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.
Highlights
We have preferred to focus our attention on two points: the first is the coherence of the results with the conventional finite element method; the second point is concerned with the influence of the inflation pressure in the results which is of great importance for inflatable structures
The equations of motion have been written in lagrangian variables for a Timoshenko beam in order to take into account the following forces due to the internal pressure and the shear behaviour of this kind of thinwalled fabric structure
We first have dealt with the continuous element method to establish the dynamic stiffness matrix, which allows us to get exact results
Summary
The type of material used, the geometrical characteristics of the beams, and the internal pressure lead to the strength and stiffness of the inflatable structure. Equations are written by the use of the virtual work principle in lagrangian variables with finite rotations This approach has been extended in this paper by introducing the dynamic terms in order to predict the influence of the pressure effects on the natural frequencies. The equations of motion have to be written on the current configuration, which explains the choice of the lagrangian approach This means that the follower load effect due to the pressure can be taken into account properly, which is of importance for these kinds of structures. Comparisons are made with experimental results and show the accuracy of the theory
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