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Quasi-periodic Motions of a Pendulum with Vibrating Suspension Point

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Abstract

Introduction

The dynamical behavior of a suspension system that consisted of a slide block and a pendulum is investigated under the condition of small amplitudes. The effects of parameters on responses of the suspension system are discussed by calculating the rates of the change of the energy in the slide block and the pendulum, respectively.

Methods

The two frequencies of the suspension system are analytically derived by applying the averaging method. The energy method is employed to calculate the rates of the change of the energy of the suspension system.

Conclusion

The ratio between two frequencies nearly always is irrational, so the suspension system generally has quasi-periodic motions. Under the no damping condition, the direction of flow of the mechanical energy between the slide block and the pendulum depends on the initial phase difference between them. Furthermore, the exchange quantity of energy between the slide block and the pendulum increases with the stiffness of the slide block as well as the ratio between the masses of the pendulum and the slide block for the given length of the pendulum and initial conditions.

Practical implications

The research may contribute to the analysis and design of the pendulum-tuned mass damper.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant nos.11472160, 11672185).

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Authors and Affiliations

  1. College of Textiles, Donghua University, Shanghai, 201620, People’s Republic of China

    R. Wen

  2. School of Environment and Architecture, University of Shanghai for Science and Technology, Shanghai, 200093, People’s Republic of China

    T. T. Li & B. Zhen

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  1. R. Wen
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  2. T. T. Li
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  3. B. Zhen
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Correspondence to B. Zhen.

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Wen, R., Li, T.T. & Zhen, B. Quasi-periodic Motions of a Pendulum with Vibrating Suspension Point. J. Vib. Eng. Technol. 7, 519–532 (2019). https://doi.org/10.1007/s42417-019-00175-4

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