On two improved numerical algorithms for vibration analysis of systems involving fractional derivatives
DOI:
https://doi.org/10.15625/08667136/15758Keywords:
vibration, fractional differential equation, numerical algorithm, dynamical systemsAbstract
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 RungeKuttaNyström 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 RungeKuttaNyström 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 RungeKuttaNyström 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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National Foundation for Science and Technology Development
Grant numbers 107.042020.28