Coupled vibration characteristics analysis of elastic beam under arbitrary boundary conditions

LI Haihong1, WANG Hao1, GUO Shanguo2, LIU Zhiqi1, LI Wangduo1

Journal of Vibration and Shock ›› 2022, Vol. 41 ›› Issue (17) : 48-54.

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PDF(1671 KB)
Journal of Vibration and Shock ›› 2022, Vol. 41 ›› Issue (17) : 48-54.

Coupled vibration characteristics analysis of elastic beam under arbitrary boundary conditions

  • LI Haihong1, WANG Hao1, GUO Shanguo2, LIU Zhiqi1, LI Wangduo1
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Abstract

A coupled model was established to analyze the transverse, longitudinal, and torsional vibration of elastic beams under arbitrary boundary conditions based on the Spectro-Geometric method. The vibration displacement functions of elastic beams were respectively expressed as improved Fourier series whose auxiliary functions were trigonometric series. The boundary restraining springs were introduced at both ends of the beam and the stiffness value of springs was changed to simulate arbitrary boundary conditions. Hamilton’s principle was employed to derive the Lagrangian function of the structure and the Ritz method was used to get the solution. The first 6 order natural frequencies under different boundaries of beams were calculated, with the maximum error of 0.02% compared with literature solutions. The correctness and fast convergence of the method were validated. The displacement function representation form and modal characteristic solution equations of the transverse, longitudinal, and torsional vibration of elastic beams were unified. The results show that coupled vibration characteristics of elastic beams could be adjusted with changing boundary spring stiffness coefficients, which provides a method for parametric studies on the optimization of the dynamic performance of elastic beams.
Key words: elastic beams; coupled vibration; Spectro-Geometric method; arbitrary boundary conditions

Key words

elastic beams / coupled vibration / Spectro-Geometric method / arbitrary boundary conditions

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LI Haihong1, WANG Hao1, GUO Shanguo2, LIU Zhiqi1, LI Wangduo1. Coupled vibration characteristics analysis of elastic beam under arbitrary boundary conditions[J]. Journal of Vibration and Shock, 2022, 41(17): 48-54

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