The novelty of the current study is the development of an enhanced finite shell model using the first order shear deformation theory (FSDT) to study the vibration characteristics of imperfect functionally graded (FGM) plates and shells including porosities. Unlike standard (FSDT) theory, the proposed model presents an improvement of the FSDT via the introduction of a quadratic shear function allowing the exact representation of the parabolic distribution of the shear strains and avoiding the utilization of shear correction factors which are computationally costs. The finite element method is used for the discretization of the equations of motion and the assumed natural transverse shear strain (ANS) method is employed to avoid shear locking problems. The effect of porosity parameter and its distributions, namely even and uneven forms, is investigated through different numerical illustrative examples. The present finite shell element model provides better agreement with exact solutions in comparison by other theories. Finally, effects of different factors on vibrational behavior of imperfect FGM porous plates and shells are examined in detail.

当前研究的新颖之处在于使用一阶剪切变形理论 (FSDT) 开发了增强型有限壳模型，以研究不完美的功能梯度 (FGM) 板和壳的振动特性，包括孔隙度。与标准 (FSDT) 理论不同，所提出的模型通过引入二次剪切函数对 FSDT 进行了改进，该函数允许精确表示剪切应变的抛物线分布，并避免使用剪切校正因子，这在计算上是有成本的。有限元方法用于运动方程的离散化，并采用假定的自然横向剪切应变 (ANS) 方法来避免剪切锁定问题。孔隙度参数及其分布的影响，即均匀和不均匀形式，通过不同的数值说明示例进行研究。与其他理论相比，目前的有限壳单元模型与精确解的一致性更好。最后，详细研究了不同因素对不完美 FGM 多孔板和壳的振动行为的影响。