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Purpose <p>In this study, the analytical solution of the dynamic response of a two-parameter foundation beam considering the tangential&#xa0;effect under a moving harmonic load is <i>newly</i> derived.</p> Methods <p>Firstly, the double Fourier transform is used to transform the vertical and horizontal control equations of the infinite beam&#xa0;into algebraic ones to obtain the dynamic response of the infinite beam in the frequency domain. Then, the double Fourier inverse&#xa0;transform is employed to transfer it to the time-domain, and the residue theorem is used to calculate the indefinite integral to get the&#xa0;theoretical solution of the displacement response. The degenerate solution by ignoring the horizontal spring stiffness and the shear&#xa0;modulus in the derived equations and the built-in <i>quadgk</i> function in MATLAB platform are adopted to verify the correctness of the&#xa0;theoretical solution.</p> Results <p>The research shows that the derived theoretical solution agrees well with the numerical and degenerate solutions. The&#xa0;dynamic responses of the two - parameter foundation beam considering the tangential effect are greatly affected by the foundation&#xa0;parameters. Differently, the delay effect of foundation damping on the vertical displacement response of the infinite beam is not&#xa0;obvious for the Pasternak foundation beam in considering tangential effect. Besides, a large difference in the dynamic responses&#xa0;between the two-parameter foundation beam considering and ignoring the tangential effect is presented as the load frequency is less&#xa0;than 30Hz. The moving speed makes the position of the maximum vertical displacement response shift to the right but weakens its&#xa0;excitation effect on the dynamic response of the infinite beam.</p>

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Vibration Response Analysis of Infinite Beam on a Two-Parameter Pasternak Foundation Considering Tangential Effect Under a Moving Harmonic Load

  • 期刊论文

  • 发表日期：

    2025年8月16日

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  • K. Shi,
  • D. S. Deng,
  • P. Yuan,
  • S. Y. Gao,
  • Z. Zheng,
  • J. R. Deng

摘要

Purpose

In this study, the analytical solution of the dynamic response of a two-parameter foundation beam considering the tangential effect under a moving harmonic load is newly derived.

Methods

Firstly, the double Fourier transform is used to transform the vertical and horizontal control equations of the infinite beam into algebraic ones to obtain the dynamic response of the infinite beam in the frequency domain. Then, the double Fourier inverse transform is employed to transfer it to the time-domain, and the residue theorem is used to calculate the indefinite integral to get the theoretical solution of the displacement response. The degenerate solution by ignoring the horizontal spring stiffness and the shear modulus in the derived equations and the built-in quadgk function in MATLAB platform are adopted to verify the correctness of the theoretical solution.

Results

The research shows that the derived theoretical solution agrees well with the numerical and degenerate solutions. The dynamic responses of the two - parameter foundation beam considering the tangential effect are greatly affected by the foundation parameters. Differently, the delay effect of foundation damping on the vertical displacement response of the infinite beam is not obvious for the Pasternak foundation beam in considering tangential effect. Besides, a large difference in the dynamic responses between the two-parameter foundation beam considering and ignoring the tangential effect is presented as the load frequency is less than 30Hz. The moving speed makes the position of the maximum vertical displacement response shift to the right but weakens its excitation effect on the dynamic response of the infinite beam.