Static and Dynamic Analyses of Free-Hinged-Hinged-Hinged-Free Beam in Non-Homogeneous Gravitational Field: Application to Gravity Gradiometry

TL;DR

This paper presents the first analytical evaluation of a free-hinged-hinged-hinged-free beam designed for gravity gradiometry, optimizing hinge placement to maximize sensitivity to gravity gradients while minimizing deflection due to gravity.

Contribution

It introduces a novel analytical approach for evaluating a triple-hinged beam's deflections and discusses manufacturing methods and error factors for gravity gradiometry sensors.

Findings

Optimized hinge placement reduces symmetric deflection under gravity.

The beam's deflections are synchronized, enabling precise displacement measurements.

Analytical evaluation provides insights into manufacturing and error factors.

Abstract

The first analytical evaluation of free-hinged-hinged-hinged-free beam, proposed to be used as a primary sensing element for gravity gradiometry, is presented. The results of the evaluation, obtained in quadratures, are applied to the beam's structure such as the locations of hinges that form the beam's boundary conditions allowing only free rotations around the nodal axes. The latter are purposely chosen to minimize the beam's symmetric free ends deflection under the uniform force of gravity while simultaneously permitting the beam's maximum possible mirror-symmetric free ends deflection due to a gravity gradient along its length. The flexible triple hinged beam's deflection from its unperturbed position is internally entangled at all locations including free ends and this allows for synchronized mechanical displacements measurements at any beam's deflection point. Some methods of manufacturing such sensing element and the corresponding error factors are also discussed for the first time.