Complex Variable Function Solution Of An Open Trench-wave Impeding Block Combined Vibration Isolation In Two Dimension Foundation

Nowadays,China's urban and rural construction and modernization industry is developing rapidly.Among them,the entire society exposed to high frequency of load cycles and emerge of various vibration problems,meanwhile,affects individual's daily lives.It is to note that open trench and wave impeding block(WIB)barrier against isolation effectively.However,its isolation performance of open trenches affected by its own depth intensively.This paper notes a new type of open trench-wave impeding block(superimposes two kinds of isolation barriers to form a new isolation barrier)combined isolation system in terms of the advantages of isolation trench and wave resistance plate and only applicable to medium and high frequency vibrations.At present,the methods for studying isolation performance of open trench and wave resistance plates are mainly numerical simulations and experimental verifications because of less analysis of isolation performance of open trench and wave resistance plates.Therefore,this study using wave function expansion and complex variable function method assess performance of wave resistance plate and open trench-wave resistance plate not only offers important theoretical support,but also provides value references for similar isolation design.This research content of this article mainly includes:(1)Application of Elastodynamics Theory and Complex Function MethodDisplacement expressions of the dynamic equations are deduced by mathematical methods rely on the basic elastic dynamics equations and a large number of literature.Through simplify motion equation displacement expression of the SH wave equation has obtained,furthermore,described the detail of continuous barrier in isolation mechanism,and elastic wave analyzed according to the problems in this study.The variable function method theory simplifies control equations and stress components,and explains the conformal change of the complex variable function method correspondingly,then analysis boundary value problem in detail for the research question of this topic.(2)Complex function solution of two-dimensional base wave impeding block isolationTheoretical analysis for complex variable isolation of the two-dimensional elastic foundation wave baffles.Firstly,establish control equations for the scattering of wave fields by rectangular wave baffles in two-dimensional elastic foundations,with the help of elastic mechanics complex theory.Secondly,performance of the two-dimensional foundation wave baffle plate plane SH waves has considered according to continuity interface conditions between wave baffles and half-spaces,and using the wave function expansion method to obtain the analytical solution of isolation.Finally,analysing the ratio of shear slab modulus to shear modulus of the foundation,corrugated plate depth,incidence of the acoustic wave angle affects isolation by the vary of the amplitude attenuation coefficient(amplitude ratio when barrier exist or not).The results show that with the increase of the wave-resistance plate shear modulus has obviously improvement in isolation performance,furthermore,isolation performance of the surface displacement gradually decreases with depth increase of wave impeding block.It is important that elastic incident wave angle has great effect on isolation,performance significantly improved by decreasing incident angle isolation and vice versa.(3)Complex variable function solution of open trench and wave impeding block combined isolation in two dimension foundationA new type of open trench-wave impeding block isolation system address by their feature,and theoretically analysis this two-dimensional elastic ground system under SH wave-impeding.Firstly,a control equation for the wave field scattering problem of a hollow groove-wave resistance plate on a two-dimensional elastic foundation has established with the aid of elastic mechanics complex theory as well as considering SH incidence.Secondly,its performance of isolation obtained by wave function expansion method according continuity condition at the interface.Finally,through vary of the amplitude attenuation coefficient(amplitude ratio when barrier exist or not)analyzed this system's isolation performance in shear modulus ratio,depth of the baffle plate,and incident angle of the elastic wave.Moreover,comparison of non-isolation barrier,with wave impeding block and open trench-wave impeding block.The results show that isolation performance is improved significantly when increasing shear modulus of wave impeding block and decreasing incident angle,however,effects of isolation on the surface displacement is gradually reduced with wave impeding block buried depth increasing.It is essential to note that open trench-wave impeding block has significant on isolation efforts.