| Citation: | ZHANG Xiayang, ZHANG Kai, ZHAO Qijun, et al. Application analysis of Durbin method in solving dynamic response of damped beam[J]. Journal of Beijing University of Aeronautics and Astronautics, 2022, 48(1): 67-78. doi: 10.13700/j.bh.1001-5965.2020.0550(in Chinese)
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Based on Timoshenko's beam theory and K-V damping model, the method for the frequency domain vibration solution of the non-proportionally damped beam under a stationary impact load is studied. The dynamic response of the damped beam is derived by introducing traditional Laplace transformation and Durbin's Laplace inverse transformation (Laplace method). Three typical beam boundaries are taken into consideration in the derivation of Laplace method to demonstrate its applicability. Thereafter, the numerical method is validated under a special proportional damping condition and compared with the modal superposition method. The numerical experiments fully investigate the impact of algorithmic parameters and system parameters. The calculation results indicate that the dynamic responses of the fundamental damped beam system can be reasonably computed by the Laplace method under various boundary and loading conditions, showing comparable accuracy with the modal superposition method. However, the Laplace method is slightly affected by the slenderness ratio of the system. Although Laplace method is easier to manipulate than traditional modal superposition method, its accuracy is affected by its inherent numerical parameters and step external load type, and thus the algorithm stability needs further improvement.
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