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Singular Trajectories of Forced Vibrations

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Oscillators and Oscillatory Signals from Smooth to Discontinuous

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Abstract

As shown earlier by Zhuravlev, harmonically loaded linear conservative systems possess an alternative physically reasonable basis, which is generally different from that associated with the conventional concept of principal coordinates. Briefly, such a basis determines directions of harmonic loads along which the system response is equivalent to a single oscillator. The corresponding definition (singular directions of forced vibrations) is losing sense in nonlinear case, when the linear tool of eigenvectors becomes inapplicable. However, it will be shown in this chapter that nonlinear formulation is still possible in terms of eigenvector-functions of time given by NSTT boundary value problems. Physical meaning of the corresponding nonlinear definitions for both discrete and continual models is discussed.

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Pilipchuk, V.N. (2023). Singular Trajectories of Forced Vibrations. In: Oscillators and Oscillatory Signals from Smooth to Discontinuous. Springer, Cham. https://doi.org/10.1007/978-3-031-37788-4_11

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