CN103093055A - Linkage type row pile vibration isolation structure - Google Patents

Abstract

The invention relates to a linkage type row pile isolation structure. The structure is provided with a periodic row pile structure on the walking direction of row piles, and pile tops of the row piles are in mutually rigid linkage through linkage beams. Each pile in the same row of the piles is a concrete pile with arbitrary cross section, and is provided with same geometry material parameters; and piles in different rows can have different parameters. The linkage beams in the same groups have same geometry material parameters, and the linkage beams in different groups can have different parameters. Floquet transformation and a boundary element method are adopted, and a pile-soil boundary element model in a wave number domain is built. The linkage beams on the upper portion are processed through a transfer matrix method. The pile-soil boundary element model, coupling conditions and periodic conditions of the pile tops and the beams are adopted, and a calculation model of the linkage type row piles is built. Compared with free type row piles with pile tops not restricted, the linkage type row pile isolation structure can effectively reduce vibration isolation coefficients and improve vibration isolation effects.

Description

Coupling type Vibration Isolation by Piles in Rows structure

Technical field

The present invention proposes a kind of Novel pile foundation structure that is used for vibration isolation, i.e. coupling type campshed, and utilize Floquet conversion and Element BEM to set up the periodic boundary meta-model of this Novel pile basis vibration insulation structure.

Background technology

Enter 21st century, the Modern Traffic facilities such as high-speed railway, highway, subway and light rail of China are universal rapidly, and correspondingly, the caused vibration problem of above-mentioned means of transportation also causes the extensive concern of engineering circles; Meanwhile, because the caused vibration problems of construction activities such as machine vibration, explosion and piling are also day by day serious, daily life a lot of inconvenience have been brought.Therefore, the vibration isolating effect that improves all kinds of vibration isolation facilities is to people's production and live significant.

Campshed is a kind of novel vibration insulation structure, and because it arranges the impact that is not subjected to underground water table and soil body stability, therefore, the Vibration Isolation by Piles in Rows structure more and more is subject to civil engineer's attention at present.The cardinal principle of Vibration Isolation by Piles in Rows is to realize passive vibration isolation by the route of transmission of controlling elastic wave, namely utilizes the reflection of row of piles and scattering function to hinder the propagation of all kinds of elastic waves in the soil body, to realize the purpose of vibration isolation.It is worthy of note existing research about Vibration Isolation by Piles in Rows, all adopt the campshed of common form, namely the stake top is without the free style campshed of any constraint.Existing studies show that, in the situation that the incident of low-frequency elastic ripple, the vibration isolating effect of free style campshed is also bad.Therefore, the vibration isolating effect of raising campshed remains a problem that is worth further investigation.In addition, in existing research, due to the restriction that is subjected to computer capacity, all campshed is reduced to limited several piles, obviously, the Vibration Isolation by Piles in Rows system that comprises tens of piles even up to a hundred in this and engineering reality does not meet.Because the stake quantity that adopts in the vibration isolation numerical simulation has obvious impact to its vibration isolating effect, therefore, simulating the Vibration Isolation by Piles in Rows system with several piles has its limitation.Because the numerical simulation to Vibration Isolation by Piles in Rows is a 3-D Dynamic problem, so when numerical methods such as adopting finite element or boundary element was simulated Vibration Isolation by Piles in Rows, the demand that reach calculator memory computing time can be Exponential growth with the increase of stake number.Therefore, the numerical evaluation model of the campshed that the suitable stake of development number is a lot of is significant to the Vibration Absorbing System Design of campshed.

Summary of the invention

In order to improve the vibration isolating effect of campshed, the present invention proposes a kind of novel pile foundation vibration insulation structure, i.e. coupling type Vibration Isolation by Piles in Rows structure (single, double and three row), this structure can improve the vibration isolating effect of campshed under the same terms effectively.

