Analytical Investigation on the Dynamic Behavior of Multi-Span Continuous Beams Supported on Soil with Finite Depth

Abstract

This paper investigates the influence of soil with finite depth on the vibrational behavior of a multi-span continuous beam resting on an elastic foundation. The simplified model of the Timoshenko beam supported on soil with finite depth is established, introducing the foundation displacement decay function. The numerical solution of the continuous beam’s vibration response on the elastic foundation is obtained by using the transfer matrix method (TMM) and fourth-order Runge-Kutta method (RK4). Taking a two-span continuous beam as an illustrative example, the validity of the calculation theory is validated by comparing it with the outcomes obtained from the finite element method (FEM). Utilizing numerical computation and parametric analysis, the vibration response of continuous beams is evaluated in terms of its influence by various factors such as soil thickness, viscous damping coefficient of the soil, subgrade reaction coefficient, and span ratio. The findings indicate that the inertial motion of the soil with a finite depth significantly reduces the continuous beam’s inherent frequency and enhances the structure’s resonance effect. The rise of the subgrade response coefficient increases the system’s resonant frequency while decreasing the displacement response amplitude. The ratio between the adjacent spans determines the effect of beam span vibration energy transfer to adjacent spans. In addition, compared with the span directly excited by a concentrated harmonic load, the impact of soil thickness, subgrade reaction coefficient, and viscous damping, the coefficient of the soil is more significant on the indirect influence span of a continuous beam.