We study nonlinear dynamics and vibrations through theory, computation and carefully designed experiments. The work falls into four connected themes.

Theme 1

We identify nonlinear normal modes experimentally and from data. Our methods track how modal frequencies and shapes change with energy, giving backbone curves and frequency-energy dependence that linear modal analysis cannot capture.

Key papers

• Characteristic value decomposition: A unifying paradigm for data-driven modal analysis. Mechanical Systems and Signal Processing, 2025. doi:10.1016/j.ymssp.2024.111769
• Continuation of nonlinear normal modes using reduced-order models based on generalized characteristic value decomposition. Nonlinear Dynamics, 2025. doi:10.1007/s11071-024-10239-0
• Smooth mode decomposition: Theory and its applications in full-field output-only modal analysis. Mechanical Systems and Signal Processing, 2023. doi:10.1016/j.ymssp.2023.110541
• Subband decomposition based output-only modal analysis. Journal of Vibration and Acoustics, 2023. doi:10.1115/1.4055135

Theme 2

We build reduced-order models that stay dynamically consistent as amplitude grows, using smooth orthogonal decomposition and manifold-based reduction. The aim is models small enough to analyze and accurate enough to predict.

Key papers

• Persistent model order reduction for complex dynamical systems using smooth orthogonal decomposition. Mechanical Systems and Signal Processing, 2017. doi:10.1016/j.ymssp.2017.04.005
• A new approach to model reduction of nonlinear control systems using smooth orthogonal decomposition. International Journal of Robust and Nonlinear Control, 2018. doi:10.1002/rnc.4238
• Robust and dynamically consistent model order reduction for nonlinear dynamic systems. Journal of Dynamic Systems, Measurement, and Control, 2014. doi:10.1115/1.4028470

Theme 3

We use multivariate and nonlinear time-series analysis to track slow damage hidden in fast vibration data. Phase space warping and related methods estimate damage states and predict remaining life in structures and materials.

Key papers

• Ball tree structure-informed phase space warping: a robust algorithm for dynamic degradation tracking under variable speed conditions. Advanced Engineering Informatics, 2026. doi:10.1016/j.aei.2025.104288
• Geometry-informed phase space warping for reliable fatigue damage monitoring. Structural Health Monitoring, 2024. doi:10.1177/14759217231174894
• Fatigue life estimation of structures under statistically and spectrally similar variable amplitude loading. Mechanical Systems and Signal Processing, 2021. doi:10.1016/j.ymssp.2021.107856

Theme 4

We design passive nonlinear absorbers and energy harvesters that exploit internal resonance and targeted energy transfer. Current work examines geometry-programmed internal resonance and nonlinear mechanical metamaterials.

Key papers

• Multifaceted vibration absorption of a rotating magnetic nonlinear energy sink. Mechanical Systems and Signal Processing, 2025. doi:10.1016/j.ymssp.2024.112122
• Irrational nonlinearity enhances the targeted energy transfer in a rotary nonlinear energy sink. Journal of Computational and Nonlinear Dynamics, 2024. doi:10.1115/1.4065193

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The full list is on the Publications page. Our research has been supported by NSF, NIH, the U.S. Army, ONR and AFRL.