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<p>The paper considers a new mathematical model for solving a dynamic (shock) skew-symmetric boundary-value problem for a layer weakened by a through hole with sliding sealing of its ends. A new method based on the system of 3<i>k</i> (<i>k</i> = 1, 2, …) singular integral equations of the 2nd kind is developed and tested numerically. A highly accurate numerical study demonstrated that the relative circumferential stress increases with an increase in the impulse length. Short impulses result in a wave-like attenuating process, i.e., in the <i>ε</i>-neighborhood of the origin of coordinates, due to the inertia of the system, a zone of negative stresses appears, which, interacting with a positive impulse, give rise to this process. A similar situation is observed when the impulse is removed. The corresponding graphs are shown.</p>

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Modeling the Impulse Excitation of a Layer Weakened by a Through Hole (Skew-Symmetric Case)

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • Yu. D. Kovalev

摘要

The paper considers a new mathematical model for solving a dynamic (shock) skew-symmetric boundary-value problem for a layer weakened by a through hole with sliding sealing of its ends. A new method based on the system of 3k (k = 1, 2, …) singular integral equations of the 2nd kind is developed and tested numerically. A highly accurate numerical study demonstrated that the relative circumferential stress increases with an increase in the impulse length. Short impulses result in a wave-like attenuating process, i.e., in the ε-neighborhood of the origin of coordinates, due to the inertia of the system, a zone of negative stresses appears, which, interacting with a positive impulse, give rise to this process. A similar situation is observed when the impulse is removed. The corresponding graphs are shown.