Continuous and Finite Element Methods for the Vibrations of Inflatable Beams

Abstract

Inflatable structures are under increasing development in various domains. Their study is often carried out by using 3D membrane finite elements and for static loads. There is a lack of knowledge in dynamic conditions, especially for simple and accurate solutions for inflatable beams. This paper deals with the research on the natural frequencies of inflatable Timoshenko beams by an exact method: The continuous element method (CEM), and by the classical finite element method (FEM). The dynamic stiffness matrix D(ω) is here established for an inflatable beam; it depends on the natural frequency and also on the inflation pressure. The stiffness and mass matrixes used in the FEM are deduced from D(ω). Natural frequencies and natural modes of a simply supported beam are computed, and the accuracy of the CEM is checked by comparisons with the finite element method and also with experimental results.