Fusion of two stable elastic structures resulting in an unstable system

TL;DR

This paper demonstrates that combining two individually stable elastic structures can result in an overall unstable system, with implications for design and theoretical mechanics.

Contribution

It reveals how a compound elastic structure with two degrees of freedom can become unstable through fusion, challenging assumptions of stability in combined systems.

Findings

Instability occurs under non-conservative follower loads.

The instability is absent under dead loads.

Numerical simulations confirm the nonlinear instability.

Abstract

It is shown that a compound elastic structure, which displays a dynamic instability, may be designed as the union (or 'fusion') of two structures which are stable when separately analyzed. The compound elastic structure has two degrees of freedom and is made up of a rigid rod connected with two springs to a smooth support, which evidences a jump in the curvature at the equilibrium configuration. Instability is proven in a linearized context and is related to the application of a non-conservative load of the follower type, so that the instability disappears under dead loads. In the fully nonlinear range, the instability is also confirmed through numerical simulations. The obtained results may be useful in the design of new mechanical sensors, or devices for energy harvesting, or architected materials. In addition, our findings have conceptual implications on piecewise-linear theories of mechanics such as for instance plasticity or frictional contact.