Free vibration analysis of inflatable beam made of orthotropic woven fabric: Fid-Bau Portal

Free vibration analysis of inflatable beam made of orthotropic woven fabric

Apedo, K.L. / Ronel, S. / Jacquelin, E. / Tiem, S.

Abstract The free vibration of inflatable beams was studied using the dynamic stiffness method. A 3D Timoshenko beam with a homogeneous orthotropic woven fabric (OWF) was considered. Using the usual total Lagrangian form of the virtual work principle, the model took the geometric nonlinearities and the inflation pressure follower force effect into account. The nonlinear equilibrium equations were then linearized around the prestressed reference configuration. The exact dynamic stiffness matrix was developed by directly solving the governing differential equations of a 3D loaded inflatable beam in a free vibration. The effects of the inflation pressure, fabric mechanical properties and the boundary conditions on the natural frequencies and mode shapes of the inflatable beams were demonstrated. The proposed model was validated favorably through its comparison with a 3D thin shell finite element model and an isotropic fabric model found in the literature.

Highlights • The free vibration of inflatable beams using the dynamic stiffness method was modeled. • A 3D Timoshenko beam with a homogeneous orthotropic woven fabric (OWF) was considered. • The geometric nonlinearities and the inflation pressure follower force effect were taken into account. • Changes in the natural frequencies and mode shapes due to the inflation pressure, the fabric mechanical properties and the boundary conditions were examined. • The influence of the inflation pressure on the natural frequencies depends strongly on the mechanical properties of the fabric, on the orthotropic character of the fabric and also on the rotational inertia term of the beam.