Static and dynamic analyses of free-hinged-hinged-hinged-free beam in non-homogeneous gravitational field: application to gravity gradiometry

The first analytical evaluation of a free-hinged-hinged-hinged-free beam proposed for use as the primary sensing element of a new gravity gradiometer is presented. Results of the evaluation obtained in quadratures are applied to the beam’s structure, including locating the hinges that form the beam’s boundary conditions allowing only free rotations around its nodal axes. These are deliberately chosen to minimize the beam’s symmetric free ends deflections under the uniform body loading of gravity while simultaneously permitting the beam’s maximum possible mirror-symmetric free ends deflections owing to a gravity gradient distributed along its length. The flexible triple-hinged beam deformation from its nominal unloaded geometry is naturally elastically coupled throughout, including free ends, allowing synchronized mechanical displacement measurements at any deflection point. Some methods of manufacturing such sensing elements and their respective error mechanisms are also discussed and presented for the first time.