engleski

Convergence of Eigenvalues of Monodromy Matrix of Piecewise Linear Oscillators

Prediction of dynamical stability of piecewise linear oscillators’ responses significantly depends on very small harmonic terms of the actual time domain response. The influence of these small harmonic terms on convergence of piecewise linear oscillators’ monodromy matrix eigenvalues (that determine the dynamical stability of the steady-state response) is considered in this paper. For this purpose, a simple one degree-of-freedom system with a piecewise-linear force-displacement relationship subjected to a harmonic excitation is analysed. Stability of the periodic response obtained in the frequency domain by the incremental harmonic balance method is determined by using the Floquet-Liapounov theorem. Responses in the time domain are obtained by a method of piecing the exact solutions. Using the frequency plot of maximum modulus of the eigenvalues of the monodromy matrix is proposed in order to make the stability and the bifurcation analysis of piecewise linear oscillators more reliable and efficacious.

dynamical stability; Floquet-Liapounov theorem; piecewise-linear ocsillator

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