Nonlinear vibrational-state excitation and piezoelectric energy conversion in harmonically driven granular chains

Area of Science:

• Physics
• Nonlinear Dynamics
• Condensed Matter Physics

Background:

• Spatially extended dynamical systems exhibit complex behaviors.
• Granular materials display unique nonlinear contact mechanics.
• Understanding vibrational modes is crucial for energy transfer.

Purpose of the Study:

• To explore vibrational state excitation in a granular chain.
• To validate theoretical models against experimental data.
• To analyze energy conversion in nonlinear systems.

Main Methods:

• Theoretical analysis using the nonlinear Schrödinger equation.
• Experimental setup with harmonic boundary excitation of a granular chain.
• Application of an electromechanical model for energy conversion.

Main Results:

• Broad frequency regions support various vibrational states due to system nonlinearity.
• The nonlinear Schrödinger equation accurately predicts modes in specific parametric regions.
• The electromechanical model precisely predicts mechanical-to-electrical energy conversion.

Conclusions:

• Nonlinear Hertzian contact forces in granular chains facilitate diverse vibrational modes.
• Theoretical models can effectively describe and predict these complex dynamics.
• Accurate prediction of energy conversion is achievable with appropriate electromechanical models.