An improved equivalent beam model of large periodic beam-like space truss structures

Abstract

Space truss structures are essential components for space-based remote sensing loads with high spatial and temporal resolutions. To achieve high-precision vibration control, an accurate and efficient dynamics model is essential. In addition to the current equivalent beam model (EBM) based on the classical continuum theory, an improved equivalent beam model (IEBM) is proposed that considers the impact of the distinction between trusses and beams on torsional and shear deformations, as well as the impact of shear deformation on flexural rigidity. According to the displacement expressions of spatial beams, torsional, shear, and bending correction coefficients are introduced to derive expressions of strain energy and kinetic energy. The energy equivalence principle is then utilized to calculate the elasticity and inertia matrices, and dynamics equations are established using the finite element method. Subsequently, an IEBM is constructed by employing the particle swarm optimization approach to determine the correction coefficients with the truss natural frequency as the optimization target. The natural vibration characteristics of the structure are estimated for various material properties. Compared with the full-scale finite element model, the EBM reaches a maximum error of 80% for a low modulus of elasticity, while the maximum error of the IEBM is less than 2% for any given parameters, indicating its superior accuracy to the EBM.