Free Vibration of a Panel Supported by a Shear Compliant Two-Flexure Hinge

Abstract

Elastically deformable hinges or deployable booms commonly follow architectures with face-skin layers only, cutting out the core to facilitate folding. This significantly reduces the shear stiffness of the hinge, which might reduce the first resonance frequency of the structure. We rationalize the free vibration of the system and the interplay between shearing and bending deformation by deriving an analytical formulation using Timoshenko’s beam theory. The framework is derived for a general beam and applied to a case of two flexures of arbitrary geometry with no core. Investigating the specific geometry of flat flexures reveals the existence of two nondimensional length ratios that capture the interplay between inertia, bending stiffness, and shear stiffness of the hinge. Our model explains the dependence of the frequency on the parameters of the system, as well as the dimensions that determine the transition between bending- and shear-dominated vibration modes. Comparison with finite element simulations shows that our analytic framework is able to predict the first natural frequency with less than 1% error. Additionally, an experimental validation was carried out using steel flexures and acrylic panels, showing good agreement with the predictions.