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Rotary motion of the parametric and planar pendulum under stochastic wave excitation |
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| Institution: | 1. Centre for Applied Dynamics Research, School of Engineering, University of Aberdeen, UK;2. Department of Mechanical Engineering, Indian Institute of Technology, Madras, India;1. Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai 600036, India;2. Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai 600036, India;1. Department of Mathematics and Natural Sciences, Jan Kochanowski University, Kielce, Poland;2. Institute of Mechanical, Process & Energy Engineering, Heriot-Watt University, Edinburgh, UK;1. Division of Dynamics, Lodz University of Technology, ul. Stefanowskiego 1/15, 90-924 Lodz, Poland;2. Department of Mechanics and Mechatronics, Gdansk University of Technology, ul. Narutowicza 11/12, 80-233 Gdansk, Poland;3. Institute of Machine Tools and Production Engineering, Lodz University of Technology, ul. Stefanowskiego 15, 90-924 Lodz, Poland;1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang 110819, PR China;2. Key Laboratory of Vibration and Control of Aero-propulsion Systems, Northeastern University, Shenyang 110819, PR China |
| Abstract: | In this paper a rotary motion of a pendulum subjected to a parametric and planar excitation of its pivot mimicking random nature of sea waves has been studied. The vertical motion of the sea surface has been modelled and simulated as a stochastic process, based on the Shinozuka approach and using the spectral representation of the sea state proposed by Pierson–Moskowitz model. It has been investigated how the number of wave frequency components used in the simulation can be reduced without the loss of accuracy and how the model relates to the real data. The generated stochastic wave has been used as an excitation to the pendulum system in numerical and experimental studies. For the first time, the rotary response of a pendulum under stochastic wave excitation has been studied. The rotational number has been used for statistical analysis of the results in the numerical and experimental studies. It has been demonstrated how the forcing arrangement affects the probability of rotation of the parametric pendulum. |
| Keywords: | Parametric and planar pendulums Rotations Simulation of random processes Stochastic excitation Rotational number |
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