Continuum Modeling of an Innovative Space-Based Radar Antenna Truss

Abstract

Many proposed inflatable designs for space applications consist of truss-like or lattice structures due to their simplicity of construction coupled with large stiffness to density ratios. An analytical approach is presented here in order to derive the governing partial differential equations of motion which are decoupled for bending and rotational coordinates of vibrations and applies this formulation to the truss structure model of an innovative space-based radar antenna. Kinetic and potential energy expressions are written in terms of nodal velocities and strain components of bar members within a repeating truss element. Hamilton’s principle is then employed to find the equations of motion for the system. The equations for bending are presented in their decoupled form in order to derive an equivalent Timoshenko beam model for the truss. Finally, the physical characteristics of the continuum model are written in terms of the material and geometrical properties of the original truss, which provide a simple tool for comparing dynamic characteristics of lattices with different properties. The natural frequencies are found for each of the bending coordinates of vibration and are compared to those of a standard finite-element method (FEM) solution, for the purpose of validation. The partial differential equations predictions of the natural frequencies for the truss are very close to the FEM. Finally the errors in the frequency estimations are found in terms of the wavelength of the traveling waves.