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This study aimed to analyze the free vibration of an axis-symmetric hemispherical shell of revolution based on modified couple stress theory (MCST). The virtual strain energy was used to formulate the problem. The Hamilton’s principle and the variational process give the differential equations of motion and natural boundary conditions. Two different numerical approaches are presented for the free vibration analysis: the generalized differential quadrature (GDQ) method and the finite element method (FEM). The material behavior is assumed to be linear elasticity and isotropic. Convergence studies of the two methods were examined to ensure their results are suitable for numerical investigation. The numerical results obtained from GDQ were validated with FEM under different boundary conditions. Furthermore, the size-dependent effects of the natural frequencies and mode shapes on hemispherical shells were investigated and are presented herein.

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Size-Dependent Effect on Natural Frequency of Hemispherical Shells Based on Modified Couple Stress Theory

  • 会议论文

  • 发表日期：

    2025年

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  • Piyawat Suwankornkij,
  • Tawich Pulngern,
  • Weeraphan Jiammeepreecha,
  • Chanachai Tangbanjongkij,
  • Somchai Chucheepsakul

摘要

This study aimed to analyze the free vibration of an axis-symmetric hemispherical shell of revolution based on modified couple stress theory (MCST). The virtual strain energy was used to formulate the problem. The Hamilton’s principle and the variational process give the differential equations of motion and natural boundary conditions. Two different numerical approaches are presented for the free vibration analysis: the generalized differential quadrature (GDQ) method and the finite element method (FEM). The material behavior is assumed to be linear elasticity and isotropic. Convergence studies of the two methods were examined to ensure their results are suitable for numerical investigation. The numerical results obtained from GDQ were validated with FEM under different boundary conditions. Furthermore, the size-dependent effects of the natural frequencies and mode shapes on hemispherical shells were investigated and are presented herein.