Effects of Frequency Dependency of Materials Behavior on the Dynamic Response of the Viscoelastic Beam Under the Moving Mass

This research analyzes the dynamic behavior of a viscoelastic beam using the Kelvin–Voigt model and frequency-dependent method under the moving mass, which is crucial for the design and construction of various types of bridges, employing the quasi-3D theory of shear deformation. Viscoelastic materials have intricate molecular chains that influence macroscopic characteristics, including stiffness and damping. The system’s equations are established via Hamilton’s principle. The equations of motion are solved using Navier’s analytical technique in the spatial domain and Newmark’s numerical method in the temporal domain. To verify the correctness of the produced findings, comparisons with established responses for specific scenarios will be provided. The difference between the Kelvin–Voigt model and the frequency-dependent model is analyzed on the dynamic response and critical velocity of the moving mass, and the influence of various parameters on the dynamic response and critical velocity of the moving mass for both models has been examined and studied. One of the significant findings of this research is that the frequency-dependent method demonstrates greater suitability and reasonableness for the investigated structure compared to the Kelvin–Voigt model, as evidenced by the latter’s critical velocity being 18% lower. This underscores the advantages of the frequency-dependent approach in accurately modeling the system’s behavior.