CN106049953A - Seismic vibration response control method for double-tower connected structure - Google Patents

Abstract

The invention relates to a seismic vibration response control method for a double-tower connected structure. The seismic vibration response control method for the double-tower connected structure comprises the following steps that a calculation model of the double-tower connected structure is established; a basic vibration control equation of dampers arranged between a first tower and a corridor as well as between a second tower and the corridor is determined according to the calculation model; the average relative vibration energy of the first tower and the second tower is determined through the basic vibration control equation and an average relative vibration energy formula; and target control is conducted on the average relative vibration energy of the first tower and the second tower, and an analytical solution of zero-frequency damping ratios chi of the dampers is determined. According to the control method, the double-tower connected structure is simplified into a three-single-degree-of-freedom model, the optimal parameter expression for damper arrangement between the towers when the double-tower connected structure is under the earthquake or wind load effect is derived, and the purpose of control over the vibration of the double-tower connected structure is achieved.

Description

A kind of control method of connected double_towers structure seismic response

Technical field

The present invention relates to engineering structure technical field, particularly to the controlling party of a kind of connected double_towers structure seismic response Method.

Background technology

High-rise conjoined structure is favored by architect, simultaneously because of the contact between the moulding of its uniqueness and convenient high building Also bring challenges for structural engineer: the energy-dissipating and shock-absorbing design of conjoined structure increasingly comes into one's own.Currently, with respect to utilizing disjunctor The analysis that part carries out double tower or multi-tower structure energy-dissipating and shock-absorbing is less, and major part research concentrates on the adjacent structure of non-disjunctor.Even The earthquake response of body structure and effectiveness in vibration suppression depend on the parameter of attachment means and arrange, and the optimization of Connecting quantity and high building frequency The phase closely such as rate ratio, high building mass ratio, vestibule and the when vestibule position of the damped coefficient of Connecting quantity between high building mass ratio, vestibule Close, at present, less in the research of this aspect, it is impossible to realize the vibration control of turret structure.

Summary of the invention

The invention provides the control method of a kind of connected double_towers structure seismic response, solve or part solves existing There is the control method in technology cannot realize the technical problem of connected double_towers structure vibration control, by by connected double_towers structure letter Turn to three one degree of freedom modelings, derive connected double_towers structure under earthquake or wind action, between turret structure, arrange damping The optimized parameter expression formula of device, it is achieved that the technique effect of connected double_towers structure vibration control purpose.

The control method of a kind of connected double_towers structure seismic response that the present invention provides, described connected double_towers structure bag Including: the first high building, the second high building and vestibule, described vestibule connects described first high building and described second high building, described controlling party Method comprises the following steps:

Set up the computation model of described connected double_towers structure；

Determine described first high building according to described computation model, between described second high building and described vestibule, be provided with damping The fundamental vibration governing equation of device；

Described first high building and described is determined by described fundamental vibration governing equation and average relative vibrational energy formula The average relative vibrational energy of the second high building；

The average relative vibrational energy of described first high building and described second high building is carried out target control, determines described resistance The analytic solutions of zero-frequency damping ratio χ of Buddhist nun's device.

As preferably, when setting up the computation model of described connected double_towers structure, described connected double_towers structure is reduced to by Three single-degree-of-freedom systems that spring is connected with described antivibrator.

As preferably, described determine described first high building, described second high building and described vestibule according to described computation model Between be provided with the fundamental vibration governing equation of antivibrator, including:

The power output of described antivibrator is substituted into the equation of motion of described connected double_towers structure, determines described fundamental vibration control First expression formula of equation processed；

By setting up dummy excitation, described first expression formula is converted to the second expression formula；

By setup parameter value, described second expression formula is converted to the 3rd expression formula；

By setting constraints, described 3rd expression formula is converted to described fundamental vibration governing equation.

As preferably, the first expression formula of described fundamental vibration governing equation is:

$m_1{\stackrel{\·\·}{x}}_1+c_1{\stackrel{\·}{x}}_1+k_1{x}_1-f_{\mathrm{\Γ}1}=-m_1{\stackrel{\·\·}{x}}_g;$

$m_2{\stackrel{\·\·}{x}}_2+c_2{\stackrel{\·}{x}}_2+k_2{x}_2-f_{\mathrm{\Γ}2}=-m_2{\stackrel{\·\·}{x}}_g;$

$m_3{\stackrel{\·\·}{x}}_3+f_{\mathrm{\Γ}1}+f_{\mathrm{\Γ}2}=-m_3{\stackrel{\·\·}{x}}_g;$

$f_{\mathrm{\Γ}1}+{\mathrm{\λ}}_{01}\frac{{\mathrm{df}}_{\mathrm{\Γ}1}}{dt}=c_{01}({\stackrel{\·}{x}}_3-{\stackrel{\·}{x}}_1);$

$f_{\mathrm{\Γ}2}+{\mathrm{\λ}}_{02}\frac{{\mathrm{df}}_{\mathrm{\Γ}2}}{dt}=c_{02}({\stackrel{\·}{x}}_3-{\stackrel{\·}{x}}_2).$

As preferably, described dummy excitation is:

Described second expression formula is:

${\left(i\mathrm{\ω}\right)}^2{m}_1{x}_1+\left(i\mathrm{\ω}\right)c_1{x}_1+k_1{x}_1-f_{\mathrm{\Γ}1}=-m_1{\stackrel{\·\·}{x}}_g;$

${\left(i\mathrm{\ω}\right)}^2{m}_2{x}_2+\left(i\mathrm{\ω}\right)c_2{x}_2+k_2{x}_2-f_{\mathrm{\Γ}2}=-m_2{\stackrel{\·\·}{x}}_g;$

${\left(i\mathrm{\ω}\right)}^2{m}_3{x}_3+f_{\mathrm{\Γ}1}+f_{\mathrm{\Γ}2}=-m_3{\stackrel{\·\·}{x}}_g;$

f_Γ1+(iω)λ₀₁f_Γ1=(i ω) c₀₁(x₃-x₁)；

f_Γ2+(iω)λ₀₂f_Γ2=(i ω) c₀₂(x₃-x₂)；

ByAnd f_Γ1+(iω)λ₀₁f_Γ1=(i ω) c₀₁(x₃-x₁) can obtain

ByAnd f_Γ2+(iω)λ₀₂f_Γ2=(i ω) c₀₂(x₃-x₂) can ?

