Dynamic Soil–Structure–Equipment Interaction (II): Closed-form Analytical Solution for Incident Plane SH-wave Based on Flexible Foundation Model

ABSTRACT

We study a two-dimensional structure–equipment model standing on a semi-circular flexible foundation embedded in the homogeneous half-space subjected with plane SH-waves, as a companion to the previous study of dynamic soil–structure–equipment interaction based on rigid-foundation model. We obtain the analytical solution of the system response that demonstrates the influence of foundation stiffness on the response of the soil–structure–equipment interaction system. The results show that, after considering the influence of the foundation stiffness, the effective foundation input motion is amplified, and the maximum amplification percentage can reach to 32.8%. The peak of the floor relative response is amplified by 18.5% and the frequency corresponding to the peak shifts to the lower range with the maximum shift percentage 16.1%. The peak of the equipment relative response can be amplified by 76.7%. There is significant relative deformation in the foundation when the wave is obliquely incident. The equipment-structure frequency ratio and mass ratio are important parameters that reflect the dynamic characteristics of the soil-structure–equipment system. When the equipment-structure frequency ratio is between 0.5 and 1.0, the dynamic characteristics of the structure–equipment system change. We propose a parameter (Ψ) to measure the extent to which the equipment participates in the soil–structure interaction.

KEYWORDS:

• Structure-equipment interaction
• soil-structure interaction (SSI)
• flexible foundation
• analytical solution
• wave function expansion method
• SH wave

Acknowledgments

This study is supported by the National Natural Science Foundation of China under Grants 51808290, and this project is also funded by China Postdoctoral Science Foundation 2018M642232, which are gratefully acknowledged.