Geometrically nonlinear free vibration analysis of shear deformable laminated composite elliptic plates using the <i>p</i> -version FEM

This study examines the large amplitude free vibration behavior of symmetric and antisymmetric constant stiffness composite laminated (CSCL) and variable stiffness composite laminated (VSCL) elliptic plates, addressing a gap in nonlinear vibration research on elliptic composite structures. A curved rectangular <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> </mml:math> -element, based on the first-order shear deformation theory (FSDT) and Von Kármán nonlinearity, accurately model their dynamic responses. The nonlinear equations of motion are transformed into the frequency domain using the harmonic balance method and solved iteratively via the linearized updated mode method. The model’s efficiency and accuracy are validated through convergence and comparison studies. Parametric studies reveal that aspect ratio, thickness ratio, stacking sequence, boundary conditions, modulus ratio, and fiber orientation angles significantly influence the nonlinear frequency response, hardening behavior, and mode shapes. VSCL plates, in particular, demonstrate greater potential for tailoring nonlinear vibrations through fiber path customization. Simply supported plates exhibit stronger hardening effects, while clamped plates yield higher nonlinear fundamental frequencies. Additionally, symmetric configurations exhibit greater hardening behavior than antisymmetric ones. These findings enhance nonlinear vibration modeling and provide key insights for designing composite structures under large amplitude vibrations, serving as benchmark data for future studies on nonlinear dynamics and optimization.