Vibration Analysis of Three-Phase Functionally Graded Composite Curved Panels

This paper presents a comprehensive free vibration analysis of three-phase functionally graded composite cylindrical and conical panels. The effective material properties are evaluated through a two-stage micromechanical homogenization framework, the Halpin-Tsai model is applied to characterize the GPL-enhanced matrix, followed by the Mori-Tanaka scheme to account for the carbon fiber reinforcement. The theoretical formulation is established within the first-order shear deformation theory (FSDT) framework, incorporating von Kármán-type geometric nonlinearity to capture large deformation effects. Chebyshev polynomials combined with specially constructed boundary functions that inherently satisfy essential geometric constraints are employed as admissible functions in the Ritz minimization procedure. The reliability of the proposed modeling framework is validated through extensive comparisons with existing literature and finite element simulations. Subsequently, a systematic parametric investigation is carried out to elucidate the influences of key design variables on the natural frequency of the system. The results demonstrate that GPL content significantly enhances structural stiffness. Specifically, increasing the GPL weight fraction from 0% to 1% leads to an increase in the fundamental natural frequency of the fully clamped cylindrical panel from 130.73 Hz to 198.64 Hz, corresponding to an enhancement of approximately 52%. Meanwhile, ply orientation offers effective tuning capability, particularly for higher vibration modes. The present study provides an efficient computational framework for the vibration analysis of three-phase composite panels, offering valuable insights for the design and optimization of lightweight, high-stiffness panels in aerospace and advanced engineering applications.