12 September 2014 Modeling large deflection of circular membranes for applications in active optical elements
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Abstract
Our work is focused on a theoretical description and mathematical modeling of the shape of a circular edge clamped pressure actuated elastic membrane, which can be used as an optical surface of an active optical element such as the membrane lens. While the theory of small deformations of elastic membranes is well developed and the calculation of a deflection of the membrane can be done with a relatively good accuracy, modeling of large membrane deflections is more complicated. Classical approaches given in literature adopt certain approximations that affect the accuracy of the calculated shape of a membrane. In our work a generalized nonlinear differential equation describing a given problem is derived and the method for solving this equation is proposed. The numerical solution is based on the expansion of the solution into series and transformation of the problem into the constraint optimization problem. It is shown on examples that the deviation of the shape calculated using the proposed generalized equation and the classical solution is not negligible in terms of the requirements on the optical surface accuracy. The influence of the membrane shape on the optical quality of membrane fluidic lenses is also investigated.
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Pavel Novák, Jiří Novák, Antonín Mikš, "Modeling large deflection of circular membranes for applications in active optical elements", Proc. SPIE 9193, Novel Optical Systems Design and Optimization XVII, 91931C (12 September 2014); doi: 10.1117/12.2061039; https://doi.org/10.1117/12.2061039
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