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RISThe Phase Transition of Covariant Lyapunov Vector Precisely Locates a Stability Reversal of Quasi-Periodic Response
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: Assessing the stability of quasi-periodic (QP) response is crucial, as the bifurcation of QP response is usually accompanied by a stability reversal. The largest Lyapunov exponent (LLE), as an important indicator for chaotic ...
Twice Harmonic Balance Method for Stability and Bifurcation Analysis of QuasiPeriodic Responses
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: A twice harmonic balance (THB) method is proposed to compute and analyze quasiperiodic (QP) responses of nonlinear dynamical systems, with emphasis on the stability and bifurcation of QP responses. In the first harmonic ...
A Novel Method for Solving the Bagley-Torvik Equation as Ordinary Differential Equation
Publisher: American Society of Mechanical Engineers (ASME)
Abstract: We present a novel method to solve the Bagley-Torvik equation by transforming it into ordinary differential equations (ODEs). This method is based on the equivalence between the Caputo-type fractional derivative (FD) of ...
A Modified Incremental Harmonic Balance Method Combined With Tikhonov Regularization for Periodic Motion of Nonlinear System
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: In this paper, a modified incremental harmonic balance (IHB) method combined with Tikhonov regularization has been proposed to achieve the semi-analytical solution for the periodic nonlinear system. To the best of our ...