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Consider a propagating wave Green’s function, u(t, x) excited by a point moving-oscillating load, \(Q=Q_0 \textrm{e}^{\textrm{i}\omega _0t}\delta (\eta ), \eta = x-vt\), where v and \(\omega _0\) are the load speed and frequency constants, respectively. In the steady-state mode, the over-the-period energy flux from the load to the wave must be positive (otherwise, the wave has no energy to propagate). It follows that the load and the corresponding particle velocity of the wave oscillate with the same frequency (but not necessary of the same phase)

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Wave Excitation, Steady-State Limit and Causality Principle

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  • 发表日期：

    2026年

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  • Leonid I. Slepyan

摘要

Consider a propagating wave Green’s function, u(t, x) excited by a point moving-oscillating load, \(Q=Q_0 \textrm{e}^{\textrm{i}\omega _0t}\delta (\eta ), \eta = x-vt\), where v and \(\omega _0\) are the load speed and frequency constants, respectively. In the steady-state mode, the over-the-period energy flux from the load to the wave must be positive (otherwise, the wave has no energy to propagate). It follows that the load and the corresponding particle velocity of the wave oscillate with the same frequency (but not necessary of the same phase)