Byf_Γ1+(iω)λ₀₁f_Γ1=(i ω) c₀₁(x₃-x₁) and f_Γ2+(iω)λ₀₂f_Γ2=(i ω) c₀₂(x₃-x₂) can obtain

$\[{\left(i\mathrm{\ω}\right)}^2{m}_2+\left(i\mathrm{\ω}\right)c_2+k_2+\frac{\left(i\mathrm{\ω}\right)c_{02}}{1+\left(i\mathrm{\ω}\right){\mathrm{\λ}}_{02}}\]x_2-\frac{\left(i\mathrm{\ω}\right)c_{02}}{1+\left(i\mathrm{\ω}\right){\mathrm{\λ}}_{02}}{x}_3=-m_2{\stackrel{\·\·}{x}}_g.$

As preferably, described setup parameter value includes:

Set the mass ratio of described first high building and described second high building as μ=m₁/m₂；

Set the mass ratio of described vestibule and described first high building as μ₀₁=m₃/m₁；

Set the frequency ratio of described first high building and described second high building as β=ω₂/ω₁；

The mass ratio of the damped coefficient and described first high building and described second high building that set described antivibrator is respectively Δ₀₁ =c₀₁/m₁、Δ₀₂=c₀₂/m₁, wherein,ξ₁=c₁/2m₁ω₁,ξ₂=c₂/2m₂ω₂；

Described 3rd expression formula is:

$\[{\left(i\mathrm{\ω}\right)}^2+\left(i\mathrm{\ω}\right)2{\mathrm{\ξ}}_1{\mathrm{\ω}}_1+{\mathrm{\ω}}_1^2+\frac{\left(i\mathrm{\ω}\right){\mathrm{\Δ}}_{01}}{1+\left(i\mathrm{\ω}\right){\mathrm{\λ}}_{01}}\]x_1-\frac{\left(i\mathrm{\ω}\right){\mathrm{\Δ}}_{01}}{1+\left(i\mathrm{\ω}\right){\mathrm{\λ}}_{01}}{x}_3=-{\stackrel{\·\·}{x}}_g;$

$\[{\left(i\mathrm{\ω}\right)}^2+\left(i\mathrm{\ω}\right)2{\mathrm{\ξ}}_2{\mathrm{\ω}}_2+{\mathrm{\ω}}_2^2+\frac{\left(i\mathrm{\ω}\right){\mathrm{\μ\Δ}}_{02}}{1+\left(i\mathrm{\ω}\right){\mathrm{\λ}}_{02}}\]x_2-\frac{\left(i\mathrm{\ω}\right){\mathrm{\μ\Δ}}_{02}}{1+\left(i\mathrm{\ω}\right){\mathrm{\λ}}_{02}}{x}_3=-{\stackrel{\·\·}{x}}_g;$

$\[{\left(i\mathrm{\ω}\right)}^2+\frac{\left(i\mathrm{\ω}\right){\mathrm{\μ}}_{01}{\mathrm{\Δ}}_{01}}{1+\left(i\mathrm{\ω}\right){\mathrm{\λ}}_{01}}+\frac{\left(i\mathrm{\ω}\right){\mathrm{\μ}}_{01}{\mathrm{\Δ}}_{02}}{1+\left(i\mathrm{\ω}\right){\mathrm{\λ}}_{02}}\]x_3-\frac{\left(i\mathrm{\ω}\right){\mathrm{\μ}}_{01}{\mathrm{\Δ}}_{02}}{1+\left(i\mathrm{\ω}\right){\mathrm{\λ}}_{02}}{x}_2-\frac{\left(i\mathrm{\ω}\right){\mathrm{\μ}}_{01}{\mathrm{\Δ}}_{01}}{1+\left(i\mathrm{\ω}\right){\mathrm{\λ}}_{01}}{x}_1=-{\stackrel{\·\·}{x}}_g.$

As preferably, described set constraints as: described antivibrator is velocity correlation type energy-dissipating device, sets λ₀₁= λ₀₂=0, ξ₁=ξ₂=0；

Described fundamental vibration governing equation is:

D=a₀(iω)⁵+a₁(iω)⁴+a₂(iω)³+a₃(iω)²+a₄(iω)+a₅；

Wherein, a₀=1；a₁=Δ₀₁+μΔ₀₂+Δ₀₁μ₀₁+Δ₀₂μ₀₁；

$a_2={\mathrm{\ω}}_1^2+{\mathrm{\ω}}_2^2+{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}\mathrm{\μ}+{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}+{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ\μ}}_{01};$

$a_3={\mathrm{\Δ}}_{01}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_1^2+{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_1^2+{\mathrm{\Δ}}_{02}{\mathrm{\μ\ω}}_1^2+{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^2+{\mathrm{\Δ}}_{01}{\mathrm{\ω}}_2^2+{\mathrm{\Δ}}_{01}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^2;$

$a_4={\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ\μ}}_{01}{\mathrm{\ω}}_1^2+{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^2+{\mathrm{\ω}}_1^2{\mathrm{\ω}}_2^2;$

$a_5={\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_1^2{\mathrm{\ω}}_2^2+{\mathrm{\Δ}}_{01}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_1^2{\mathrm{\ω}}_2^2;$

α₁=b₁₃(iω)³+b₁₂(iω)²+b₁₁(iω)+b₁₀；Wherein, b₁₃=1；b₁₂=Δ₀₂μ+Δ₀₁μ₀₁+Δ₀₂μ₀₁+ Δ₀₁；

α₂=b₂₃(iω)³+b₂₂(iω)²+b₂₁(iω)+b₂₀, wherein, b₂₃=1；b₂₂=Δ₀₁+Δ₀₂μ+Δ₀₂μ₀₁+Δ₀₁ μ₀₁；

As preferably, the relative vibration energy of described first high building is

The relative vibration energy of described second high building is

Described average relative vibrational energy formula is:

The average relative vibrational energy of described first high building is

The average relative vibrational energy of described second high building is

And,

$g_{n2}\left(i\mathrm{\ω}\right)=b_{23}^2{\left(i\mathrm{\ω}\right)}^8+2b_{21}{b}_{23}{\left(i\mathrm{\ω}\right)}^6-b_{22}^2{\left(i\mathrm{\ω}\right)}^6-2b_{20}{b}_{22}{\left(i\mathrm{\ω}\right)}^4+b_{21}^2{\left(i\mathrm{\ω}\right)}^4-b_{20}^2{\left(i\mathrm{\ω}\right)}^2;$

h_n(i ω)=D=a₀(iω)⁵+a₁(iω)⁴+a₂(iω)³+a₃(iω)²+a₄(iω)+a₅；

Then

Wherein,

$\begin{array}{c}{M}_{52}=b_0^{\′}(-a_0{a}_4{a}_5+a_1{a}_4^2+a_2^2{a}_5-a_2{a}_3{a}_4)\\ +a_0{b}_1^{\′}(-a_2{a}_5+a_3{a}_4)\\ +a_0{b}_2^{\′}(a_0{a}_5-a_1{a}_4)\\ +a_0{b}_3^{\′}(-a_0{a}_3+a_1{a}_2)\\ +\frac{a_0{b}_4^{\′}}{a_5}(-a_0{a}_1{a}_5+a_0{a}_3^2+a_1^2{a}_4-a_1{a}_2{a}_3)\end{array};$

${\mathrm{\Δ}}_5=a_0^2{a}_5^2-2a_0{a}_1{a}_4{a}_5-a_0{a}_2{a}_3{a}_5+a_0{a}_3^2{a}_4+a_1^2{a}_4^2+a_1{a}_2^2{a}_5-a_1{a}_2{a}_3{a}_4;$

