Study on analytical global modes for a multi-panel structure connected with flexible hinges

A dynamic modeling method for a multi-panel structure connected with flexible hinges is proposed in this paper. For the solar array composed of several flexible rectangular panels, the global explicit modal functions of spatial coordinates are obtained by employing the Rayleigh-Ritz method, which are in favor of deriving the lower-dimension discrete dynamic equations and the design of controllers for the system in the further research. The Gram-Schmidt characteristic orthogonal polynomials are adopted to construct the flexible deformation expressions of the solar panel. The Lagrange multipliers are introduced to describe the constraint at flexible hinges. The eigen equation of the multi-panel structure is derived to obtain the natural frequencies and corresponding global modes of the system through the Rayleigh-Ritz procedure. Considering the natural frequency calculated from the finite element method as a reference value, the correctness of the modeling process is validated by comparing results with those obtained from the finite element method. Moreover, a high accuracy of the proposed method are confirmed by a very good agreement between results from ANSYS and the theoretical method proposed here. The proposed method derives analytical global modes of the whole system which can be conveniently used to design the controller and work out the nonlinear dynamic model and with a few degree-of-freedoms directly. Finally, the interesting mode interchanged phenomenon is observed with the variation of the stiffness of the rotation spring at flexible hinges.