纵向剪切波作用下长型地下结构与Pasternak地基相互作用研究

Research on Dynamic Soil-Long-Underground-Structure Interaction Under the Action of Shear Wave Propagates Along Axial Direction of Structure Based on Pasternak Foundation

为了研究在剪切波沿地下长型结构纵向传播情况下,惯性力对于结构与地基动力相互作用的影响,采用Pasternak地基模型,分别建立长型地下结构静力平衡方程、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,考虑地基土硬度对于地基基床系数k0、剪切波速vs、泊松比υ、地基土剪切模量G0的影响,比较并分析静力平衡方程解与强迫振动方程解的差别,得出当地基土硬度较大的情况下惯性力影响较小的结论.

To study the influence of inertia force on dynamic interaction between underground structure and soil when shear wave propagates along axial direction of long underground structure, static equilibrium equation,free vibration motion equation and forced vibration motion equation are developed based on Pasternak foundation model. By applying mode superposition method the partial differential equation is converted into ordinary differential equation. These equations are solved analytically based on differential operator method. For evaluating the influence of foundation soil rigidity on foundation bed coefficient k0,shear wave velocity vs,Poisson ratio υ,foundation soil shear modulus G0,numerical example is given and the solutions for static equilibrium equation and forced vibration equation are compared. Comparison shows that the influence of inertial force on forced vibration of structure is relatively small when foundation soil rigidity is relatively high.