Domain Expansion Method for Analyzing Vibration Propagation from Large-Scale Dynamic Machinery

Large-scale complex dynamic machines — characterized by high power output, broad frequency bandwidths, and intricate foundation configurations — can generate adverse vibration impacts propagating across kilometer-scale sites. To address the computational challenges in simulating such systems, we propose a novel Domain Expansion Method (DEM) that synergistically integrates the Finite Element Method (FEM) and Spectral Element Method (SEM). Building upon Bielak’s Domain Reduction Method (DRM), the DEM innovatively decomposes the machine foundation-site system into a refined internal FE domain and a large-scale external SE domain. A leapfrog interpolation scheme enables seamless FE-SE grid transitions without the need for irregular transitional elements. The accuracy is verified and the applicability is validated by using the data from the National Facility for Earthquake Engineering Simulation (NFEES) in China, featuring the world’s largest earthquake simulation shaking table (16[Formula: see text]m×20[Formula: see text]m platform, 1[Formula: see text]350-ton maximum load capacity, [Formula: see text] horizontal/vertical peak accelerations). Kilometer-scale vibration attenuation contour maps are generated to quantitatively assess the ground vibration attenuation. The results indicate that the [Formula: see text]-vibration level at a distance of 100[Formula: see text]m east of the NFEES foundation reaches approximately 80[Formula: see text]dB (under full-load and full-acceleration seismic-excitation), and it exhibits an attenuation rate of 6[Formula: see text]dB over 0–100[Formula: see text]m. Compared to conventional FE modeling, the DEM achieves a 67% reduction in computational time and an 80% decrease in memory usage, demonstrating its effectiveness in addressing both the accuracy and efficiency for kilometer-scale vibration propagation analyses.