| Citation: | MA Binjie, ZHOU Shutao, JIA Liang, et al. Vibration response analytical solutions of cantilever beam with tip mass and spring constraints[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45(5): 883-892. doi: 10.13700/j.bh.1001-5965.2018.0482(in Chinese)
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According to the eigenvalue condition of cantilever beam with tip mass and spring, this paper proposes a characteristic transformation method, and obtains the analytical solutions of generalized mass and vibration response of cantilever beam with constraints. By analyzing the variational regularities of amplification factors of root bending moment, tip displacement, tip velocity, and tip acceleration for this cantilever beam, the results indicate that the stiffness of tip spring has notable effect on static and first-order load responses, the restriction of tip mass can be relaxed in the load reduction design, and the analysis order of load response is between the analysis orders of velocity and acceleration. The proposed characteristic transformation method can be used to obtain the vibration response analytical solutions of cantilever beam with other loading distribution, boundary conditions and tip constraints.
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