Related Experiment Video
Updated: Dec 2, 2025

Characterizing Dissipative Elastic Metamaterials Produced by Additive Manufacturing
Published on: June 28, 2024
Necessary and sufficient conditions for resonant mixing of plane waves in elastic solids with quadratic nonlinearity
1Department of Mechanical Engineering, Tufts University, Medford, Massachusetts 02155, USA.
Abstract:
This paper studies the interactions of two plane waves in elastic solids with quadratic nonlinearity. In particular, the necessary and sufficient conditions for resonant mixing of two plane waves are derived. It is shown that the conventional resonance condition for resonant mixing of plane waves is only a necessary condition, not sufficient. Based on the newly derived necessary and sufficient conditions, resonant mixing of various types of plane waves are investigated and specific conditions for generating a resonant mixed wave are obtained for each case. These results are useful for developing nonlinear ultrasonic nondestructive evaluation techniques using the wave mixing method.
Related Concept Videos
Sound Waves: Resonance
Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity
Standing Waves in a Cavity
Concept of Resonance and its Characteristics
Speed of Sound in Solids and Liquids
Equation of the Elastic Curve
Consider a cantilever beam with a point load at its free end (for instance, a diving board). When analyzing beam deflection with small slopes, the shape of the beam's elastic curve becomes key. The governing equation for this analysis involves the bending moment and the beam's flexural rigidity,...