Coupling type Vibration Isolation by Piles in Rows structure proposed by the invention, campshed has periodically along the trend of stake, be in campshed each along the stake move towards maintenance fixed range, this fixed range is called the cycle of campshed, each campshed keeps the relative changing of the relative positions of certain distance each other along the campshed trend, stake in campshed can be various types of stakes, as: prefabricated or cast-in-situ bored pile, the arbitrary section concrete-pile of each in same campshed for having identical geometry and material parameter, the stake that belongs to different rows can have different geometry and material parameter.Fig. 1, Fig. 2 and Fig. 3 have provided respectively single, the vertical view of double and three Volleyball Association's eliminant Vibration Isolation by Piles in Rows structures.Each in campshed stake is pushed up by periodicity binding-beam fixed connection, all binding-beams that can overlap by on the strike translation cycle integral multiple are called one group of binding-beam, for example: in single stake, one group of binding-beam (Fig. 1) is arranged, four groups of binding-beams (Fig. 2) are arranged in double-row pile, seven groups of binding-beams (Fig. 3) are arranged in three campsheds, the binding-beam that belongs to mutually on the same group has identical geometry and material parameter, and the binding-beam that belongs to not on the same group can have different relevant parameters.

The computation model of coupling type Vibration Isolation by Piles in Rows structure is also contained in the present invention, utilizes this computation model and the related software can be to geometry and the material parameter of pile foundation, and geometry and the material parameter of concrete binding-beam are optimized design.

Coupling type Vibration Isolation by Piles in Rows structure proposed by the invention, its computation model relates to following steps:

Step 1: use Floquet conversion and Element BEM, set up respectively stake, native boundary integral equation expression formula in wavenumber domain.

Step 2: utilize Element BEM respectively stake, native boundary integral equation in wavenumber domain to be carried out discrete, and the boundary element of stake, the representative cellular of soil institute is carried out integration, obtain in wavenumber domain, native boundary element row formula.

Step 3: utilize the condition of continuity of stake in wavenumber domain, native boundary element row formula and the native displacement of stake and face power, the native periodic boundary meta-model of stake that obtains being coupled.

Step 4: use Transfer Matrix Method, the top binding-beam is processed, and utilize stake top and beam-ends coupling condition and periodicity condition, set up the computation model of coupling type Vibration Isolation by Piles in Rows structure.

The present invention can effectively reduce amplitude under the same conditions than (amplitude is than the ratio of the amplitude that refers to adopt half-space surface point perpendicular displacement after the Vibration Isolation by Piles in Rows structure corresponding perpendicular displacement amplitude in free wave field when there is no vibration insulation structure), improves the vibration isolating effect of campshed.

Description of drawings

Fig. 1 is single coupling type Vibration Isolation by Piles in Rows structure vertical view.L is the cycle of single coupling type Vibration Isolation by Piles in Rows structure, i.e. the pile spacing of adjacent studs in row.

Fig. 2 is double coupling type Vibration Isolation by Piles in Rows structure vertical view.L is the cycle of double coupling type Vibration Isolation by Piles in Rows structure, the pile spacing of adjacent studs in namely each is arranged, and adjacent studs pile spacing of each row is identical; d _RRepresent the row's spacing in double coupling type Vibration Isolation by Piles in Rows structure; d _sRepresent the relative changing of the relative positions distance between two campsheds in double coupling type Vibration Isolation by Piles in Rows structure; 1., 2., 3., 4. represent the representative beam in four groups of binding-beams.

Fig. 3 is three Volleyball Association's eliminant Vibration Isolation by Piles in Rows structure vertical views.L is the cycle of three Volleyball Association's eliminant Vibration Isolation by Piles in Rows structures, the pile spacing of adjacent studs in namely each is arranged, and adjacent studs pile spacing of each row is identical; d _RThe row's spacing that represents adjacent row in three Volleyball Association's eliminant Vibration Isolation by Piles in Rows structures, it is identical that adjacent row arranges spacing; 1., 2., 3., 4., 5., 6., 7. represent the representative beam in seven groups of binding-beams.

In Fig. 4 ,-1 ^th, 0 ^th, 1 ^thRepresent successively-1,0 and No. 1 cellular; P ₁, P ₂, P ₃Represent the first, the second, No. three stake in representative cellular; Beam label b ₁₂The first digit of subscript 12 represents stake numbering namely to represent the first pile, and second digit represents the beam numbering with this connection, i.e. second beam, so, b ₁₂Second beam that in expression and cellular, the first pile connects, the label meaning of all the other beams is the same.

Fig. 4 is the stake and the connection sketch of beam in three Volleyball Association's eliminant Vibration Isolation by Piles in Rows structures.

Fig. 5 is that the amplitude of double coupling type Vibration Isolation by Piles in Rows structure compares isogram.

Fig. 6 is that the amplitude of double free style Vibration Isolation by Piles in Rows structure compares isogram.