$b_0=b_{13}^2=1;$

$b_1=2b_{11}{b}_{13}-b_{12}^2=-{\mathrm{\μ}}^2{\mathrm{\Δ}}_{02}^2-2{\mathrm{\μ\Δ}}_{02}^2{\mathrm{\μ}}_{01}-{\mathrm{\Δ}}_{01}^2{\mathrm{\μ}}_{01}^2-2{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}^2-{\mathrm{\Δ}}_{02}^2{\mathrm{\μ}}_{01}^2-2{\mathrm{\Δ}}_{01}^2{\mathrm{\μ}}_{01}-{\mathrm{\Δ}}_{01}^2+2{\mathrm{\ω}}_2^2;$

$\begin{array}{c}{b}_2=b_{11}^2-2b_{10}{b}_{12}={\mathrm{\μ}}^2{\mathrm{\μ}}_{01}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2+2{\mathrm{\μ}}^2{\mathrm{\μ}}_{01}{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2+2{\mathrm{\μ\μ}}_{01}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2+{\mathrm{\μ}}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2-2{\mathrm{\μ\μ}}_{01}{\mathrm{\Δ}}_{02}^2{\mathrm{\ω}}_2^2\\ +{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2{\mathrm{\μ}}_{01}^2-2{\mathrm{\μ}}_{01}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\ω}}_2^2-4{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}^2{\mathrm{\ω}}_2^2-2{\mathrm{\Δ}}_{02}^2{\mathrm{\μ}}_{01}^2{\mathrm{\ω}}_2^2-4{\mathrm{\Δ}}_{01}^2{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^2-2{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^2-2{\mathrm{\Δ}}_{01}^2{\mathrm{\ω}}_2^2+{\mathrm{\ω}}_2^4\end{array};$

$b_3=-b_{10}^2=-{\mathrm{\μ}}_{01}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\ω}}_2^4-2{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}^2{\mathrm{\ω}}_2^4-{\mathrm{\Δ}}_{02}^2{\mathrm{\μ}}_{01}^2{\mathrm{\ω}}_2^4-2{\mathrm{\Δ}}_{01}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^4-{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^4-{\mathrm{\Δ}}_{01}^2{\mathrm{\ω}}_2^4;$

b₄=0；

$b_1^{\′}=2b_{21}{b}_{13}-b_{22}^2=-{\mathrm{\μ}}^2{\mathrm{\Δ}}_{02}^2-2{\mathrm{\μ\Δ}}_{02}^2{\mathrm{\μ}}_{01}-{\mathrm{\Δ}}_{01}^2{\mathrm{\μ}}_{01}^2-2{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}^2-{\mathrm{\Δ}}_{02}^2{\mathrm{\μ}}_{01}^2-2{\mathrm{\Δ}}_{01}^2{\mathrm{\μ}}_{01}-{\mathrm{\Δ}}_{01}^2+2{\mathrm{\ω}}_2^2;$

$\begin{array}{c}{b}_2^{\′}=b_{21}^2-2b_{20}{b}_{22}={\mathrm{\μ}}^2{\mathrm{\μ}}_{01}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2+2{\mathrm{\μ}}^2{\mathrm{\μ}}_{01}{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2+2{\mathrm{\μ\μ}}_{01}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2+{\mathrm{\μ}}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2\\ +2{\mathrm{\μ\μ}}_{01}{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2-2{\mathrm{\μ\μ}}_{01}{\mathrm{\Δ}}_{02}^2{\mathrm{\ω}}_2^2+{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2{\mathrm{\μ}}_{01}^2-2{\mathrm{\μ}}_{01}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\ω}}_2^2-4{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}^2{\mathrm{\ω}}_2^2\\ -2{\mathrm{\Δ}}_{02}^2{\mathrm{\μ}}_{01}^2{\mathrm{\ω}}_2^2-4{\mathrm{\Δ}}_{01}^2{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^2-2{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^2-2{\mathrm{\Δ}}_{01}^2{\mathrm{\ω}}_2^2+{\mathrm{\ω}}_2^4\end{array};$

$b_3^{\′}=-b_{20}^2=-{\mathrm{\μ}}_{01}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\ω}}_2^4-2{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}^2{\mathrm{\ω}}_2^4-{\mathrm{\Δ}}_{\mathrm{02}}^2{\mathrm{\μ}}_{01}^2{\mathrm{\ω}}_2^4-2{\mathrm{\Δ}}_{\mathrm{01}}^2{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^4-2{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{\mathrm{01}}{\mathrm{\ω}}_2^4-{\mathrm{\Δ}}_{01}^2{\mathrm{\ω}}_2^4;$

b′₄=0.

As preferably, the average relative vibrational energy of described first high building and described second high building is carried out target control, Determine the analytic solutions of zero-frequency damping ratio χ of described antivibrator, including:

Set the damped coefficient of described antivibrator than η=Δ₀₂/Δ₀₁, the zero-frequency damping ratio χ=Δ of described antivibrator₀₁/2 ω₁=c₀₁/2m₁ω₁；

By m₁=μm₂、Δ₀₂=η Δ₀₁、ω₁=Δ₀₁/ 2 χ and ω₂=β ω₁=β Δ₀₁/ 2 χ substitute into described the The average relative vibrational energy of one high building and the average relative vibrational energy of described second high building, draw described first high building and The Mean Oscillation energy of two high buildings is structural parameters μ, μ₀₁, η, β, χ and Δ₀₁Function:

M₅₁=h₆₁(ημμ₀₁β)χ⁶+h₄₁(ημμ₀₁β)χ⁴+h₂₁(ημμ₀₁β)χ²+h₀₁(ημμ₀₁β)；

M₅₂=h₆₂(ημμ₀₁β)χ⁶+h₄₂(ημμ₀₁β)χ⁴+h₂₂(ημμ₀₁β)χ²+h₀₂(ημμ₀₁β)；

2a₀Δ₅=g₄(Δ₀₁ημμ₀₁β)χ⁴+g₂(Δ₀₁ημμ₀₁β)χ²+g₀(Δ₀₁ημμ₀₁β)；

Described target control includes: make the Mean Oscillation energy of described first high buildingMinimum；Make described second high building Mean Oscillation energyMinimum；Make described first high building and the grand mean vibrational energy of described second high buildingMinimum；

According to described target control, determine that passive coupling unit optimizes design equation；

The parsing that design equation i.e. can determine that zero-frequency damping ratio χ of described antivibrator is optimized according to described passive coupling unit Solve.

As preferably, described passive coupling unit optimizes design equation and is:

Or

k₁₀(ημμ₀₁β)χ¹⁰+k₈(ημμ₀₁β)χ⁸+k₆(ημμ₀₁β)χ⁶+k₄(ημμ₀₁β)χ⁴+k₂(ημμ₀₁β)χ²+k₀(ημμ₀₁β) =0；

Wherein, k () is μ, μ₀₁, the function of η, β；

The analytic solutions of zero-frequency damping ratio χ of described antivibrator are and the mass ratio of described first high building Yu described second high building μ, described vestibule and the mass ratio μ of described first high building₀₁, damping ratio η of described antivibrator, described first high building and described second The value relevant for frequency ratio β of high building.

