Natural Frequencies of an Innovative Space Based Radar Antenna by Continuum Modeling

Abstract

*† ‡ An analytical approach is presented here to find the equations of motion for an equivalent continuum model of a Radar Antenna. Such a structure consists of a 3dimensional lattice with the radar panel mounted on one side of the truss. Due to the relatively large mass of the radar panel, a dynamic solution for the integrated system is necessary. To account for the kinetic energy of the panel it is modeled as point masses over the face of the truss. 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 have a form similar to an extended Timoshenko beam. Both Euler Bernoulli and Timoshenko formulations are derived in this work. The Timoshenko model shows higher accuracy in natural frequency estimations compared to the Euler Bernoulli model. It is shown that the dynamics of the system changes significantly due to the addition of the panel, hence, the longitudinal and the torsional vibrations are also coupled with the bending as opposed to the original truss. The natural frequencies are in good agreement with the FEA.