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In this paper, a first‐order approximation coupling (FOAC) model is investigated to analyze the dynamics of the hub‐beam system, which is based on the Hamilton theory and the finite element discretization method. The FOAC model for the hub‐beam system considers the second‐order coupling quantity of the axial displacement caused by the transverse displacement of the beam. The dynamic characteristics of the system are studied through numerical simulations under twos cases: the rotary inertia of the hub is much larger than, and is close to, that of the flexible beam. Simulation and comparison studies using both the traditional zeroth‐order approximation coupling (ZOAC) model and the FOAC model shows that when large motion of the system is unknown, possible failure exists by using the ZOAC model, whereas the FOAC model is valid. When the rotary inertia of the hub is much larger than that of the beam, the result using the ZOAC model is similar to that using the FOAC model. But when the rotary inertia of the hub is close to that of the beam, the ZOAC model may lead to a large error, while the FOAC model can still accurately describe the dynamic hub‐beam system.

The purpose of this paper is to analyze the effect of the space thermal effect on satellite antenna.

In this paper, according to the geometric characteristics of parabolic reflector, the transient temperature field of an element along its thickness direction is built for shell structures using finite element discretization and the quadratic function interpolation, and heat conduction equations are derived based on the theory of the thermo-elastic dynamics. The modeling theory of rigid–flexible coupling system considering thermal effect is extended to the satellite antenna system. Then, the coupling dynamic equations are established including coupling stiffness matrix and thermal loaded undergoing a large overall motion. Finally, an adaptive controller is proposed and the adaptive update laws are designed under the parameter uncertainty.

The results of dynamic characteristic analysis show that the dynamic thermal loaded coupled with structure deformation induce the unstable vibration and coupled flutter. Further, the coupling effect degrades the antenna pointing accuracy seriously and leads to disturbances on satellite base. The results of the simulation show that the adaptive controller can ensure that antenna pointing closes to the expected trajectory progressively, and it demonstrates that the proposed control scheme is feasible and effective.

The paper considers only the effect of space thermal effect to satellite antenna. Further research could be done on the flexible multibody system by considering joint clearance in the future research.

The conclusions of this paper would be an academic significance and engineering value for the analysis and control of satellite antenna pointing.

This paper aims to investigate analytical solutions of natural frequencies and mode shapes of Euler-Bernoulli beams with step changes in the stiffness.

In this work, analytical solutions for a beam with a single discontinuity was performed. Subsequently, based on an effective matrix formulation, the closed-form expressions of the single discontinuity beam could be conveniently extended to stepped beams with multiple stiffness discontinuities.

The results of the study show that the natural frequency of the beam can be adjusted by the local stiffness variation, and step location plays a significant role in free vibration responses.

The effects of the stiffness of the segment and step location on the natural frequencies of the stepped beams under different boundary conditions were examined using the proposed analytical scheme. This study provides insights into the design of variable-stiffness beam structures with the capability to adjust natural frequencies.