One or more technical schemes provided herein, at least have the following technical effect that or advantage:

By setting up the computation model of connected double_towers structure；The first high building, the second high building and company is determined according to computation model The fundamental vibration governing equation of antivibrator it is provided with between corridor；Public by fundamental vibration governing equation and average relative vibrational energy Formula determines the average relative vibrational energy of the first high building and the second high building；To the first high building and the average relative of described second high building Vibrational energy carries out target control, determines the analytic solutions of zero-frequency damping ratio χ of antivibrator；This control method can be used for macroseism or strong Under wind effect the unification of actual complex adjacent architectural especially band vestibule two tall buildings structure, simple possible, theoretical correct Passive Design Optimization for Vibration method, the vibration control to structure has important theory significance and engineer applied is worth.This Sample, efficiently solves control method of the prior art and cannot realize the technical problem of connected double_towers structure vibration control, it is achieved The technique effect of connected double_towers structure vibration control purpose.

Accompanying drawing explanation

The computation model of antivibrator in the connected double_towers structure that Fig. 1 provides for the present invention；

The computation model of the connected double_towers structure that Fig. 2 provides for the present invention；

The top layer displacement time-history curves of the first high building in three one degree of freedom modelings that Fig. 3 provides for the present invention；

The top layer displacement time-history curves of the second high building in three one degree of freedom modelings that Fig. 4 provides for the present invention；

The vibrational energy time-history curves of the first high building in three one degree of freedom modelings that Fig. 5 provides for the present invention；

The vibrational energy time-history curves of the second high building in three one degree of freedom modelings that Fig. 6 provides for the present invention；

In three one degree of freedom modelings that Fig. 7 provides for the present invention, the vibration energy time-histories of the first high building and the second high building is bent Line；

The top layer displacement time-histories of the first high building under different vestibule positions in the Multi-freedom model that Fig. 8 provides for the present invention Curve；

The top layer displacement time-histories of the second high building under different vestibule positions in the Multi-freedom model that Fig. 9 provides for the present invention Curve；

In the Multi-freedom model that Figure 10 provides for the present invention during vibrational energy of the first high building under different vestibule positions Journey curve；

In the Multi-freedom model that Figure 11 provides for the present invention during vibrational energy of the second high building under different vestibule positions Journey curve；

The first high building under different vestibule positions and the second high building in the Multi-freedom model that Figure 12 provides for the present invention Vibration energy time-history curves；

The first high building top layer displacement time-histories under different slack times in the Multi-freedom model that Figure 13 provides for the present invention Curve；

The second high building top layer displacement time-histories under different slack times in the Multi-freedom model that Figure 14 provides for the present invention Curve.

Detailed description of the invention

The embodiment of the present application provides the control method of a kind of connected double_towers structure seismic response, solves or part solves Control method of the prior art of having determined cannot realize the technical problem of connected double_towers structure vibration control, by by double tower disjunctor Structure is reduced to three one degree of freedom modelings, derives connected double_towers structure and (is reduced to white noise swash at random in earthquake or wind load Encourage) effect under, arrange the optimized parameter expression formula of antivibrator between turret structure, it is achieved that connected double_towers structure vibration control purpose Technique effect.

The control method of a kind of connected double_towers structure seismic response that the present invention provides, comprises the following steps:

S1: set up the computation model of connected double_towers structure.

S2: determine the first high building according to computation model, be provided with the fundamental vibration of antivibrator between the second high building and vestibule Governing equation.

S3: determine the first high building and the second high building by fundamental vibration governing equation and average relative vibrational energy formula Average relative vibrational energy.

S4: the average relative vibrational energy of the first high building and described second high building is carried out target control, determines antivibrator The analytic solutions of zero-frequency damping ratio χ.

Further, see attached Fig. 1 and 2, when setting up the computation model of connected double_towers structure, only consider connected double_towers structure The vibration of horizontal direction and the impact of first vibration mode, see accompanying drawing 2, connected double_towers structure be reduced to by spring and antivibrator Three single-degree-of-freedom systems connected.

Further, determine the first high building according to computation model, between the second high building and vestibule, be provided with the base of antivibrator This vibration governing equation, including:

The power output of antivibrator is substituted into the equation of motion of connected double_towers structure, determines the first of fundamental vibration governing equation Expression formula.By setting up dummy excitation, the first expression formula is converted to the second expression formula；By setup parameter value, by the second table Reach formula and be converted to the 3rd expression formula；By setting constraints, the 3rd expression formula is converted to fundamental vibration governing equation.

Further, the first expression formula of fundamental vibration governing equation is:

$m_1{\stackrel{\·\·}{x}}_1+c_1{\stackrel{\·}{x}}_1+k_1{x}_1-f_{\mathrm{\Γ}1}=-m_1{\stackrel{\·\·}{x}}_g;$

$m_2{\stackrel{\·\·}{x}}_2+c_2{\stackrel{\·}{x}}_2+k_2{x}_2-f_{\mathrm{\Γ}2}=-m_2{\stackrel{\·\·}{x}}_g;$

$m_3{\stackrel{\·\·}{x}}_3+f_{\mathrm{\Γ}1}+f_{\mathrm{\Γ}2}=-m_3{\stackrel{\·\·}{x}}_g;$

$f_{\mathrm{\Γ}1}+{\mathrm{\λ}}_{01}\frac{{\mathrm{df}}_{\mathrm{\Γ}1}}{dt}=c_{01}({\stackrel{\·}{x}}_3-{\stackrel{\·}{x}}_1);$

$f_{\mathrm{\Γ}2}+{\mathrm{\λ}}_{02}\frac{{\mathrm{df}}_{\mathrm{\Γ}2}}{dt}=c_{02}({\stackrel{\·}{x}}_3-{\stackrel{\·}{x}}_2).$

Further, dummy excitation is:

Second expression formula is:

${\left(i\mathrm{\ω}\right)}^2{m}_1{x}_1+\left(i\mathrm{\ω}\right)c_1{x}_1+k_1{x}_1-f_{\mathrm{\Γ}1}=-m_1{\stackrel{\·\·}{x}}_g;$

${\left(i\mathrm{\ω}\right)}^2{m}_2{x}_2+\left(i\mathrm{\ω}\right)c_2{x}_2+k_2{x}_2-f_{\mathrm{\Γ}2}=-m_2{\stackrel{\·\·}{x}}_g;$

${\left(i\mathrm{\ω}\right)}^2{m}_3{x}_3+f_{\mathrm{\Γ}1}+f_{\mathrm{\Γ}2}=-m_3{\stackrel{\·\·}{x}}_g;$

f_Γ1+(iω)λ₀₁f_Γ1=(i ω) c₀₁(x₃-x₁)；

f_Γ2+(iω)λ₀₂f_Γ2=(i ω) c₀₂(x₃-x₂)；

ByAnd f_Γ1+(iω)λ₀₁f_Γ1=(i ω) c₀₁(x₃-x₁) can obtain

ByAnd f_Γ2+(iω)λ₀₂f_Γ2=(i ω) c₀₂(x₃-x₂) can ?

