Shape Control for Experimental Continuation

TL;DR

This paper introduces a shape control method to experimentally locate unstable equilibria in nonlinear structures, enabling direct measurement of their mechanical response which was previously only possible through numerical analysis.

Contribution

The paper presents a novel experimental technique using shape control to identify unstable equilibrium segments of nonlinear structures for the first time.

Findings

Successfully identified unstable segments of a shallow arch's equilibrium path.

Demonstrated the effectiveness of shape control in experimental continuation.

Expanded capabilities for measuring nonlinear structural responses.

Abstract

An experimental method has been developed to locate unstable equilibria of nonlinear structures quasi-statically. The technique involves loading a structure by application of either a force or a displacement at a main actuation point, while simultaneously controlling the overall shape using additional probe points. The method is applied to a shallow arch, and unstable segments of its equilibrium path are identified experimentally for the first time. Shape control is a fundamental building block for the experimental---as opposed to numerical---continuation of nonlinear structures, which will significantly expand our ability to measure their mechanical response.