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<p>Effect of the damping model to dynamic responses of cracked functionally graded (FG) microbeams on the Winkler–Pasternak elastic foundation subjected to a moving load is investigated based on the modified couple stress theory (MCST) and the Kelvin–Voigt damping model. Mechanical properties of the FG microbeam vary in the thickness direction. The Mori–Tanaka homogenization technique is used to determine the effective material properties of the FG microbeam. Equations of motion for the microbeams are established based on the finite element method (FEM). Non-classical shape functions of the microbeam element are derived based on the governing vibration equations for the FG microbeam using the MCST and the Timoshenko beam theory (TBT). The stiffness matrix of a cracked beam element is obtained by adding an overall additional flexibility matrix to the flexibility matrix of the corresponding intact beam element to achieve remarkable accuracy. The influences of geometrical, material, foundation, length scale, damping, crack and moving load velocity parameters on the dynamic responses of FGM microbeams are investigated in detail.</p>

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Effect of the damping model to dynamic responses of the cracked functionally graded microbeams on the elastic foundation subjected to moving load

  • 期刊论文

  • 发表日期：

    2025年5月16日

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  • Le Thi Ha,
  • Tran Van Lien

摘要

Effect of the damping model to dynamic responses of cracked functionally graded (FG) microbeams on the Winkler–Pasternak elastic foundation subjected to a moving load is investigated based on the modified couple stress theory (MCST) and the Kelvin–Voigt damping model. Mechanical properties of the FG microbeam vary in the thickness direction. The Mori–Tanaka homogenization technique is used to determine the effective material properties of the FG microbeam. Equations of motion for the microbeams are established based on the finite element method (FEM). Non-classical shape functions of the microbeam element are derived based on the governing vibration equations for the FG microbeam using the MCST and the Timoshenko beam theory (TBT). The stiffness matrix of a cracked beam element is obtained by adding an overall additional flexibility matrix to the flexibility matrix of the corresponding intact beam element to achieve remarkable accuracy. The influences of geometrical, material, foundation, length scale, damping, crack and moving load velocity parameters on the dynamic responses of FGM microbeams are investigated in detail.