Response analysis of Timoshenko beam based on K-V damping model

Based on Timoshenko beam theory, this paper has analyzed the dynamic properties when a clamped beam subjected to step load and moving load respectively. In addition, K-V damping model is considered to study the influence of damping on dynamic performance of the system. To acquire the theoretical solution, proportional damping utilization condition is derived, the real modal superposition method is applied, and eventually obtain the analytical responses when beam subjected to external loads. The numerical analysis results indicate that the solving process is accurate and reliable, providing a measurement reference to other methods, like Laplace transformation. The results of damping cases demonstrate that the high modes inherit over damping property, while in low modes present oscillation convergent characteristic. Sometimes, the damping can have significantly impact on the whole system, and for large slender ratios, the amplitude under moving load is even enlarged. Furthermore, the dynamic response subjected to step load is dominated by the low modes.