Byf_Γ1+(iω)λ₀₁f_Γ1=(i ω) c₀₁(x₃-x₁) and f_Γ2+(iω)λ₀₂f_Γ2=(i ω) c₀₂(x₃-x₂) can obtain

$\[{\left(i\mathrm{\ω}\right)}^2{m}_2+\left(i\mathrm{\ω}\right)c_2+k_2+\frac{\left(i\mathrm{\ω}\right)c_{02}}{1+\left(i\mathrm{\ω}\right){\mathrm{\λ}}_{02}}\]x_2-\frac{\left(i\mathrm{\ω}\right)c_{02}}{1+\left(i\mathrm{\ω}\right){\mathrm{\λ}}_{02}}{x}_3=-m_2{\stackrel{\·\·}{x}}_g.$

Further, setup parameter value includes:

Set the mass ratio of the first high building and described second high building as μ=m₁/m₂；Set vestibule and described first high building Mass ratio is μ₀₁=m₃/m₁；Set the frequency ratio of the first high building and described second high building as β=ω₂/ω₁；Set antivibrator The mass ratio of damped coefficient and the first high building and described second high building is respectively Δ₀₁=c₀₁/m₁、Δ₀₂=c₀₂/m₁, wherein,ξ₁=c₁/2m₁ω₁,ξ₂=c₂/2m₂ω₂。

3rd expression formula is:

$\[{\left(i\mathrm{\ω}\right)}^2+\left(i\mathrm{\ω}\right)2{\mathrm{\ξ}}_1{\mathrm{\ω}}_1+{\mathrm{\ω}}_1^2+\frac{\left(i\mathrm{\ω}\right){\mathrm{\Δ}}_{01}}{1+\left(i\mathrm{\ω}\right){\mathrm{\λ}}_{01}}\]x_1-\frac{\left(i\mathrm{\ω}\right){\mathrm{\Δ}}_{01}}{1+\left(i\mathrm{\ω}\right){\mathrm{\λ}}_{01}}{x}_3=-{\stackrel{\·\·}{x}}_g;$

$\[{\left(i\mathrm{\ω}\right)}^2+\left(i\mathrm{\ω}\right)2{\mathrm{\ξ}}_2{\mathrm{\ω}}_2+{\mathrm{\ω}}_2^2+\frac{\left(i\mathrm{\ω}\right){\mathrm{\μ\Δ}}_{02}}{1+\left(i\mathrm{\ω}\right){\mathrm{\λ}}_{02}}\]x_2-\frac{\left(i\mathrm{\ω}\right){\mathrm{\μ\Δ}}_{02}}{1+\left(i\mathrm{\ω}\right){\mathrm{\λ}}_{02}}{x}_3=-{\stackrel{\·\·}{x}}_g;$

$\[{\left(i\mathrm{\ω}\right)}^2+\frac{\left(i\mathrm{\ω}\right){\mathrm{\μ}}_{01}{\mathrm{\Δ}}_{01}}{1+\left(i\mathrm{\ω}\right){\mathrm{\λ}}_{01}}+\frac{\left(i\mathrm{\ω}\right){\mathrm{\μ}}_{01}{\mathrm{\Δ}}_{02}}{1+\left(i\mathrm{\ω}\right){\mathrm{\λ}}_{02}}\]x_3-\frac{\left(i\mathrm{\ω}\right){\mathrm{\μ}}_{01}{\mathrm{\Δ}}_{02}}{1+\left(i\mathrm{\ω}\right){\mathrm{\λ}}_{02}}{x}_2-\frac{\left(i\mathrm{\ω}\right){\mathrm{\μ}}_{01}{\mathrm{\Δ}}_{01}}{1+\left(i\mathrm{\ω}\right){\mathrm{\λ}}_{01}}{x}_1=-{\stackrel{\·\·}{x}}_g.$

Further, set constraints as: antivibrator is velocity correlation type energy-dissipating device, set λ₀₁=λ₀₂=0, ξ₁= ξ₂=0.

Fundamental vibration governing equation is:

D=a₀(iω)⁵+a₁(iω)⁴+a₂(iω)³+a₃(iω)²+a₄(iω)+a₅；

Wherein, a₀=1；a₁=Δ₀₁+μΔ₀₂+Δ₀₁μ₀₁+Δ₀₂μ₀₁；

$a_2={\mathrm{\ω}}_1^2+{\mathrm{\ω}}_2^2+{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}\mathrm{\μ}+{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}+{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ\μ}}_{01};$

$a_3={\mathrm{\Δ}}_{01}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_1^2+{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_1^2+{\mathrm{\Δ}}_{02}{\mathrm{\μ\ω}}_1^2+{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^2+{\mathrm{\Δ}}_{01}{\mathrm{\ω}}_2^2+{\mathrm{\Δ}}_{01}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^2;$

$a_4={\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ\μ}}_{01}{\mathrm{\ω}}_1^2+{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^2+{\mathrm{\ω}}_1^2{\mathrm{\ω}}_2^2;$

$a_5={\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_1^2{\mathrm{\ω}}_2^2+{\mathrm{\Δ}}_{01}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_1^2{\mathrm{\ω}}_2^2;$

α₁=b₁₃(iω)³+b₁₂(iω)²+b₁₁(iω)+b₁₀；Wherein, b₁₃=1；b₁₂=Δ₀₂μ+Δ₀₁μ₀₁+Δ₀₂μ₀₁+ Δ₀₁；

α₂=b₂₃(iω)³+b₂₂(iω)²+b₂₁(iω)+b₂₀, wherein, b₂₃=1；b₂₂=Δ₀₁+Δ₀₂μ+Δ₀₂μ₀₁+Δ₀₁ μ₀₁；

Further, the relative vibration energy of the first high building is

The relative vibration energy of the second high building is

Average relative vibrational energy formula is:

The average relative vibrational energy of the first high building is

The average relative vibrational energy of the second high building is

And,

$g_{n2}\left(i\mathrm{\ω}\right)=b_{23}^2{\left(i\mathrm{\ω}\right)}^8+2b_{21}{b}_{23}{\left(i\mathrm{\ω}\right)}^6-b_{22}^2{\left(i\mathrm{\ω}\right)}^6-2b_{20}{b}_{22}{\left(i\mathrm{\ω}\right)}^4+b_{21}^2{\left(i\mathrm{\ω}\right)}^4-b_{20}^2{\left(i\mathrm{\ω}\right)}^2;$

h_n(i ω)=D=a₀(iω)⁵+a₁(iω)⁴+a₂(iω)³+a₃(iω)²+a₄(iω)+a₅；

Then

Wherein,

$\begin{array}{c}{M}_{52}=b_0^{\′}(-a_0{a}_4{a}_5+a_1{a}_4^2+a_2^2{a}_5-a_2{a}_3{a}_4)\\ +a_0{b}_1^{\′}(-a_2{a}_5+a_3{a}_4)\\ +a_0{b}_2^{\′}(a_0{a}_5-a_1{a}_4)\\ +a_0{b}_3^{\′}(-a_0{a}_3+a_1{a}_2)\\ +\frac{a_0{b}_4^{\′}}{a_5}(-a_0{a}_1{a}_5+a_0{a}_3^2+a_1^2{a}_4-a_1{a}_2{a}_3)\end{array};$

${\mathrm{\Δ}}_5=a_0^2{a}_5^2-2a_0{a}_1{a}_4{a}_5-a_0{a}_2{a}_3{a}_5+a_0{a}_3^2{a}_4+a_1^2{a}_4^2+a_1{a}_2^2{a}_5-a_1{a}_2{a}_3{a}_4;$

