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Variational Principle and Approximate Solution for the Fractal Vibration Equation in a Microgravity Space

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Iranian Journal of Science and Technology, Transactions of Mechanical Engineering Aims and scope Submit manuscript

Abstract

Under the microgravity space, many theories derived from the earth's surface become untenable, so a modified vibration equation with fractal derivative is presented in this work. With the help of the semi-inverse method, we successfully develop the fractal variational principle, which not only provides conservation laws in an energy form but also provides physical insight into the nature structures of the solutions. Finally, the variational iteration method, together with the two-scale transform, is applied to find the solution of the fractal vibration equation. The obtained results show that the method is powerful and accurate.

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Acknowledgment

This work is supported by Program of Henan Polytechnic University (No. B2018-40), the Program of Henan Province Office of Education, China (Grant Number: 19B510004), and Innovative Scientists and Technicians Team of Henan Provincial High Education (21IRTSTHN016).

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Authors and Affiliations

  1. School of Physics and Electronic Information Engineering, Henan Polytechnic University, Jiaozuo, 454003, China

    Kang-Jia Wang

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  1. Kang-Jia Wang
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Correspondence to Kang-Jia Wang.

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Wang, KJ. Variational Principle and Approximate Solution for the Fractal Vibration Equation in a Microgravity Space. Iran J Sci Technol Trans Mech Eng 46, 161–165 (2022). https://doi.org/10.1007/s40997-020-00414-0

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  • DOI: https://doi.org/10.1007/s40997-020-00414-0

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