This paper evaluates the vibration characteristics of structures with viscoelastic materials. The mechanical properties of viscoelastic layers have been described with the complex modulus approach. The equations of motion are derived using the principle of virtual displacement (PVD), and they are solved through the finite element method (FEM). Higher-order beam elements have been derived with the Carrera Unified Formulation (CUF), which enables one to go beyond the assumptions of the classical one-dimensional (1D) theories. According to the layerwise approach, Lagrange-like polynomial expansions have been adopted to develop the kinematic assumptions. The complex nonlinear dynamic problem has been solved through an iterative technique in order to consider both constant and frequency-dependent material properties. The results have been reported in terms of frequencies and modal loss factors, and they have been compared with available results in the literature and numerical three-dimensional (3D) finite element (FE) solutions. The proposed beam elements have enabled bending, torsional, shell-like, and coupled mode shapes to be detected.

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