Embodiment

Embodiment 1

The below is briefly described computation model step of the present invention.

According to the Floquet transform method, utilize the boundary integral equation of the soil body in spatial domain, obtain the boundary integral equation of Soil In Half Space in following wavenumber domain

$c_{\mathrm{ij}}{\tilde{u}}_j^{\left(S_{\mathrm{II}}\right)}(\mathrm{\κ},x^{\left(e\right)})=\underset{{\mathrm{\Γ}}_S^{\left(e\right)}}{\∫}{\tilde{U}}_{\mathrm{ij}}^{\left(S_F\right)}(\mathrm{\κ},x^{\left(e\right)}-y^{\left(e\right)}){\tilde{t}}_j^{\left(S_{\mathrm{II}}\right)}(\mathrm{\κ},y^{\left(e\right)})\mathrm{d\Γ}\left(y^{\left(e\right)}\right)$

$-\underset{{\mathrm{\Γ}}_S^{\left(e\right)}}{\∫}{\tilde{T}}_{\mathrm{ij}}^{\left(S_F\right)}(\mathrm{\κ},x^{\left(e\right)}-y^{\left(e\right)}){\tilde{u}}_j^{\left(S_{\mathrm{II}}\right)}(\mathrm{\κ},y^{\left(e\right)})\mathrm{d\Γ}\left(y^{\left(e\right)}\right),x^{\left(e\right)}\∈{\mathrm{\Γ}}_S^{\left(e\right)}---\left(1\right)$

Wherein,

The displacement and the face power that represent respectively Soil In Half Space in wavenumber domain; The Green function that represents respectively the interior land movement of wavenumber domain and face power;

The border of the representative cellular of Soil In Half Space in the expression wavenumber domain.Utilize the boundary integral equation of stake in spatial domain, obtain the boundary integral equation of stake in following wavenumber domain

$c_{\mathrm{ij}}{\tilde{u}}_j^{\left(P_{\mathrm{\α}}\right)}(\mathrm{\κ},x^{\left(e\right)})=\underset{{\mathrm{\Γ}}_{p_{\mathrm{\α}}}^{\left(e\right)}}{\∫}{U}_{\mathrm{ij}}^{\left(P_{\mathrm{\α}}\right)}(y^{\left(e\right)}-x^{\left(e\right)}){\tilde{t}}_j^{\left(P_{\mathrm{\α}}\right)}(\mathrm{\κ},y^{\left(e\right)})\mathrm{d\Γ}\left(y^{\left(e\right)}\right)$

$-\underset{{\mathrm{\Γ}}_{p_{\mathrm{\α}}}^{\left(e\right)}}{\∫}{T}_{\mathrm{ij}}^{\left(P_{\mathrm{\α}}\right)}(y^{\left(e\right)}-x^{\left(e\right)}){\tilde{u}}_j^{\left(P_{\mathrm{\α}}\right)}(\mathrm{\κ},y^{\left(e\right)})\mathrm{d\Γ}\left(y^{\left(e\right)}\right),x^{\left(e\right)}\∈{\mathrm{\Γ}}_{P_{\mathrm{\α}}}^{\left(e\right)},\mathrm{\α}=1~N_R---\left(2\right)$

Wherein,

The displacement and the face power that represent respectively stake in wavenumber domain;

Represent respectively the displacement of stake and the Green function of face power;

The boundary surface of α pile in representative cellular in the expression wavenumber domain; N _RRepresent the number of contained stake in a cellular, for example: being one to a campshed, is two to two campsheds.

A boundary integral equation mistake to Soil In Half Space in wavenumber domain! Do not find Reference source.Utilize Element BEM to carry out discrete, and the boundary element of the representative cellular of all soil bodys is carried out integration, can obtain the boundary element row formula in the Soil In Half Space wavenumber domain

${\tilde{G}}^{\left(S\right)}\left(\mathrm{\κ}\right){\tilde{t}}^{\left(S_{\mathrm{II}}\right)}\left(\mathrm{\κ}\right)={\tilde{H}}^{\left(S\right)}\left(\mathrm{\κ}\right){\tilde{u}}^{\left(S_{\mathrm{II}}\right)}\left(\mathrm{\κ}\right)---\left(3\right)$

Wherein,

Represent respectively in wavenumber domain displacement and the face power of node on the representative cellular of Soil In Half Space border; The matrix of coefficients that expression is corresponding.Similarly, utilize the boundary integral equation mistake of stake in wavenumber domain! Do not find Reference source., can get in wavenumber domain the boundary element row formula of α pile in representative cellular

