Pendulum's rotational motion governed by a stochastic Mathieu equation |
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| Affiliation: | 1. Department of Mechanical Engineering, Heriot-Watt University, Edinburgh, UK;2. Department of Mathematical Sciences, NTNU, Trondheim, Norway;1. Guangdong Provincial Key Laboratory of Micro/Nano Optomechatronics Engineering, College of Mechatronics and Control Engineering, Shenzhen University, Shenzhen 518060, PR China;2. Engineering Research Center of Energy Saving Technology and Equipment of Thermal Energy System, Ministry of Education, Zhengzhou University, Zhengzhou 450000, PR China;3. School of Mechatronics Engineering, Nanchang University, Nanchang 330031, PR China;4. Institute of Mechanical, Process & Energy Engineering, Heriot-Watt University, Edinburgh EH14 4AS, UK;1. IMPEE, Heriot-Watt University, Edinburgh, UK;2. Institute for Infrastructure & Environment, Heriot-Watt University, Edinburgh, UK;3. School of Mechatronics Engineering, Nanchang University, Nanchang 330031, People’s Republic of China;4. Key Laboratory of Lightweight and High Strength Structural Materials of Jiangxi Province, Nanchang University, Nanchang 330031, People’s Republic of China;5. Department of Mathematics and Natural Sciences, Jan Kochanowski University, Kielce, Poland;1. School of Chemical Engineering and Energy, Zhengzhou University, Zhengzhou 450000, China;2. School of Aeronautics, Northwestern Polytechnical University, Xi’an 710049, China;3. Engineering Research Center of Energy Saving Technology and Equipment of Thermal Energy System, Ministry of Education, Zhengzhou 450000, China;4. Institute of Mechanical, Process & Energy Engineering, Heriot-Watt University, Edinburgh EH14 4AS, UK |
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| Abstract: | This paper considers rotational motion of a nonlinear Mathieu equation with a narrow-band stochastic excitation. The path integration technique is utilized to obtain the joint probability density function of the response, which is used to construct domains of rotational motion in parameter space. |
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