The natural frequency of drum-deployed thin-walled open tubular booms

Abstract

Thin-walled tape springs are extended from cylindrical deployment drums to support instruments and sensors in a cantilevered manner on spacecraft. Attaching tape springs onto the deployment drums results in a partially flattened and partially restrained cross section, which is far from the ideal case of a fixed-free beam. The consequence is a more compliant root condition that has the potential to couple and amplify on-board microvibrations with the natural frequency of the extended instrumentation. In this paper it is shown that an Euler–Bernoulli beam model can be used to calculate the natural frequency of drum-deployed tape springs using elastic boundary conditions to represent the root condition. A Finite Element (FE) model and experimental data are used to validate the beam model’s correctly predicted relationships between the natural frequency and tape spring length, f1,Res.∝L−1.5, and its rotational stiffness, f1,Res.∝krot0.5. For the investigated beryllium copper tape springs the FE model and beam model are in excellent agreement with experiment, with the error <10%. For carbon fibre epoxy tape springs there is also strong agreement between the FE model and experiment, and approximately 10%–20% error with the beam model. On a scale from a hinged beam to a fixed-free beam, the non-dimensionalised beam equation reveals that the drum-deployed tape springs are close to the hinged beam end of the scale. Two stiffening methods are proposed to increase the stiffness of the tape springs, and hence move the tape springs towards being a fixed-free beam.