$G^{\left(P_{\mathrm{\α}}\right)}{\tilde{t}}^{\left(P_{\mathrm{\α}}\right)}\left(\mathrm{\κ}\right)=H^{\left(P_{\mathrm{\α}}\right)}{\tilde{u}}^{\left(P_{\mathrm{\α}}\right)}\left(\mathrm{\κ}\right),\mathrm{\α}=1~N_R---\left(4\right)$

Wherein, Represent respectively in wavenumber domain in representative cellular displacement and the face power of node on α pile border; The matrix of coefficients that expression is corresponding.

The surface of contact place of pile foundation and Soil In Half Space in the representative cellular of wavenumber domain, its displacement and face power have following relation:

${\tilde{u}}_j^{\left(P_{\mathrm{\α}}\right)}(\mathrm{\κ},x^{\left(e\right)})={\tilde{u}}_j^{\left(S\right)}(\mathrm{\κ},x^{\left(e\right)}),{\tilde{t}}_j^{\left(P_{\mathrm{\α}}\right)}(\mathrm{\κ},x^{\left(e\right)})=-{\tilde{t}}_j^{\left(S\right)}(\mathrm{\κ},x^{\left(e\right)}),x^{\left(e\right)}\∈{\mathrm{\Γ}}_{I_{\mathrm{\α}}}^{\left(e\right)},\mathrm{\α}=1~N_R---\left(5\right)$

Wherein,

With

Represent respectively stake and the native displacement at the interior stake soil contact face of wavenumber domain place;

The stake and the native face power that represent respectively the interior stake soil contact face of wavenumber domain place;

The surface of contact of expression pile foundation and Soil In Half Space.In addition, in the representative cellular of wavenumber domain, the boundary displacement of Soil In Half Space and face power have respectively following expression:

${\tilde{u}}_j^{\left(S\right)}(\mathrm{\κ},x^{\left(e\right)})={\tilde{u}}_j^{\left(S_I\right)}(\mathrm{\κ},x^{\left(e\right)})+{\tilde{u}}_j^{\left(S_{\mathrm{II}}\right)}(\mathrm{\κ},x^{\left(e\right)}),$

${\tilde{t}}_j^{\left(S\right)}(\mathrm{\κ},x^{\left(e\right)})={\tilde{t}}_j^{\left(S_I\right)}(\mathrm{\κ},x^{\left(e\right)})+{\tilde{t}}_j^{\left(S_{\mathrm{II}}\right)}(\mathrm{\κ},x^{\left(e\right)}),x^{\left(e\right)}\∈{\mathrm{\Γ}}_S^{\left(e\right)}---\left(6\right)$

Wherein,

The total displacement and the total face power that represent respectively Soil In Half Space border in wavenumber domain;

Displacement and the face power on the Soil In Half Space border that represents respectively to be produced by the free wave place.

The Soil In Half Space boundary surface can be divided into two parts: the native contact portion of stake and Soil In Half Space Free Surface part.By the formula mistake! Do not find Reference source., can be with the formula mistake! Do not find Reference source.Be converted into

$\left[{\tilde{H}}_I^{\left(S\right)}\left(\mathrm{\κ}\right){\tilde{H}}_H^{\left(S\right)}\left(\mathrm{\κ}\right)\right]\left\{\begin{array}{c}{\tilde{u}}_I^{\left(S\right)}\left(\mathrm{\κ}\right)\\ {\tilde{u}}_H^{\left(S\right)}\left(\mathrm{\κ}\right)\end{array}\right\}-{\tilde{G}}_I^{\left(S\right)}\left(\mathrm{\κ}\right){\tilde{t}}_I^{\left(S\right)}\left(\mathrm{\κ}\right)=\left[{\tilde{H}}_I^{\left(S\right)}\left(\mathrm{\κ}\right){\tilde{H}}_H^{\left(S\right)}\left(\mathrm{\κ}\right)\right]\left\{\begin{array}{c}{\tilde{u}}_I^{\left(S_I\right)}\left(\mathrm{\κ}\right)\\ {\tilde{u}}_H^{\left(S_I\right)}\left(\mathrm{\κ}\right)\end{array}\right\}$

