A Multi Fidelity Framework Integrating CLT, Vinson–Sierakowski Method, and 3D Finite Element Analysis for Modal Prediction and Parametric Design of Symmetrically Laminated CFRP Beams

Laminated carbon fiber reinforced polymer (CFRP) beams are widely used in lightweight structures, yet their vibration response depends strongly on laminate architecture, boundary conditions, thickness, and material anisotropy. Previous studies often examined these effects separately or relied on a single analytical or numerical approach. This study presents a multi fidelity framework integrating classical laminate theory (CLT), the Vinson–Sierakowski (VS) equivalent modulus method, and three-dimensional finite element analysis for modal prediction and parametric design of symmetric CFRP laminated beams. Three stacking sequences, [0/0/0/0], [0/45/45/0], and [0/90/90/0], were evaluated under clamped-free (CF) and clamped-clamped (CC) conditions. ANSYS models using quadratic HEX20 solid elements served as the numerical reference. Across 36 validation frequencies, the mean absolute percentage errors were 3.05% for CLT and 2.28% for VS, giving VS a 25.1% lower average error. The [0/0/0/0] laminate produced the highest frequencies. The first numerical frequency increased from 36.37 to 230.20 Hz when the boundary condition changed from clamped-free to clamped-clamped. Increasing thickness from 2 to 8 mm raised the first frequency from 18.20 to 72.62 Hz, while increasing E1/E2 from 10 to 30 raised it from 30.80 to 53.85 Hz. The framework supports rapid screening, laminate level interpretation, and detailed numerical verification for vibration-oriented composite beam design.