Dynamic analysis of free-free Timoshenko beams on elastic foundation under transverse transient ground deformation

Underground infrastructure such as pipelines and tunnels can be vulnerable to transient ground deformation (TGD) generated by earthquakes, traffic, and other vibration sources. Current design methods rely on simplified analytical models that idealize soil movement as a traveling sinusoidal wave, neglecting system inertia and relative soil-structure displacement. As shown in this study, such assumptions may be inadequate for large-diameter buried pipelines and tunnels, where accurate dynamic analysis under axial and transverse TGD is required. This paper introduces a new semi-analytical model for the dynamic response of buried Timoshenko beams on Winkler foundation subjected to transverse TGD. A closed-form solution of the governing differential equation shows that the vibration spectrum is divided into four parts, separated by three transition frequencies that depend on the system's mechanical and geometric properties. These transitions govern changes in modal behavior and significantly influence dynamic amplification. The model is verified through a case study of a buried 107 cm (42 in) steel water pipeline with varying lengths and operating conditions. Analytical predictions show excellent agreement with finite-element modal and dynamic analyses. Additional validation using high-resolution free-vibration measurements and multi-point shaking-table experiments further confirms the accuracy and robustness of the formulation. Frequency-response analysis highlights conditions under which dynamic amplification becomes significant, particularly when forcing frequencies approach the system's fundamental frequency, which may lie within the range of dominant seismic frequencies. The proposed methodology provides a rigorous analytical framework for understanding the key factors governing the dynamic behavior of buried beams under diverse sources of ground vibration.