Displacement reconstruction of slender beam based on polynomial fitting method

MA Yexuan, XU Wanhai, XU Zengwei

Journal of Vibration and Shock ›› 2020, Vol. 39 ›› Issue (11) : 152-157.

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PDF(1058 KB)
Journal of Vibration and Shock ›› 2020, Vol. 39 ›› Issue (11) : 152-157.

Displacement reconstruction of slender beam based on polynomial fitting method

  • MA Yexuan, XU Wanhai, XU Zengwei
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Abstract

Vibrations of slender flexible beam are induced easily by the inner and outer interference factors, which may cause severe fatigue damage and threaten the safety of the structure. Real-time reconstruction of structural vibration displacement is the key technology for structural health monitoring (SHM) and intelligent oscillation control. Nowadays, modal analysis approach is widely used in the displacement reconstruction of slender flexible beam. When the slender flexible beam has complex boundary conditions and strong nonlinear factors, modal analysis approach is not convenient to reconstruct the displacement. Hence, displacement reconstruction method for slender flexible beam based on polynomial fitting is put forward. The approach of extending structure boundary is employed to avoid the Runge phenomenon which usually occurs in polynomial fitting. The accuracy and feasibility of displacement reconstruction method based on polynomial fitting are validated by finite element simulation and reconstruction of experimental data. Some conclusions are drawn from the results. The displacement reconstruction method based on polynomial fitting is effective for the displacement reconstruction of linear and nonlinear vibrations of slender flexible beams. Extending structure boundary is useful to reduce the Runge phenomenon caused by polynomial fitting. When the extended length is 0.875L-1.125L (L is the length of slender flexible beam) and the magnitude of strains at the virtual measuring points is less than or equal to the magnitude of the maximum strain at the real measuring points, the reconstructed displacements have high accuracy.

Key words

displacement reconstruction / polynomial fitting / slender flexible beam / Runge phenomenon / structural extension;

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MA Yexuan, XU Wanhai, XU Zengwei. Displacement reconstruction of slender beam based on polynomial fitting method[J]. Journal of Vibration and Shock, 2020, 39(11): 152-157

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