Filtering property of periodic in-filled trench barrier for underground moving loads

The filtering properties of a 2-dimensional (2D) periodic in-filled trench barrier system subjected to anti-plane and in-plane moving loads are investigated separately by combining the spatial Fourier transform and periodic structure theory. By the aid of spatial Fourier transform, the governing equation of the periodic system is reduced in dimension. Based on the periodic structure theory, the closed-form solution of the dispersion equation for anti-plane wave is obtained; while for in-plane wave, the State-Space-Transfer-Matrix-Method (SSTMM) is introduced to solve the dispersion relation. Furthermore, the attenuation zones (AZs) varying with the transformed wave number, i.e., the AZs -kx graph, are obtained. Comparing the load-speed-line cluster of the moving excitation source with the obtained AZs -kx graph, the vibration isolation regions of the 2D periodic in-filled trench barrier in frequency-wave number space under moving loads can be found. To validate the present theoretical results, the performances of a 2D finite periodic in-filled trench barrier embedded in soil matrix and subjected to anti-plane and in-plane moving loads are numerically simulated, respectively. It is found that the AZs -kx graph plays a crucial role in revealing the isolation mechanism of the periodic in-filled trench barrier under moving loads. Theoretically speaking, it can be used to derive the vibration isolation regions for arbitrary excitation time histories of the moving-load inputs. The methodology proposed in the present paper can be used to design the continuous-type periodic wave barrier for isolating ambient vibration induced by moving loads.