Pasta–Ulam-like, and mixed lattices were investigated. The pinned ILMs, particularly in the mixed lattice, were destabilized by parametric resonances, which were determined by comparing the shapes of the unstable regions with those in the Mathieu differential equation. In addition, traveling ILMs could be generated by parametric excitation.