Free vibration analysis of damped composite beams and laminated reinforced panels via damped dynamic stiffness method and CUF-based component-wise theory

This paper presents an efficient framework for the free vibration analysis of damped composite beams and laminated panels. The method integrates the Carrera Unified Formulation (CUF) with the Damped Dynamic Stiffness Method (DDSM) to achieve accurate and computationally efficient characterization of damped composite structures. Within the CUF framework, the three-dimensional displacement field is expanded using Lagrange polynomials, enabling refined modeling of complex cross-sections through layer-wise and component-wise descriptions. Intrinsic damping is incorporated directly into the constitutive equations, while the component-wise approach captures non-uniform material loss factors essential for realistic damping modeling. The governing equations and natural boundary conditions are derived via the principle of virtual displacements, and an exact damped dynamic stiffness matrix is formulated by relating the amplitudes of harmonic loads and structural responses. The transcendental eigenvalue problem is efficiently solved using a hybrid Wittrick-Williams and homotopy perturbation method, ensuring accurate broadband complex eigenvalue extraction. Comparative studies with three-dimensional finite element models verify the superior accuracy and computational efficiency of the CUF-DDSM approach. The proposed framework provides a robust analytical foundation for broadband vibration prediction and optimal damping design of advanced composite structures.