$b_0=b_{13}^2=1;$

$\begin{array}{c}{b}_1=2b_{11}{b}_{13}-b_{12}^2=-{\mathrm{\μ}}^2{\mathrm{\Δ}}_{02}^2-2{\mathrm{\μ\Δ}}_{02}^2{\mathrm{\μ}}_{01}-{\mathrm{\Δ}}_{01}^2{\mathrm{\μ}}_{01}^2-2{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}^2-{\mathrm{\Δ}}_{02}^2{\mathrm{\μ}}_{01}^2-2{\mathrm{\Δ}}_{01}^2{\mathrm{\μ}}_{01}-{\mathrm{\Δ}}_{01}^2+2{\mathrm{\ω}}_2^2;\\ \begin{array}{c}{b}_2=b_{11}^2-2b_{10}{b}_{12}={\mathrm{\μ}}^2{\mathrm{\μ}}_{01}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2+2{\mathrm{\μ}}^2{\mathrm{\μ}}_{01}{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2+2{\mathrm{\μ\μ}}_{01}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2+{\mathrm{\μ}}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2-2{\mathrm{\μ\μ}}_{01}{\mathrm{\Δ}}_{02}^2{\mathrm{\ω}}_2^2\\ +{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2{\mathrm{\μ}}_{01}^2-2{\mathrm{\μ}}_{01}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\ω}}_2^2-4{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}^2{\mathrm{\ω}}_2^2-2{\mathrm{\Δ}}_{02}^2{\mathrm{\μ}}_{01}^2{\mathrm{\ω}}_2^2-4{\mathrm{\Δ}}_{01}^2{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^2-2{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^2-2{\mathrm{\Δ}}_{01}^2{\mathrm{\ω}}_2^2+{\mathrm{\ω}}_2^4\end{array};\end{array}$

$b_3=-b_{10}^2=-{\mathrm{\μ}}_{01}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\ω}}_2^4-2{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}^2{\mathrm{\ω}}_2^4-{\mathrm{\Δ}}_{02}^2{\mathrm{\μ}}_{01}^2{\mathrm{\ω}}_2^4-2{\mathrm{\Δ}}_{01}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^4-{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^4-{\mathrm{\Δ}}_{01}^2{\mathrm{\ω}}_2^4;$

b₄=0；

$b_1^{\′}=2b_{21}{b}_{13}-b_{22}^2=-{\mathrm{\μ}}^2{\mathrm{\Δ}}_{02}^2-2{\mathrm{\μ\Δ}}_{02}^2{\mathrm{\μ}}_{01}-{\mathrm{\Δ}}_{01}^2{\mathrm{\μ}}_{01}^2-2{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}^2-{\mathrm{\Δ}}_{02}^2{\mathrm{\μ}}_{01}^2-2{\mathrm{\Δ}}_{01}^2{\mathrm{\μ}}_{01}-{\mathrm{\Δ}}_{01}^2+2{\mathrm{\ω}}_2^2;$

$\begin{array}{c}{b}_2^{\′}=b_{21}^2-2b_{20}{b}_{22}={\mathrm{\μ}}^2{\mathrm{\μ}}_{01}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2+2{\mathrm{\μ}}^2{\mathrm{\μ}}_{01}{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2+2{\mathrm{\μ\μ}}_{01}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2+{\mathrm{\μ}}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2\\ +2{\mathrm{\μ\μ}}_{01}{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2-2{\mathrm{\μ\μ}}_{01}{\mathrm{\Δ}}_{02}^2{\mathrm{\ω}}_2^2+{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2{\mathrm{\μ}}_{01}^2-2{\mathrm{\μ}}_{01}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\ω}}_2^2-4{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}^2{\mathrm{\ω}}_2^2\\ -2{\mathrm{\Δ}}_{02}^2{\mathrm{\μ}}_{01}^2{\mathrm{\ω}}_2^2-4{\mathrm{\Δ}}_{01}^2{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^2-2{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^2-2{\mathrm{\Δ}}_{01}^2{\mathrm{\ω}}_2^2+{\mathrm{\ω}}_2^4\end{array};$

$b_3^{\′}=-b_{20}^2=-{\mathrm{\μ}}_{01}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\ω}}_2^4-2{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}^2{\mathrm{\ω}}_2^4-{\mathrm{\Δ}}_{\mathrm{02}}^2{\mathrm{\μ}}_{01}^2{\mathrm{\ω}}_2^4-2{\mathrm{\Δ}}_{\mathrm{01}}^2{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^4-2{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{\mathrm{01}}{\mathrm{\ω}}_2^4-{\mathrm{\Δ}}_{01}^2{\mathrm{\ω}}_2^4;$

b′₄=0.

Further, the average relative vibrational energy of the first high building and the second high building is carried out target control, determines damping The analytic solutions of zero-frequency damping ratio χ of device, including:

Set the damped coefficient of antivibrator than η=Δ₀₂/Δ₀₁, the zero-frequency damping ratio χ=Δ of antivibrator₀₁/2ω₁=c₀₁/ 2m₁ω₁；By m₁=μm₂、Δ₀₂=η Δ₀₁、ω₁=Δ₀₁/ 2 χ and ω₂=β ω₁=β Δ₀₁/ 2 χ substitute into the first high building Average relative vibrational energy and the average relative vibrational energy of the second high building, draw averagely shaking of the first high building and the second high building Energy is structural parameters μ, μ₀₁, η, β, χ and Δ₀₁Function:

M₅₁=h₆₁(ημμ₀₁β)χ⁶+h₄₁(ημμ₀₁β)χ⁴+h₂₁(ημμ₀₁β)χ²+h₀₁(ημμ₀₁β)；

M₅₂=h₆₂(ημμ₀₁β)χ⁶+h₄₂(ημμ₀₁β)χ⁴+h₂₂(ημμ₀₁β)χ²+h₀₂(ημμ₀₁β)；

2a₀Δ₅=g₄(Δ₀₁ημμ₀₁β)χ⁴+g₂(Δ₀₁ημμ₀₁β)χ²+g₀(Δ₀₁ημμ₀₁β)；

Target control includes: make the Mean Oscillation energy of the first high buildingMinimum；Make the Mean Oscillation energy of the second high buildingMinimum；Make the grand mean vibrational energy of the first high building and the second high buildingMinimum.

According to target control, determine that passive coupling unit optimizes design equation.

The analytic solutions that design equation i.e. can determine that zero-frequency damping ratio χ of antivibrator are optimized according to passive coupling unit.

Further, passive coupling unit optimization design equation is:

Or

k₁₀(ημμ₀₁β)χ¹⁰+k₈(ημμ₀₁β)χ⁸+k₆(ημμ₀₁β)χ⁶+k₄(ημμ₀₁β)χ⁴+k₂(ημμ₀₁β)χ²+k₀(ημμ₀₁β) =0；

Wherein, k () is μ, μ₀₁, the function of η, β.The analytic solutions of zero-frequency damping ratio χ of antivibrator be with the first high building with The mass ratio μ of the mass ratio μ of the second high building, vestibule and the first high building₀₁, damping ratio η of antivibrator, the first high building and the second high building Value relevant for frequency ratio β.

The effectiveness of control method that the application provides is verified below by specific embodiment:

Certain double tower band vestibule steel structure system, the number of plies of the first high building and the second high building is 10 layers, and floor height is 3.3m； First high building each floor lumped mass is 1.6 × 10⁶Kg, shearing rigidity average is 5.4 × 10⁹N/m；Second high building each floor collection Middle quality is identical with the first high building, and shearing rigidity average is 1.5 × 10⁹N/m；Vestibule quality is 1.6 × 10⁷kg.First high building with Second high building the first rank natural frequency of vibration is respectively 8.683 and 4.576rad/s, and the first high building and the second high building gross mass are 1.6 ×10⁷kg.Maxwell model it is connected, it is assumed that the zero frequency of Maxwell model between vestibule and the first high building between vestibule with high building Damped coefficient is c₀₁, slack time is λ₀₁；Between vestibule and the second high building, the zero frequency damped coefficient of Maxwell model is c₀₂, Slack time is λ₀₂；And assume η=c₀₁/c₀₂=Δ₀₁/Δ₀₂.Use Rayleigh damping model, the first high building and the second high building First and second rank damping ratio all takes 0.02.

3-SDOF result of calculation

Connected double_towers structure is equivalent to 3-SDOF model (three one degree of freedom modelings), uses MATLAB programming, to 3- SDOF model carries out time-history analysis, and earthquake motion excitation uses Kobe ripple, and acceleration amplitude modulation is 0.2g, only considers horizontal direction earthquake Dynamic excitation.Control target for making two turret structure vibration energy minimum, then can try to achieve the first high building by above-mentioned theory analysis It is respectively 1.39 × 10 with the zero frequency damped coefficient of the second high building⁸N s/m and 6.95 × 10⁷N s/m, during programming even Two ends, corridor take λ slack time₀₁=λ₀₂=0.00001 (about 0).(wherein μ=1.0, μ₀₁=1.0, β=0.527, ξ₁=ξ₂= 0.02.It is computed η=0.5, χ=0.5)

Seeing accompanying drawing 5,6 and 7, the first high building, the second high building are at band vestibule and arrange Maxwell antivibrator and without vestibule And top layer displacement time-history curves when being not connected to antivibrator.And give difference (λ slack time₀₁=λ₀₂=0.00001, λ₀₁= λ₀₂=0.001, λ₀₁=λ₀₂=0.01) the displacement time-histories under, to observe the slack time of the impact on two turret structures.

By accompanying drawing 3 and 4 it can be seen that the Maxwell zero frequency damping calculated by theoretical expression is equal to two high buildings There is fabulous control effect, demonstrate the effectiveness of theoretical expression.And can be seen that the time-history curves under different slack time Almost without any difference, it was demonstrated that to be reduced to the reasonability of the analytical expression derivation of 0 slack time.

Seeing accompanying drawing 5,6 and 7, the first high building, the second high building are at band vestibule and arrange Maxwell antivibrator and without vestibule And the time-history curves of high building vibrational energy when being not connected to antivibrator and vibration energy (controls target for making two high building global vibrations Energy is minimum), also give the vibrational energy curve under different slack time simultaneously.

See accompanying drawing 5,6 and 7, the carried analytical expression of the application the Maxwell antivibrator parameters optimization calculated is to two The control effect of turret structure vibrational energy is all preferable, and can be seen that the high building vibrational energy curve under different slack time Almost without any difference, again demonstrate the reasonability of the analytical expression derivation assuming that slack time is 0 herein.

MDOF result of calculation

In order to verify that the analytic solutions of the Maxwell antivibrator parameters optimization with 3-SDOF gained are equally applicable to MDOF model (Multi-freedom model), is reduced to connected double_towers structure multiple degrees of freedom shear model, and takes high building two ends Maxwell damping The damping optimization coefficient of device is respectively 1.39 × 10⁸N s/m and 6.95 × 10⁷N s/m (with 3-SDOF model), when taking lax Between be 0.00001 (being approximately 0).Using MATLAB programming, MDOF model carries out time-history analysis, earthquake motion excitation is same to be used Kobe ripple, acceleration amplitude modulation is 0.2g, only considers horizontal direction earthquake motion excitation.Control target for making two turret structure global vibrations Energy is minimum.

Vestibule position in high building, emerges from the programming process of MDOF model, and accompanying drawing 8 and 9 gives Two turret structures are without vestibule and antivibrator and band vestibule and antivibrator and make vestibule be arranged in the top layer position of various location Move time-history curves.Wherein icon " 1,3,5,7,9 " represent vestibule be arranged in the 1st of two turret structures the, the 3rd, the 5th, the 7th and 9th layer.

Seeing accompanying drawing 8 and 9, (vestibule and Maxwell damper arrangement are same to Maxwell antivibrator for vestibule position One layer) control effect have considerable influence, when vestibule is arranged in the 5th layer, i.e. the intermediate layer of turret structure, the position of two turret structures Move response minimum.Therefore, the analytic solutions of the Maxwell antivibrator parameters optimization obtained with 3-SDOF model are equally applicable to MDOF Model, it was demonstrated that the effectiveness of carried control strategy herein.Can also be found out by Fig. 8 and 9, vestibule is not suitable for being arranged in two high buildings The bottom of structure or top layer.

Seeing accompanying drawing 10,11 and 12, two turret structures are without vestibule and antivibrator and band vestibule and antivibrator the company of making Corridor is arranged in the high building vibrational energy time-history curves of various location.Wherein icon " 1,3,5,7,9 " represents that vestibule is respectively arranged At two turret structures the 1st, the 3rd, the 5th, the 7th and the 9th layer.Vestibule position is the biggest on the impact of high building vibrational energy, If especially vestibule and damper arrangement are even larger than high building not at the vibrational energy of bottom (the 1st layer) high building of turret structure The situation of control；When vestibule is arranged in high building top layer (such as the 7th, the 9th layer), the vibrational energy of high building is the biggest；Vestibule optimal Position is the intermediate layer (the 5th layer) of high building, and under this position, the vibrational energy of high building is the most minimum.As can be seen here, even The intermediate layer that optimal placement position is turret structure of corridor.

See attached Figure 13 and 14 high building top layer when being the intermediate layer that vestibule is arranged in turret structure, under different slack times Displacement time-history curves.When vestibule is arranged in high building intermediate layer, Maxwell antivibrator all has preferably control to two high building displacements Effect；Time-history curves under different slack times is almost without any difference, it was demonstrated that slack time is reduced to the resolution table of 0 Reach the formula effective suitability in MDOF model.

