Vibration Absorption in a Nonlinear Metamaterial Beam Incorporating Shape Memory Alloys

Locally resonant metamaterials are capable of demonstrating low-frequency vibration absorption due to the formation of stop-bands. In this work, the multi-mode vibration absorption capability of an adaptive nonlinear metamaterial beam is investigated. The metamaterial beam is idealized as a hinged-hinged finite Euler-Bernoulli beam with a von-Kármán geometric type nonlinearity that is attached to a distributed cellular array of shape memory alloy (SMA) spring–mass resonators. Numerical studies are performed to evaluate the effects of dissipation and change in elastic modulus due to material phase change of SMA pseudoelasticity on the dynamic response of the beam. Using a modal analysis approach, stop-bands are generated at the first three nonlinear frequencies of the beam. The frequency response demonstrates a hardening behavior at a temperature significantly higher than the austenite finish temperature while conversely demonstrating a softening behavior at a temperature slightly above the austenite finish temperature.