Nonlinear dynamics of multistable metastructures

Interdisciplinary Areas: Autonomous and Connected Systems, Smart City, Infrastructure, Transportation, Power, Energy, and the Environment

Project Description

The idea of creating metamaterials to realize effective, unconventional macroscopic properties by engineering units at the micrometer or millimeter scales has attracted significant attention. However, the effective dynamical properties in metamaterials strongly depend on the units’ size, and the attainable characteristic frequencies are typically restricted to be in and above the acoustic range (> 1 kHz). A promising approach addressing this need leverages interactions between strongly nonlinear waves that exhibit particle-like behavior—e.g., transition waves—and structures. This project aims to derive a mathematical framework modeling the nonlinear interactions between waves and vibrational modes in metastructures featuring geometrically multistable units. We propose to leverage the induced vibrations triggered by transition waves in metastructures constructed from multistable lattices to achieve this objective. These transition waves will excite structural modes, regardless of the input excitation frequency. Conversely, excitation of metastructural vibrations can induce sufficiently large in-plane deflections to trigger transition waves, resulting in the new nonlinear interaction that enables the energy exchange between frequency bands orders of magnitude apart. The enabled energy exchange allows for obtaining metamaterials with unconventional properties at low frequencies, yielding wave manipulation and vibration attenuation for smart infrastructure, and energy harvesting for interconnected devices.

Start Date

February, 2022

Postdoctoral Qualifications

We seek an applicant with a strong background in nonlinear waves and dynamics of metamaterials. Prior experience with the analysis of multistable lattice and the dynamics of transition waves is particularly advantageous. Analytical and modelling skills for dealing with nonlinear systems are essential. We expect the applicant to conduct analysis, experiments, and implementation of the studied metamaterials for applications in wave manipulation, dissipation, and energy harvesting.


Main advisor:
Andres F. Arrieta
Assistant Professor
School of Mechanical Engineering and Ray W. Herrick Laboratories
School of Aeronautics and Astronautics Engineering (by courtesy)

Shirley Dyke
Professor of Civil Engineering


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2. N. Nadkarni, C. Daraio, and D.M. Kochmann. “Dynamics of periodic mechanical structures containing bistable elastic elements: From elastic to solitary wave propagation.” Physical Review E, 2014, 90,23204.
3. N. Nadkarni, A.F. Arrieta, C. Chong, D.M. Kochmann, and C. Daraio. “Unidirectional Transition Waves in Bistable Lattices.” Physical Review Letters, 2016, 116,.
4. M. Hwang and A.F. Arrieta. “Input-Independent Energy Harvesting in Bistable Lattices from Transition Waves.” Scientific Reports, 2018, 8,.
5. M. Hwang and A.F. Arrieta. “Extreme Frequency Conversion from Soliton Resonant Interactions.” Physical Review Letters, 2021, 126,073902. Available from: