On two improved numerical algorithms for vibration analysis of systems involving fractional derivatives

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DOI:

https://doi.org/10.15625/0866-7136/15758

Keywords:

vibration, fractional differential equation, numerical algorithm, dynamical systems

Abstract

Zhang and Shimizu (1998) proposed a numerical algorithm based on Newmark method to calculate the dynamic response of mechanical systems involving fractional derivatives. On the basis of Runge-Kutta-Nyström method and Newmark method, the present study proposes two new numerical algorithms, namely, the improved Newmark algorithm using the second order derivative and the improved Runge-Kutta-Nyström algorithm using the second order derivative to solve the fractional differential equations of vibration systems. The accuracy of new algorithms is investigated in detail by numerical simulation. The simulation result demonstrated that the Runge-Kutta-Nyström algorithm using the second order derivative for the vibration analysis of systems involving fractional derivatives is more effective than the Newmark algorithm of Zhang and Shimizu.

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Published

21-06-2021

How to Cite

Khang, N. V., Duong, L. V., & Chung, P. T. (2021). On two improved numerical algorithms for vibration analysis of systems involving fractional derivatives. Vietnam Journal of Mechanics, 43(2), 171–182. https://doi.org/10.15625/0866-7136/15758

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