Open AccessOn two improved numerical algorithms for vibration analysis of systems involving fractional derivatives
Author(s) -
Nguyễn Văn Khang,
Lac Van Duong,
Phạm Thanh Chung
Publication year - 2021
Publication title -
vietnam journal of mechanics/mechanics
Language(s) - English
Resource type - Journals
eISSN - 2815-5882
pISSN - 0866-7136
DOI - 10.15625/0866-7136/15758
Subject(s) - newmark beta method , fractional calculus , runge–kutta methods , algorithm , mathematics , vibration , numerical analysis , derivative (finance) , order (exchange) , mathematical analysis , finite element method , structural engineering , engineering , physics , acoustics , financial economics , economics , finance
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.