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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 ...
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 Novel Grazing Bifurcation Inducing Quasi-Periodic Response Directly From Equilibrium in a Piecewise-Linear Aeroelastic System
Publisher: The American Society of Mechanical Engineers (ASME)
Abstract: Abstract. Grazing bifurcation is commonly encountered in nonsmooth dynamical systems, which usually results in periodic response featured with grazing on the nonsmooth border. This study reports a novel grazing bifurcation ...
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 ...