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Wavenumber Lock-in in Buckled Elastic Structures: An Analogue to Parametric Instabilities
H E Read1, G Risso1, A Djellouli1
1Harvard University, School of Engineering and Applied Sciences, Cambridge, Massachusetts 02138, USA.
Physical Review Letters
|June 7, 2026
Summary
Researchers found that static buckling patterns in elastic beams mimic dynamic parametric instabilities. Compressed elastic strips with modulated height exhibit frequency lock-in, alternating between quasiperiodic and periodic buckling modes.
Area of Science:
- Solid Mechanics
- Structural Instability
- Nonlinear Dynamics
Background:
- Parametric instabilities are common in periodically driven dynamic systems.
- Frequency lock-in in dynamic systems leads to periodically unstable responses.
- Analogous phenomena in static systems remain largely unexplored.
Purpose of the Study:
- To demonstrate a static analogue of parametric instabilities in elastic structures.
- To investigate frequency lock-in phenomena in the buckling of elastic beams on modulated foundations.
- To explore the relationship between structural and dynamic instabilities.
Main Methods:
- Computational simulations of elastic beam buckling.
- Experimental validation using compressed elastic strips.
- Analysis of buckling patterns under modulated foundation conditions.
Main Results:
- Elastic beams on modulated Winkler foundations exhibit frequency lock-in.
- Buckling patterns alternate between quasiperiodic and periodic modes.
- A direct analogy between static and dynamic instability phenomena was observed.
Conclusions:
- Static elastic structures can exhibit behaviors analogous to dynamic parametric instabilities.
- Modulated foundations can induce frequency lock-in in elastic beam buckling.
- Findings reveal novel connections between structural mechanics and nonlinear dynamics.
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