Vibration characteristics of thin plate system joined by hinges in double directions

This study investigates the free vibration characteristics of a double-direction (D-D) solar array structure connected with flexible hinges. We propose the more accurate continuity conditions in the theoretical model. The Kirchhoff plate theory is adopted to derive the energy equations of the structure. The Chebyshev polynomials are introduced as admissible functions to construct the dynamic model of each solar panel. The Lagrange multiplier method is employed to describe the continuity conditions of the flexible hinges. The natural frequencies and corresponding global mode shapes of the structure are calculated using the Rayleigh- Ritz method. Furthermore, a comparison with the results obtained from ANSYS is performed to confirm the validity of the present method. Finally, investigations are carried out to illustrate the effect of the structural parameters on the natural frequency and mode shape of the structure. A comparison study shows that the present continuity conditions can significantly improve the accuracy of the results. Different from the single direction solar panels structures, there exist coupling effect between x- and y-direction solar panels in D-D solar array structures. Moreover, unique frequency stability phenomenon and coplanar phenomenon of solar panels are discovered in D-D solar array structures. In addition, the results of frequency curves, mode shapes, and modal assurance criterion (MAC) values reveal that the variation of the hinge torsional stiffness and the solar panel aspect ratio induce a series of frequency veering and mode shift phenomena. Particularly, the mechanism of these phenomena is explored. The present theoretical study can significantly improve the calculation efficiency, and is convenient to analyze the parameter influence law, which outperforms the finite element analysis.

Automated summary

This study investigates the free vibration characteristics of a double-direction solar array structure connected with flexible hinges using Kirchhoff plate theory and Chebyshev polynomials, and calculates the natural frequencies and mode shapes of the structure. The research explores the effect of structural parameters on the frequency and mode shape, and compares the results with ANSYS to validate the method.