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摘要:
基于铁木辛柯梁理论，对两端固支梁在承受阶跃载荷和移动载荷下的响应进行了分析。借助K-V阻尼模型，研究了阻尼对系统动态性能的影响。为了进行理论求解，推导了比例阻尼的使用条件，继而运用实模态叠加法理论，最终导出了系统受载时响应的解析解。数值分析结果表明，该方法准确可靠，为其他数值算法，如拉普拉斯变换法，提供了横向对比的依据。有阻尼振动的分析表明系统在高阶模态具有过临界阻尼特性，在低阶模态为收敛振荡特性。阻尼对系统的响应有很大影响，尤其在大长细比时，甚至出现了振幅增大的情形。此外，在阶跃载荷的作用下，系统均呈现出了低频模态为主的响应特性。
Abstract: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.
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Key words:
- Timoshenko beam /
- K-V damping /
- real mode theory /
- step load /
- moving load
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图 1 Durbin数值反拉普拉斯求解效果示意图
Figure 1. Schematic of solving accuracy of Durbin's inverse Laplace
图 6 d*=0.5时无量纲位移总响应
Figure 6. Non-dimensionalized response of total displacement when d*=0.5
图 7 d*=0.25时无量纲位移总响应
Figure 7. Non-dimensionalized response of total displacement when d*=0.25
图 8 Lr=10无量纲位移总响应
Figure 8. Non-dimensionalized response of total displacement when Lr=10
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