$-\left[{\tilde{G}}_I^{\left(S\right)}\left(\mathrm{\κ}\right){\tilde{G}}_H^{\left(S\right)}\left(\mathrm{\κ}\right)\right]\begin{array}{}\end{array}\left\{\begin{array}{c}{\tilde{t}}_I^{\left(S_I\right)}\left(\mathrm{\κ}\right)\\ {\tilde{t}}_H^{\left(S_I\right)}\left(\mathrm{\κ}\right)\end{array}\right\}---\left(7\right)$

Wherein, Total displacement and total face power of expression stake soil contact face place soil boundary respectively;

The soil boundary displacement and the face power that represent respectively stake free wave place, soil contact face place generation;

Represent respectively the displacement at Soil In Half Space Free Surface place and the displacement that is produced by free wave field;

The face power that expression Soil In Half Space Free Surface place is produced by free wave field; Represent respectively the native Contact Boundary of stake and matrix of coefficients corresponding to Soil In Half Space free boundary place.The pile foundation boundary surface also can be divided into two parts: the native Contact Boundary of stake and stake top boundary part, therefore, a pile foundation boundary element row formula mistake! Do not find Reference source.Can further be expressed as

$\left[H_I^{\left(P_{\mathrm{\α}}\right)}{H}_T^{\left(P_{\mathrm{\α}}\right)}\right]\left\{\begin{array}{c}{\tilde{u}}_I^{\left(P_{\mathrm{\α}}\right)}\left(\mathrm{\κ}\right)\\ {\tilde{u}}_T^{\left(P_{\mathrm{\α}}\right)}\left(\mathrm{\κ}\right)\end{array}\right\}=\left[G_I^{\left(P_{\mathrm{\α}}\right)}{G}_T^{\left(P_{\mathrm{\α}}\right)}\right]\left\{\begin{array}{c}{\tilde{t}}_I^{\left(P_{\mathrm{\α}}\right)}\left(\mathrm{\κ}\right)\\ {\tilde{t}}_T^{\left(P_{\mathrm{\α}}\right)}\left(\mathrm{\κ}\right)\end{array}\right\},\mathrm{\α}=1~N_R---\left(8\right)$

Wherein,

Boundary displacement and the face power of the native Contact Boundary of expression stake place pile foundation respectively;

The displacement and the face power that represent respectively the pile foundation top boundary;

Represent respectively the native Contact Boundary of stake and matrix of coefficients corresponding to stake top boundary.

By stake, native boundary element row formula mistake! Do not find Reference source., mistake! Do not find Reference source.An and condition of continuity mistake of the native displacement of stake and face power! Do not find Reference source., can get the native periodic boundary meta-model of stake of following coupling

$\left[\begin{array}{ccccc}{H}_I^{\left(P\right)}& -G_I^{\left(P\right)}& H_T^{\left(P\right)}& 0& -G_T^{\left(P\right)}{\mathrm{\Φ}}_F^{\left(P\right)}\\ {\tilde{H}}_I^{\left(S\right)}\left(\mathrm{\κ}\right)& {\tilde{G}}_I^{\left(S\right)}\left(\mathrm{\κ}\right)& 0& {\tilde{H}}_H^{\left(S\right)}\left(\mathrm{\κ}\right)& 0\end{array}\right]{\widetilde{\mathrm{\Δ}}}^{\left(L\right)}=\left\{\begin{array}{c}0\\ {\tilde{R}}_S\left(\mathrm{\κ}\right)\end{array}\right\}---\left(9\right)$

Wherein,

${\widetilde{\mathrm{\Δ}}}^{\left(L\right)}={\left[{\tilde{u}}_I^{\left(P\right)T}\left(\mathrm{\κ}\right){\tilde{t}}_I^{\left(P\right)T}\left(\mathrm{\κ}\right){\tilde{u}}_T^{\left(P\right)T}\left(\mathrm{\κ}\right){\tilde{u}}_H^{\left(S\right)T}\left(\mathrm{\κ}\right){\tilde{F}}^{\left(P\right)}\left(\mathrm{\κ}\right)\right]}^T,$

