Wave Dynamics: From Linear to Nonlinear

Revealing how mechanical waves propagate, interact, localize, and transform across amplitude-dependent regimes.

What do we do? 

MOA Lab investigates mechanical-wave dynamics from small-amplitude linear motion to strongly nonlinear energy transport. We study how wave behavior evolves as structural interactions become increasingly dependent on amplitude, contact, deformation, and internal resonance.

In the linear regime, we examine dispersion, bandgaps, modal interactions, scattering, attenuation, and spatial energy localization. These concepts allow us to understand where mechanical waves can propagate, where they are blocked, and how their energy is distributed within a structure.

We then explore weakly and strongly nonlinear regimes, where waves can change their frequency, velocity, bandwidth, and direction of propagation. Nonlinearity is not treated only as an unwanted complication. Instead, we use it as a functional mechanism for frequency conversion, asymmetric transport, harmonic generation, modal energy transfer, and amplitude-dependent control.

Our long-term goal is to establish a unified understanding of mechanical waves across different amplitude scales and to use this knowledge to create structures that adapt their dynamic response to the incoming excitation.

Why does it matter?

Real mechanical systems rarely remain perfectly linear. Contact, impact, large deformation, material behavior, and geometric instability naturally introduce nonlinear effects.

Understanding the transition from linear to nonlinear dynamics allows us to move beyond passive vibration isolation. Mechanical waves can be transformed, redirected, or selectively transmitted according to their amplitude, frequency, or propagation direction. These capabilities provide foundations for adaptive vibration control, mechanical frequency conversion, energy routing, wave rectification, impact management, and mechanical signal-processing systems.

Representative Publications

1. Y. Jang*, B. Oh*, E. Kim, and J. Rho, “Bidirectional asymmetric frequency conversion in nonlinear phononic crystals,” Physical Review Letters 135, 036603 (2025).

2. Y. Jang, E. Kim, and J. Rho, “Scattering of waves in locally resonant woodpile structures with impurities,” Physical Review E (accepted) (2026).

3. B. Oh*, Y. Jang*, E. Kim, and J. Rho, “Frequency-selective wave transfer with cascaded-bandgap-induced nonreciprocity,” (under review).

4. Y. Jang, E. Kim, and J. Rho, “Rotational dynamics of asymmetric modes in cylindrical granular crystals: From bandgap tuning to vector soliton formation,” (in preparation).

5. Y. Jang*, G. Lee*, E. Kim, and J. Rho, “Impulse mitigation in nonlinear composite-based woodpile phononic crystals,” Applied Physics Letters 121 (2022).