Equivalent Plate Dynamic Modeling and Response Analysis of Truss Structures for Control-Oriented Applications

Whether for ultra-long antenna radar satellites serving airborne target detection and tracking, or for ultra-long on-orbit assembled spacecraft required for future space resource utilization and space science exploration, there is an urgent need for high-precision surface control. The spacecraft exhibit typical mechanical characteristics, including ultra-low frequencies, complex and dense modes, strong geometric nonlinearity, and strong connection nonlinearity, which present significant challenges for rapid and high-precision surface control. This paper aims to develop an equivalent plate modeling and response analysis method of periodic truss structures for control-oriented applications. Based on Mindlin's moderately thick plate theory, the strain description for the transverse vibration of the equivalent plate is formulated, and the dynamic model of the equivalent Mindlin plate for the truss structure is developed. The Legendre polynomials are employed to approximate the displacement and rotational variables of the Mindlin plate, while the artificial spring method is utilized to simulate arbitrary general boundary conditions. Based on the improved Rayleigh-Ritz method, the natural frequencies and eigenvectors are solved. Modal discretization is then performed on the equivalent plate, and the dynamic response is computed using the Newmark method. The results demonstrate that the maximum error in the first four natural frequencies between the equivalent plate model and the ANSYS model is 3.29 %. Under different excitation conditions, including free end load and uniformly distributed load at various excitation frequencies, the responses of the equivalent plate model agree well with those from ANSYS, thereby verifying the accuracy and effectiveness of the proposed dynamic modeling and response analysis model. As an analytical approach, the proposed method is more suitable for vibration controller design. Moreover, compared to ANSYS finite element simulations, the equivalent plate model exhibits significantly higher computational efficiency, making it more applicable to practical engineering applications.