Multistable internal resonance in electroelastic crystals with nonlinearly coupled modes

Area of Science:

• Nonlinear dynamics
• Solid-state physics
• Micro- and nanomechanics

Background:

• Nonlinear modal interactions are crucial for micro- and nanoscale resonators.
• Understanding is limited, primarily to clamped-clamped beams.
• Systems with geometric and material nonlinearities require further investigation.

Purpose of the Study:

• To investigate nonlinear modal interactions in electroelastic crystal plates.
• To explore multistable energy transfer between internally resonant modes.
• To provide new insights into complex modal coupling in such systems.

Main Methods:

• Utilized a mixed analytical-numerical approach.
• Analyzed energy transfer between internally resonant modes.
• Investigated bifurcation structures and dynamic behaviors.

Main Results:

• Reported multistable energy transfer in an electroelastic crystal plate.
• Revealed a rich bifurcation structure with nested regions of multistability.
• Observed diverse dynamics including Duffing bistability, multistability, and quasiperiodic motion.

Conclusions:

• The study provides new insights into nonlinear modal interactions in electroelastic systems.
• Demonstrated complex dynamics arising from coupled modes in crystal plates.
• Highlights the potential for advanced oscillator designs and fundamental physics exploration.