Free Vibration Behavior of Sandwich FGM Beams: Parametric and Uncertainty Analysis

The study aims to thoroughly analyze the free vibration behavior of symmetric and nonsymmetric functionally graded material sandwich beams (FGSBs) with hard or soft cores. The investigation focuses on understanding the impact of various parameters, such as boundary conditions (BCs), power-law index, length-to-height ratio, and face-to-face thickness ratio, on the free vibration behavior of these beams. Moreover, the influence of uncertainties in the material properties and geometric parameters on the vibration behavior is also quantified, enhancing the credibility and utility of the proposed model.

To achieve this, an efficient Hermite–Lagrangian finite element (FE) model is developed based on a new hyperbolic shear deformation theory (HYSDT), which includes only three unknowns and satisfies traction-free boundary conditions without requiring shear correction factors. The mechanical properties of the FGSB vary continuously in the thickness direction following a power-law rule. The study involves three types of FG beams: a single-layered FG beam (FGB),a sandwich beam (SB) with FG face sheets and a homogeneous core, and an SB with homogeneous face sheets and an FG core. The equations of motion are derived using the principle of Hamilton, and the numerical model is established to solve the eigenvalue problem. Additionally, a Monte-Carlo simulation (MCS) is conducted to assess the influence of uncertainties in the power law, L/h ratio, and the thicknesses of the top, core, and bottom layers on the free vibration behavior.

An extensive parametric analysis is conducted to examine the effects of boundary conditions, power-law index, length-to-height ratio, and face-to-face thickness ratio on the free vibration of FGSBs. The performance and robustness of the current FE model are validated through comparisons with established benchmarks from the literature, confirming the soundness of the proposed formulation. The analysis provides valuable insights into the behavior of symmetric and non-symmetric, as well as thin and thick FGSBs.

The findings demonstrate that factors such as boundary conditions, power-law index, length-to-height ratio, and face-to-face thickness ratio significantly impact the free vibration behavior of FGSBs. The study highlights the crucial importance of incorporating these variables into the design and analysis processes to ensure optimal performance of FGSBs in practical engineering applications.