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Frontiers of Mechanical Engineering

Front. Mech. Eng.    2020, Vol. 15 Issue (3) : 417-429
Bending and vibration of a discontinuous beam with a curvic coupling under different axial forces
Heng LIU1,2, Jie HONG1, Dayi ZHANG1()
1. School of Energy and Power Engineering, Beihang University, Beijing 100191, China
2. State Key Laboratory of Laser Propulsion and Application, Beijing Power Machinery Institute, Beijing 100074, China
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The transverse stiffness and vibration characteristics of discontinuous beams can significantly differ from those of continuous beams given that an abrupt change in stiffness may occur at the interface of the former. In this study, the equations for the deflection curve and vibration frequencies of a simply supported discontinuous beam under axial loads are derived analytically on the basis of boundary, continuity, and deformation compatibility conditions by using equivalent spring models. The equation for the deflection curve is solved using undetermined coefficient methods. The normal function of the transverse vibration equation is obtained by separating variables. The differential equations for the beam that consider moments of inertia, shearing effects, and gyroscopic moments are investigated using the transfer matrix method. The deflection and vibration frequencies of the discontinuous beam are studied under different axial loads and connection spring stiffness. Results show that deflection decreases and vibration frequencies increase exponentially with increasing connection spring stiffness. Moreover, both variables remain steady when connection spring stiffness reaches a considerable value. Lastly, an experimental study is conducted to investigate the vibration characteristics of a discontinuous beam with a curvic coupling, and the results exhibit a good match with the proposed model.

Keywords discontinuous beam      bending stiffness      transverse vibration      axial loads      gyroscopic moments     
Corresponding Author(s): Dayi ZHANG   
Just Accepted Date: 18 March 2020   Online First Date: 09 April 2020    Issue Date: 03 September 2020
 Cite this article:   
Heng LIU,Jie HONG,Dayi ZHANG. Bending and vibration of a discontinuous beam with a curvic coupling under different axial forces[J]. Front. Mech. Eng., 2020, 15(3): 417-429.
Fig.1  Discontinuous beam with the curvic coupling.
Fig.2  Illustration of the bending deflection of the discontinuous beam.
Fig.3  Illustration of the inner forces of a beam segment.
Fig.4  Influence of axial loads and torsion spring stiffness on maximum beam deformations.
Fig.5  Deflection curves of continuous and discontinuous beams.
Fig.6  First four frequencies of the discontinuous beam with (a) the same connection stiffness under different axial loads and (b) different torsion spring stiffness values under the same axial load.
Fig.7  Frequencies vs. torsion spring stiffness under different axial loads: (a) First- and (b) third-order frequencies.
Fig.8  Frequencies vs. shearing spring stiffness: (a) The first four frequencies and (b) detailed view of the second-order frequency.
Outer diameter Tangency radius Tooth width Tooth number Enveloped half pitches Pressure angle Whole depth Clearance
41 mm 18.25 mm 4.5 mm 12 11 40° 2.733 mm 0.41 mm
Tab.1  Parameters of curvic coupling
Fig.9  Specimen for modal test.
Fig.10  Diagram of the frequency response function.
Fig.11  Frequency comparisons between experimental data and analytical calculations: Results of (a) fixed stiffness and (b) fixed axial loads.
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