中文摘要：

针对饱和黏弹性半空间地基上刚性圆板基础竖向振动问题，基于Boer多孔介质动力控制方程组，应用Hankel积分变换技术并结合基础与地基土接触面混合边值条件，推导求解相关方程得到了饱和黏弹性半空间地基上刚性圆板基础的竖向动力阻抗以及振幅放大系数公式。在此基础上进一步通过数值算例对比分析探讨了液固耦合系数、基础质量比、地基土黏滞阻尼系数对所得基础竖向动力阻抗及振幅放大系数的影响规律。解析推导得出的对应竖向动力阻抗三维精确解不但丰富了基础振动理论，还可为相关工程实践提供参考和理论支持。

英文摘要：

Analytical solutions of vertical dynamic impedance and amplitude amplification coefficient for vibration of rigid circular plate on saturated viscoelastic half-space were obtained by employing Hankel＇s integral transformation and considering mixed boundary condition of plate-subsoil interfaces to solve Boer＇s dynamic governing equations on porous medium. Furthermore, effects of liquid-solid coupling coefficient, mass ratio of foundation, and viscous damping coefficient of soil on vertical dynamic impedance and amplitude amplification coefficient of plate foundation were investigated by parametric comparative analyses. The solutions and results of vertical dynamic impedance and amplitude amplification coefficient of plate foundation derived in present paper are expected to contribute to theories on foundation vibrations and to provide technical reference and theoretical support for related engineering practices.