Analytical Study On Elastic Wave Vibration Isolation Of Periodically Distributed Pile Groups

Periodically distributed pile groups can effectively block the environmental vibration and are widely used in engineering.Its essence is the problem of elastic wave scattering in the field of Engineering fluctuation.The analytical study of this problem can not only reveal the nature of the scattering of elastic waves by periodic structures,but also provide design guidance and theoretical support for engineering applications.However,limited by the theoretical development and calculation ability,most of the current research on this problem is based on the model with a small number of piles and assuming that the incident wave is plane wave,which can not well reflect the reality of a large number of densely distributed piles and near-field vibration isolation in engineering.It is more necessary to expand to the theoretical method which is convenient for calculating a large number of periodically distributed piles and considering the curvature of incident wave.Therefore,the main work of this paper is as follows1.Aiming at the vibration isolation of periodic pile group in elastic soil: firstly,the Graf addition theorem suitable for the transformation of wave function between arbitrary coordinate systems is derived,and then the wave function expansion method is used to make full use of the characteristics that the wave fields around different periodic elements are identical,but only one phase difference in frequency domain due to different positions,and only one periodic element is selected to analyze the whole pile group The scattering wave field of the barrier.On the basis of correctness verification,the results show that the isolation effect of periodic pile group on SH wave is mainly reflected in the lower frequency band of dimensionless frequency about 0.2-1.2,the isolation effect on SV wave is mainly reflected in the middle frequency band of frequency about 0.6-1.8,and the isolation effect on P wave is mainly reflected in the middle and higher frequency bands of frequency about 1.2-1.5and 2.2-2.8.2.Aiming at the vibration isolation of periodic pile groups in saturated soil:firstly,based on Biot fluid saturated porous medium wave theory,the wave field of soil skeleton and fluid part in saturated soil is analyzed,and then the scattering problem of infinite periodic piles in saturated soil is transformed into the scattering problem of only one periodic single pile by using the characteristic that the scattering wave field of different periodic elements in saturated soil has only different phase in frequency domain In addition,the computation is reduced significantly.On the basis of correctness verification,the results show that the vibration isolation ability of periodic pile groups in saturated soil is better than that in elastic soil,and the permeability of saturated soil has obvious influence on the vibration isolation ability.The worse the permeability of saturated soil is,the stronger the vibration isolation ability of pipe piles is.3.Aiming at the vibration isolation of periodic pile group under cylindrical wave source: firstly,for the finite periodic model,the free field of cylindrical wave is expressed by 0-order Hankel function.In each pile coordinate system,the boundary conditions of each pile need to be satisfied after superposing the scattered wave field;then for the infinite periodic model,the cylindrical wave is decomposed into the superposition of plane wave,and only one period needs to be selected by using the periodic characteristics Unit analysis.After obtaining the scattered wave field,combined with the free field of cylindrical wave,the analytical solutions of vibration isolation effect of finite and infinite periodic pile groups can be obtained.On the basis of correctness verification,the results show that,on the whole,the isolation effect of periodic pile group on cylindrical P-wave is better than that of cylindrical SV wave,and when the cylindrical wave source is closer to the pipe pile barrier,the displacement response of the site after pile row increases significantly,and the increase of the number of piles under the action of cylindrical wave source has little effect on the isolation effect.