${\tilde{R}}_S\left(\mathrm{\κ}\right)=\left[{\tilde{H}}_I^{\left(S\right)}\left(\mathrm{\κ}\right){\tilde{H}}_H^{\left(S\right)}\left(\mathrm{\κ}\right)\right]\left\{\begin{array}{c}{\tilde{u}}_I^{\left(S_I\right)}\left(\mathrm{\κ}\right)\\ {\tilde{u}}_H^{\left(S_I\right)}\left(\mathrm{\κ}\right)\end{array}\right\}-\left[{\tilde{G}}_I^{\left(S\right)}\left(\mathrm{\κ}\right){\tilde{G}}_H^{\left(S\right)}\left(\mathrm{\κ}\right)\right]\left\{\begin{array}{c}{\tilde{t}}_I^{\left(S_I\right)}\left(\mathrm{\κ}\right)\\ {\tilde{t}}_H^{\left(S_I\right)}\left(\mathrm{\κ}\right)\end{array}\right\}---\left(10\right)$

In following formula,

Expression is applied to the external force on α pile stake top,

Expression stake top external force is converted to the transition matrix of face power.

The coupling type campshed carries under effect outside, and therefore the coupling of pile foundation and top concrete binding-beam, carry out dynamic analysis to the coupling type campshed, must analyze coupling type campshed middle and upper part beams of concrete, and stake top and binding-beam are coupled.Be example below by three Volleyball Association's eliminant Vibration Isolation by Piles in Rows structures, the processing of top binding-beam is described.

Carry under effect outside, but in the binding-beam generating plane and out-of-plane vibration, the state vector at its arbitrary section place can be expressed as

${\widetilde{\mathrm{\ψ}}}^{\left(b_{\mathrm{\αj}}\right)}(\mathrm{\κ},x^{\left({\mathrm{\α}}_j\right)})={\{{\tilde{q}}^{{\left(b_{\mathrm{\αj}}\right)}^T},{\tilde{f}}^{{\left(b_{\mathrm{\αj}}\right)}^T}\}}^T,\mathrm{\α}=1~N_R,j=1~K_b^{\left(\mathrm{\α}\right)}---\left(11\right)$

Wherein,

And

The state vector of the j root beam section that connects of expression and α pile respectively, displacement and interior force vector;

The beam number that expression and α pile connect.

In coupling type Vibration Isolation by Piles in Rows structure, stake top and the beams of concrete rigid connection of pile foundation.Therefore, to the j root beam that connects with the α pile, under the coordinate system of pile foundation and under the notation of beam, its state vector has following relation

${\widetilde{\mathrm{\ψ}}}^{\left(b_{\mathrm{\αj}}\right)}(\mathrm{\κ},0_{+})=T_{\mathrm{Pb}}{\widetilde{\mathrm{\ψ}}}^{\left(P_{\mathrm{\αj}}\right)}\left(\mathrm{\κ}\right),{\widetilde{\mathrm{\ψ}}}^{\left(P_{\mathrm{\αj}}\right)}\left(\mathrm{\κ}\right)=T_{\mathrm{Pb}}^{-1}{\widetilde{\mathrm{\ψ}}}^{\left(b_{\mathrm{\αj}}\right)}(\mathrm{\κ},0_{+}),\mathrm{\α}=1~N_R,j=1~K_b^{\left(\mathrm{\α}\right)}---\left(12\right)$

Wherein,

The state vector of j root beam under pile foundation coordinate system and the notation at beam that expression and α pile connect; T _PbThe transition matrix of expression stake beam state vector.

Suppose beams of concrete two ends respectively with α stake and β stake fixed connection, the α stake belongs to the 0-th cellular, the β stake belongs to m-th cellular (m desirable-1,0 or 1); Suppose that numbering corresponding to beam two ends that connects with α stake and β stake is respectively j and k, this beam and the junction of α stake and β stake have two corresponding section S ^{(α j)}(0 ₊) and

Above-mentioned two state vectors corresponding to cross section are respectively: With

Utilize the equation mistake! Do not find Reference source.With the transfer matrix of this beam, can get the relation of above-mentioned two state vectors

${\widetilde{\mathrm{\ψ}}}_m^{\left(P_{\mathrm{\βk}}\right)}\left(\mathrm{\κ}\right)=T_{12}^{\left(\mathrm{xy}\right)}\left(\mathrm{\π}\right)T_{\mathrm{Rf}}{T}_{\mathrm{Pb}}{T}^{\left(b_{\mathrm{\αj}}\right)}{T}_{\mathrm{Pb}}{\widetilde{\mathrm{\ψ}}}^{\left(P_{\mathrm{\αj}}\right)}\left(\mathrm{\κ}\right),{\widetilde{\mathrm{\ψ}}}^{\left(P_{\mathrm{\αj}}\right)}\left(\mathrm{\κ}\right)=T_{12}^{\left(\mathrm{xy}\right)}\left(\mathrm{\π}\right)T_{\mathrm{Rf}}{T}_{\mathrm{Pb}}{T}^{\left(b_{\mathrm{\βk}}\right)}{T}_{\mathrm{Pb}}{\widetilde{\mathrm{\ψ}}}_m^{\left(P_{\mathrm{\βk}}\right)}\left(\mathrm{\κ}\right)---\left(13\right)$

