Dynamic Green's functions for multiple circular inclusions with imperfect interfaces using the collocation multipole method

Lee, W.M.; Chen, Jeng‐Tzong; Young, W.M.

doi:10.1016/j.enganabound.2018.06.005

Cited by 5 publications

(1 citation statement)

References 21 publications

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“…With the passage of time, the transient response stage containing free vibration ends and the system enters the steady-state response stage containing forced vibration. For fractional order systems, the existing analytical methods include Green function method, 17 Adomian decomposition method, 18 Homotopy perturbation method, 19 Homotopy analysis method, 20 and variational iteration method. 21 In addition, some scholars have also adopted undetermined coefficient method, 22,23 method of direct partition of motions, 24 multi-scale method, 25,26 and average method 27 to solve some special vibration systems.…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis of fractional oscillator system with cosine excitation utilizing the average method

Xie

Wang

Chen

et al. 2022

Math Methods in App Sciences

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In this paper, an analytical and numerical algorithm for solving displacement response of fractional oscillator system with cosine excitation is established. The analytical method is to solve steady‐state response and transient response solutions of the system by means of average method and then the total displacement response solution is the sum of steady‐state solution and transient solution. The numerical method is to use the Grünwald–Letnikov definition of fractional derivatives to discretize the fractional differential term in the system and then to reduce the order of the original system. Then, the approximate response solution of the system under the general periodic excitation is obtained by using the Fourier series expansion method and the superposition principle of linear system. Finally, the effectiveness and feasibility of the analytical technique are verified by numerical simulation, and the influence of fractional order, linear damping coefficient and fractional derivative coefficient on the amplitude of the steady‐state response and the total displacement response of the system is analyzed.

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