【摘要】 为了研究在剪切波沿地下长型结构纵向传播情况下,惯性力对地下结构与地基动力相互作用的影响,基于Winkler地基模型和Euler-Bernoulli梁模型,分别建立了长型地下结构的静力平衡方程、自由振动方程和强迫振动方程。通过振型叠加法将偏微分方程简化为常微分方程;利用微分算子法分别求得静力平衡方程;自由振动方程和强迫振动方程的解析解。通过算例计算,比较并分析了静力平衡方程解与强迫振动方程解的差别。结果表明在算例取值情况下,惯性力对结构振动的影响较小;而在地基基床系数k很小或轴向力N很大时,惯性力的影响才较为显著。更多还原

【Abstract】 To study the influence of inertia force on dynamic interaction between underground structure and foundation when shear wave propagates along axial direction of long underground structure,static equilibrium equation,free vibration motion equation and forced vibration motion equation were established based on Winkler foundation model and Euler- Bernoulli beam model. By applying mode superposition method we simplified partial differential equation into ordinary differential equation. These equations were solved analytically based on differential operator method. Numerical example was given and the results for static case and forced vibration case were compared. Comparison shows that the influence of inertial force on forced vibration of structure is relatively small in the given case,and is relatively significant when foundation bed coefficient k is small or axial force N is large.更多还原