Free vibrations of an elastica around its post-buckled configurations

The post-buckled free vibration problem of an elastica around one of its vibration modes is investigated. For this, different equilibrium states of the elastica are detected by analysing the dimensionless form of the governing equations. Then, the multiple scale method is employed to study the free vibration of the elastica in a selected post-buckled state around a specific vibration mode. At the micro-scale, the considered elastica can be supposed as an element of an architecture material with tailored mechanical behaviours. • Dimensionless forms of governing equations of an elastica are treated. • System behaviours around its different equilibria are detected. • Around its equilibria, the elastica can present softening or hardening behaviours.