Equivalent plate dynamic modeling of space periodic truss structures

Abstract

Antenna structures used in spaceflight always contain nonlinear joints distributed along their cross section; hence, an equivalent beam model (EBM) that uses a point to describe the cross section is not ideally suited to depicting connection nonlinearity in the structure. To address this difficulty, a novel orthotropic equivalent plate model (EPM) of a space periodic truss structure is proposed. Firstly, utilizing the Mindlin plate hypothesis, strain in the periodic truss element is expanded into a binary high-order Taylor series, and corrections are introduced to normal strain. Secondly, employing the principle of energy equivalence, the equivalent elastic and inertial matrices of the EPM are calculated for in-plane and out-of-plane vibration. Finally, the static condensation method is utilized to reduce the dimensions of the equivalent model to establish an orthotropic equivalent Mindlin plate dynamic model, and its inherent characteristics are analyzed. The simulations show that when in-plane shear strain is expanded to the third order, the EPM can more accurately represent torsional vibration of the periodic truss structure. By introducing normal strain correction coefficients in the longitudinal direction, lateral bending vibrations of the periodic truss structure can be simulated more precisely. Compared with the EBM, the EPM can more accurately depict mechanical characteristics along the cross section. The EPM broadens the scope of continuum equivalent modeling of periodic trusses, and is more useful in engineering practice. In addition, the frequencies and mode shapes of the analytical EPM are consistent with a model using the finite element method, which supports the accuracy and effectiveness of the EPM. The analytical EPM provides a convenient way to study the nonlinear connections and vibration control of antenna structures with multiple joints along their cross section.