In following formula,

Represent that respectively identical beam is at the transfer matrix of different local coordinate systems, Τ _RfNormal direction reverse conversion matrix,

180 degree coordinate conversion matrixs.Utilize

The periodicity condition that is satisfied

${\widetilde{\mathrm{\ψ}}}_m^{\left(P_{\mathrm{\βk}}\right)}\left(\mathrm{\κ}\right)=e^{-\mathrm{im\κL}}{\widetilde{\mathrm{\ψ}}}^{\left(P_{\mathrm{\βk}}\right)}\left(\mathrm{\κ}\right)---\left(14\right)$

Can replenish as underbeam the expression formula of equation

$T_{12}^{\left(\mathrm{xy}\right)}\left(\mathrm{\π}\right)T_{\mathrm{Rf}}{T}_{\mathrm{Pb}}{T}^{\left(b_{\mathrm{\αj}}\right)}{T}_{\mathrm{Pb}}{\widetilde{\mathrm{\ψ}}}^{\left(P_{\mathrm{\αj}}\right)}\left(\mathrm{\κ}\right)-e^{-\mathrm{im\κL}}{\widetilde{\mathrm{\ψ}}}^{\left(P_{\mathrm{\βk}}\right)}\left(\mathrm{\κ}\right)=0---\left(15\right)$

A formula mistake! Do not find Reference source.Provided and beam section S ^{(α j)}(0 ₊) and

Two state vectors that are associated

And

Between relation.

In three Volleyball Association's eliminant Vibration Isolation by Piles in Rows structures, the connection cross section of 14 beams and stake is arranged, therefore in representative cellular, 14 state vectors are arranged accordingly, these 14 state vector corresponding cross sections interconnect by 7 different beams of concretes, therefore, can set up 7 additional equations.To above-mentioned three Volleyball Association's eliminant Vibration Isolation by Piles in Rows structures, with wherein the stake and beam be reduced to respectively Points And lines (Fig. 4).0 ^thIn cellular, and the first pile (P ₁) first beam (b connecting ₁₁), be again 1 simultaneously ^thThe 4th beam (b that cellular neutralization the first pile connects ₁₄), replenish the equation mistake according to beam! Do not find Reference source., can with beam section S ⁽¹¹⁾(0 ₊) and The following relational expression of two state vectors that are associated

$T_{12}^{\left(\mathrm{xy}\right)}\left(\mathrm{\π}\right)T_{\mathrm{Rf}}{T}_{\mathrm{Pb}}{T}^{\left(b_{11}\right)}{T}_{\mathrm{Pb}}{\widetilde{\mathrm{\ψ}}}^{\left(P_{11}\right)}\left(\mathrm{\κ}\right)-e^{-\mathrm{i\κL}}{\widetilde{\mathrm{\ψ}}}^{\left(P_{14}\right)}\left(\mathrm{\κ}\right)=0---\left(16\right)$

Copy and set up the formula mistake! Do not find Reference source.Method, can set up all the other 6 additional equations of three campsheds.In single (Fig. 1) and double coupling type Vibration Isolation by Piles in Rows structure (Fig. 2), disposal route and above-mentioned three Volleyball Association's eliminant Vibration Isolation by Piles in Rows structures of binding-beam are similar, and the additional equation of beam also can copy said method to set up, and repeats no more here.

Boundary element model in the native wavenumber domain of utilization stake and the top additional equation about beam of setting up get final product the dynamic response under the effect of carrying outside of period of supervision coupling type campshed.The computation model of the above-mentioned periodicity campshed that proposes, due to being grouped in wavenumber domain, the campshedization in spatial domain calculates, therefore, the campshed in spatial domain can be converted into the pile in wavenumber domain, thereby reduce widely computing time and required calculator memory.

