Research On Vibration Isolation Performance Of One-dimensional Periodic Structure With Oblique Incidence Based On PDE Module

Periodic structure has the characteristics of band gap,which has been widely concerned as a new vibration isolation method.Among them,the research on onedimensional periodic structure of shielding surface wave is still limited to the aspect of vertical incidence,while in engineering practice,oblique incidence is a general case,so the analysis of oblique incidence on one-dimensional periodic structure has important theoretical and practical value.Based on the periodic structure theory and Partial Differential Equation（PDE）module in the finite element software COMSOL MULTIPHYSICS 5.4a,the oblique incidence of one-dimensional periodic isolation wall,different section isolated hollow ditch and filling ditch are considered respectively.The calculation method of the dispersion relation and frequency response function of one-dimensional periodic structure with oblique incident surface wave is given through theoretical derivation and numerical simulation,The influence of soil parameters,structural parameters,section form and filling material on the vibration isolation performance of one-dimensional periodic structure（vibration isolation wall and vibration isolation ditch）is discussed;The vibration isolation performance of the structure under vertical and oblique incidence conditions is compared,and the vibration isolation effect of filling ditch and empty groove with different sections is compared.The results are as follows:1.The incident direction of the surface wave has a great influence on the vibration isolation performance of the wall.With the increase of incident angle,a new band gap with lower order will be generated;The bandwidth of each band gap changes with the increase of incident angle,and the center frequency of the band gap increases;When the incident angle of the surface wave increases to a certain extent,the wall has no isolation effect on the surface wave in a specific frequency range.2.In the case of oblique incidence,the larger the shear modulus of the soil is,the better the vibration isolation performance of the wall is.However,the harder the soil is,the more sensitive its vibration isolation performance is to the incident direction.3.Compared with the isolation wall,the incidence angle has a greater impact on the vibration isolation hollow ditch.The frequency of the low-order band gap generated by the vibration isolation hollow ditch is lower than that of the normal incidence,which can shield the lower frequency vibration.4.When the ditch width is greater than 0.6 times of the period constant or the ditch depth is greater than 0.8 times of the period constant,the vibration isolation effect of the isolated hollow ditch is better than that of the normal incident wave;The shielding performance of triangular and trapezoidal hollow ditch for oblique incident waves is better than that of rectangular hollow ditch.5.The performance of hollow ditch vibration isolation is better than that of EPS foam filled ditch.If the surface wave is perpendicular or nearly perpendicular,the rectangular hollow ditch has better vibration isolation effect,otherwise,the trapezoidal section is better.6.According to the actual environmental vibration,the trapezoidal periodic vibration isolation hollow ditch is designed,and the comparison is 30 ° The vibration isolation performance of inclined arrangement and vertical arrangement.The results show that the wave attenuation is obvious in the main frequency range of the 30 ° in inclined arrangement,and the vibration isolation effect is obviously better than that for the vertical arrangement.