Stability Analysis Method for Periodic Delay Differential Equations with Multiple Distributed and Time-Varying Delays

Abstract

Dynamic stability problems leading to delay differential equations (DDEs) are found in many different fields of science and engineering. In this paper, a method for stability analysis of periodic DDEs with multiple distributed and time-varying delays is proposed, based on the well-known semidiscretization method. In order to verify the correctness of the proposed method, two typical application examples, i.e., milling process with a variable helix cutter and milling process with variable spindle speed, which can be, respectively, described by DDEs with the multidistributed and time-varying delays are considered. Then, comparisons with prior methods for stability prediction are made to verify the accuracy and efficiency of the proposed approach. As far as the milling process is concerned, the proposed method supplies a generalized algorithm to analyze the stability of the single milling systems associated with variable pith cutter, variable helix cutter, or variable spindle speed; it also can be utilized to analyze the combined systems of the aforementioned cases.

Applications of Legendre spectral collocation method for solving system of time delay differential equations

“…M Posp ı sil and F Jaro s, 21 studied the approximate solution of DDEs using the Laplace transformation. G Jin et al, 22 studied, the stability analysis method of the periodic DDEs with time-periodic and multiple delays. D Lehotzky et al, 23 extended the stability and convergence analysis of spectral-element-method for the periodic time DDEs with distributed and multiple delays.…”