Embodiment 2

Be example below by double coupling type Vibration Isolation by Piles in Rows structure, illustrate with respect to identical free style Vibration Isolation by Piles in Rows structure, the improvement situation of coupling type Vibration Isolation by Piles in Rows effect.

If the double-row pile array pitch is d _r=1.5m, in campshed, the centre distance of adjacent studs is L=2.0m, two campsheds move towards mutually to stagger 1.0m along campshed; Pile foundation adopts the Circular Section Concrete Element stake, and length is L _p=10m, diameter are d=1.0m, modulus of shearing μ _p=1.0 * 10 ¹⁰Pa, density p _p=2.4 * 10 ³Kg/m ³, Poisson ratio ν _p=0.2; The modulus of shearing of Soil In Half Space is μ _s=1.0 * 10 ⁷Pa, density is ρ _s=2.0 * 10 ³Kg/m ³, Poisson ratio ν _s=0.35; Stake top binding-beam adopts the square-section beams of concrete, and deck-siding is w _b=0.8m, deck-molding is w _b=0.5m, the modulus of shearing of beam is μ _b=5.0 * 10 ¹⁰Pa, density p _b=2.4 * 10 ³Kg/m ³, Poisson ratio ν _b=0.25.Vibration source adopts plane Rayleigh waves, and its frequency is 10Hz, wavelength X _R=6.61m, incident direction and x axle (Fig. 2) at 45 °.In calculating, the Floquet direct transform is got 69, and pile body is divided into 8 sections, and half-space surface is discrete along the y direction of principal axis is 20 layers of boundary element.Coupling type and free style campshed are at zone-0.303≤x/ λ _R≤ 0 and-2.0≤y/ λ _RMaximal value, minimum value and the mean value of≤-0.227 interior amplitude ratio see Table 1, and the isogram of amplitude ratio is seen Fig. 5 and Fig. 6.

Table 1 coupling type and free style Vibration Isolation by Piles in Rows structure amplitude are frequently

The amplitude ratio	Maximal value	Minimum value	Mean value
				The coupling type campshed	0.614	0.309	0.570
The free style campshed	0.732	0.379	0.679

Result in table 1 shows, the average amplitude of double coupling type Vibration Isolation by Piles in Rows structure with respect to identical free style Vibration Isolation by Piles in Rows Structure Decreasing 16.1%, therefore, coupling type Vibration Isolation by Piles in Rows structure proposed by the invention, can effectively reduce the vibration isolation coefficient, improve the vibration isolating effect of campshed.

Claims (5)

1. coupling type Vibration Isolation by Piles in Rows structure, is characterized in that, move towards direction at campshed and have periodically piling structure, and each stake pushed up by the mutual rigid connection of binding-beam.

2. coupling type Vibration Isolation by Piles in Rows structure according to claim 1, is characterized in that, described stake can be various types of stakes such as prefabricated or cast-in-situ bored pile, and binding-beam is cast-in-place reinforced beam.

3. coupling type Vibration Isolation by Piles in Rows structure according to claim 1, it is characterized in that: in each periodicity campshed, each keeps fixed range, each campshed keeps the relative changing of the relative positions of certain distance each other along campshed trend, and the campshed top is by binding-beam fixed connection periodically.

4. coupling type Vibration Isolation by Piles in Rows structure according to claim 1 is characterized in that: the arbitrary section concrete-pile of each in same campshed for having identical geometry and material parameter, and the stake that belongs to different rows can have different geometry and material parameter; Mutually on the same group binding-beam has identical geometry and material parameter, and on the same group binding-beam can not have different relevant parameters.

5. coupling type Vibration Isolation by Piles in Rows structure according to claim 1, its computation model relates to following steps:

Step 1: use Floquet conversion and Element BEM, set up respectively stake, native boundary integral equation expression formula in wavenumber domain;

Step 2: utilize Element BEM respectively stake, native boundary integral equation in wavenumber domain to be carried out discrete, and the boundary element of stake, the representative cellular of soil institute is carried out integration, obtain in wavenumber domain, native boundary element row formula;

Step 3: utilize the condition of continuity of stake in wavenumber domain, native boundary element row formula and the native displacement of stake and face power, the native periodic boundary meta-model of stake that obtains being coupled;

Step 4: use Transfer Matrix Method, the top binding-beam is processed, and utilize stake top and beam-ends coupling condition and periodicity condition, set up the computation model of coupling type Vibration Isolation by Piles in Rows structure.

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