A Refined Closed-Form Solution for the Large Deflections of Alekseev-Type Annular Membranes Subjected to Uniformly Distributed Transverse Loads: Simultaneous Improvement of Out-of-Plane Equilibrium Equation and Geometric Equation

Abstract

The Alekseev-type annular membranes here refer to annular membranes fixed at outer edges and connected with a movable, weightless, stiff, con-centric, circular thin plate at inner edges, which were proposed originally by Alekseev for bearing centrally concentrated loads. They are used to bear the pressure acting on both membranes and plates, which was proposed originally in our previous work for developing pressure sensors. The pressure is applied onto an Alekseev-type annular membrane, resulting in the parallel movement of the circular thin plate. Such a movement can be used to develop a capacitive pressure sensor using the circular thin plate as a movable electrode plate of a parallel plate capacitor. The pressure applied can be determined by measuring the change in capacitance of the parallel plate capacitor, based on the closed-form solution for the elastic behavior of Alekseev-type annular membranes. However, the previous closed-form solution is unsuitable for annular membranes with too large deflection, which limits the range of pressure operation of the developed sensors. A new and more refined closed-form solution is presented here by improving simultaneously the out-of-plane equilibrium equation and geometric equation, making it possible to develop capacitive pressure sensors with a wide range of pressure operations. The new closed-form solution is numerically discussed in its convergence and effectiveness and compared with the previous one. Additionally, its beneficial effect on developing the proposed capacitive pressure sensors is illustrated.