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<p>Localized waves in an Euler–Bernoulli beam on a weakly nonlinear elastic foundation, which has a specific weak structural damping, and which is under the action of a moving (constant speed) concentrated load, are studied. An asymptotic approach describing the effect of loading and damping on localized solutions (that is, on kinks and pulses), is developed. To find approximations for these kink- and pulse-like solutions, variational methods with heuristic test functions are applied. Some new effects are presented. In particular, for solitary waves we observe a resonance, when the velocity of the load and the pulse are equal, and the amplitude of the pulse increases. Also, this resonance leads to a delta-shape disturbance in the wave velocity, and leads to a jump in the pulse coordinate. Another interesting result is that for kinks there are special resonances, where the kink location experiences a jump.</p>

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On kink- and pulse-like waves in a nonlinear damped Euler–Bernoulli beam due to a moving load

  • 期刊论文

  • 发表日期：

    2026年5月13日

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  • Andrei K. Abramian,
  • Sergei A. Vakulenko,
  • Wim T. van Horssen

摘要

Localized waves in an Euler–Bernoulli beam on a weakly nonlinear elastic foundation, which has a specific weak structural damping, and which is under the action of a moving (constant speed) concentrated load, are studied. An asymptotic approach describing the effect of loading and damping on localized solutions (that is, on kinks and pulses), is developed. To find approximations for these kink- and pulse-like solutions, variational methods with heuristic test functions are applied. Some new effects are presented. In particular, for solitary waves we observe a resonance, when the velocity of the load and the pulse are equal, and the amplitude of the pulse increases. Also, this resonance leads to a delta-shape disturbance in the wave velocity, and leads to a jump in the pulse coordinate. Another interesting result is that for kinks there are special resonances, where the kink location experiences a jump.