Vibration analysis of composite beams is carried out by using a finite element-based formal asymptotic expansion method. The formulation begins with three-dimensional (3D) equilibrium equations in which cross-sectional coordinates are scaled by the characteristic length of the beam. Microscopic two-dimensional and macroscopic one-dimensional (1D) equations obtained via the asymptotic expansion method are discretized by applying a conventional finite element method. Boundary conditions associated with macroscopic 1D equations are considered to investigate the end effect. It is then described how one could form and solve the eigenvalue problems derived from the asymptotic method beyond the classical approximation. The results obtained are compared with those of 3D finite element method and those available in the literature for composite beams with solid cross section and thin-walled cross section.

An enhanced Lo–Christensen–Wu (LCW) theory is defined in the Laplace domain to predict the thermo-mechanical-viscoelastic behavior of long-term composite structures. The primary objective herein is to systematically extract the computational benefits of the conventional LCW and fifth-order zigzag model via the mixed variational theorem (MVT). Furthermore, the Laplace transform is employed to circumvent the numerical complexity of viscoelastic analysis. The relationships between the two fields were derived using the MVT constraint equations in the Laplace domain. Consequently, the proposed theory has the C⁰-based computational benefits as the conventional LCW, while improving the solution accuracy for long-term thermo-mechanical-viscoelastic behaviors.