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<p>Based on a rectangular thin plate model, this study establishes Hamiltonian dual equations governing the free vibration of layered similar materials under four-side fixed boundary conditions and develops corresponding modal analysis functions. Utilizing the orthogonality of these modal functions and Duhamel’s integral principle, a dynamic deflection distribution equation for layered soft coal bodies subjected to impact loads is derived. Analysis of the dynamic distribution characteristics of stress and strain identifies key stress concentration regions within layered specimens. Experiments reveal a cruciform damage pattern: through-going primary fractures form at short-edge centers, while non-through-going secondary fractures develop at long-edge centers, accompanied by radial micro-fractures. Numerical simulations validate these observations. Applying the third strength theory combined with Newton’s iterative method and software, the study links the 1st, 3rd, and 13th primary vibration modes to the fracture genesis and propagation. It clarifies the initiation points and growth directions of damage, elucidating the evolution mechanisms of primary, secondary, and radial micro-fractures. These findings enhance understanding of layered coal-rock mechanics, offering new theoretical and technical insights for stability analysis and damage control.</p>

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Dynamic Response and Failure Characteristics of Laminated Coal Mass Under Impact Loads: Experimental and Theoretical Investigations

  • 期刊论文

  • 发表日期：

    2026年3月14日

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  • Hanwu Liu,
  • Feng Li,
  • Zhifeng Chen,
  • Mingqian Zhang,
  • Lun Gao,
  • Yun Ma

摘要

Based on a rectangular thin plate model, this study establishes Hamiltonian dual equations governing the free vibration of layered similar materials under four-side fixed boundary conditions and develops corresponding modal analysis functions. Utilizing the orthogonality of these modal functions and Duhamel’s integral principle, a dynamic deflection distribution equation for layered soft coal bodies subjected to impact loads is derived. Analysis of the dynamic distribution characteristics of stress and strain identifies key stress concentration regions within layered specimens. Experiments reveal a cruciform damage pattern: through-going primary fractures form at short-edge centers, while non-through-going secondary fractures develop at long-edge centers, accompanied by radial micro-fractures. Numerical simulations validate these observations. Applying the third strength theory combined with Newton’s iterative method and software, the study links the 1st, 3rd, and 13th primary vibration modes to the fracture genesis and propagation. It clarifies the initiation points and growth directions of damage, elucidating the evolution mechanisms of primary, secondary, and radial micro-fractures. These findings enhance understanding of layered coal-rock mechanics, offering new theoretical and technical insights for stability analysis and damage control.