One or more technical schemes provided herein, at least have the following technical effect that or advantage:

By setting up the computation model of connected double_towers structure；The first high building, the second high building and company is determined according to computation model The fundamental vibration governing equation of antivibrator it is provided with between corridor；Public by fundamental vibration governing equation and average relative vibrational energy Formula determines the average relative vibrational energy of the first high building and the second high building；To the first high building and the average relative of described second high building Vibrational energy carries out target control, determines the analytic solutions of zero-frequency damping ratio χ of antivibrator；This control method can be used for macroseism or strong Under wind effect the unification of actual complex adjacent architectural especially band vestibule two tall buildings structure, simple possible, theoretical correct Passive Design Optimization for Vibration method, the vibration control to structure has important theory significance and engineer applied is worth.This Sample, efficiently solves control method of the prior art and cannot realize the technical problem of connected double_towers structure vibration control, it is achieved The technique effect of connected double_towers structure vibration control purpose.

Above-described detailed description of the invention, has been carried out the purpose of the present invention, technical scheme and beneficial effect further Describe in detail, be it should be understood that the detailed description of the invention that the foregoing is only the present invention, be not limited to this Bright, all within the spirit and principles in the present invention, any modification, equivalent substitution and improvement etc. done, should be included in the present invention Protection domain within.

Claims (10)

1. a control method for connected double_towers structure seismic response, described connected double_towers structure includes: the first high building, second High building and vestibule, described vestibule connects described first high building and described second high building, it is characterised in that comprise the following steps:

Set up the computation model of described connected double_towers structure；

Determine described first high building according to described computation model, between described second high building and described vestibule, be provided with antivibrator Fundamental vibration governing equation；

Described first high building and described second is determined by described fundamental vibration governing equation and average relative vibrational energy formula The average relative vibrational energy of high building；

The average relative vibrational energy of described first high building and described second high building is carried out target control, determines described antivibrator The analytic solutions of zero-frequency damping ratio χ.

2. the control method of connected double_towers structure seismic response as claimed in claim 1, it is characterised in that

When setting up the computation model of described connected double_towers structure, described connected double_towers structure is reduced to by spring and described damping Three single-degree-of-freedom systems that device connects.

3. the control method of connected double_towers structure seismic response as claimed in claim 1, it is characterised in that described according to institute State computation model to determine described first high building, between described second high building and described vestibule, be provided with the fundamental vibration control of antivibrator Equation processed, including:

The power output of described antivibrator is substituted into the equation of motion of described connected double_towers structure, determines described fundamental vibration controlling party First expression formula of journey；

By setting up dummy excitation, described first expression formula is converted to the second expression formula；

By setup parameter value, described second expression formula is converted to the 3rd expression formula；

By setting constraints, described 3rd expression formula is converted to described fundamental vibration governing equation.

4. the control method of connected double_towers structure seismic response as claimed in claim 3, it is characterised in that described substantially shake First expression formula of dynamic governing equation is:

$m_1{\stackrel{\·\·}{x}}_1+c_1{\stackrel{\·}{x}}_1+k_1{x}_1-f_{\mathrm{\Γ}1}=-m_1{\stackrel{\·\·}{x}}_g;$

$m_2{\stackrel{\·\·}{x}}_2+c_2{\stackrel{\·}{x}}_2+k_2{x}_2-f_{\mathrm{\Γ}2}=-m_2{\stackrel{\·\·}{x}}_g;$

$m_3{\stackrel{\·\·}{x}}_3+f_{\mathrm{\Γ}1}+f_{\mathrm{\Γ}2}=-m_3{\stackrel{\·\·}{x}}_g;$

$f_{\mathrm{\Γ}1}+{\mathrm{\λ}}_{01}\frac{{\mathrm{df}}_{\mathrm{\Γ}1}}{dt}=c_{01}({\stackrel{\·}{x}}_3-{\stackrel{\·}{x}}_1);$

$f_{\mathrm{\Γ}2}+{\mathrm{\λ}}_{02}\frac{{\mathrm{df}}_{\mathrm{\Γ}2}}{dt}=c_{02}({\stackrel{\·}{x}}_3-{\stackrel{\·}{x}}_2).$

5. the control method of connected double_towers structure seismic response as claimed in claim 4, it is characterised in that

Described dummy excitation is:

Described second expression formula is:

${\left(i\mathrm{\ω}\right)}^2{m}_1{x}_1+\left(i\mathrm{\ω}\right)c_1{x}_1+k_1{x}_1-f_{\mathrm{\Γ}1}=-m_1{\stackrel{\·\·}{x}}_g;$

${\left(i\mathrm{\ω}\right)}^2{m}_2{x}_2+\left(i\mathrm{\ω}\right)c_2{x}_2+k_2{x}_2-f_{\mathrm{\Γ}2}=-m_2{\stackrel{\·\·}{x}}_g;$

${\left(i\mathrm{\ω}\right)}^2{m}_3{x}_3+f_{\mathrm{\Γ}1}+f_{\mathrm{\Γ}2}=-m_3{\stackrel{\·\·}{x}}_g;$

f_Γ1+(iω)λ₀₁f_Γ1=(i ω) c₀₁(x₃-x₁)；

f_Γ2+(iω)λ₀₂f_Γ2=(i ω) c₀₂(x₃-x₂)；

ByAnd f_Γ1+(iω)λ₀₁f_Γ1=(i ω) c₀₁(x₃-x₁) can obtain

ByAnd f_Γ2+(iω)λ₀₂f_Γ2=(i ω) c₀₂(x₃-x₂) can obtain

Byf_Γ1+(iω)λ₀₁f_Γ1=(i ω) c₀₁(x₃-x₁) and f_Γ2+(iω)λ₀₂f_Γ2 =(i ω) c₀₂(x₃-x₂) can obtain

6. the control method of connected double_towers structure seismic response as claimed in claim 5, it is characterised in that

Described setup parameter value includes:

Set the mass ratio of described first high building and described second high building as μ=m₁/m₂；

Set the mass ratio of described vestibule and described first high building as μ₀₁=m₃/m₁；

Set the frequency ratio of described first high building and described second high building as β=ω₂/ω₁；

The mass ratio of the damped coefficient and described first high building and described second high building that set described antivibrator is respectively △₀₁= c₀₁/m₁、△₀₂=c₀₂/m₁, wherein,ξ₁=c₁/2m₁ω₁,ξ₂=c₂/2m₂ω₂；

Described 3rd expression formula is:

$\[{\left(i\mathrm{\ω}\right)}^2+\left(i\mathrm{\ω}\right)2{\mathrm{\ξ}}_1{\mathrm{\ω}}_1+{\mathrm{\ω}}_1^2+\frac{\left(i\mathrm{\ω}\right){\mathrm{\Δ}}_{01}}{1+\left(i\mathrm{\ω}\right){\mathrm{\λ}}_{01}}\]x_1-\frac{\left(i\mathrm{\ω}\right){\mathrm{\Δ}}_{01}}{1+\left(i\mathrm{\ω}\right){\mathrm{\λ}}_{01}}{x}_3=-{\stackrel{\·\·}{x}}_g;$

$\[{\left(i\mathrm{\ω}\right)}^2+\left(i\mathrm{\ω}\right)2{\mathrm{\ξ}}_2{\mathrm{\ω}}_2+{\mathrm{\ω}}_2^2+\frac{\left(i\mathrm{\ω}\right){\mathrm{\μ\Δ}}_{02}}{1+\left(i\mathrm{\ω}\right){\mathrm{\λ}}_{02}}\]x_2-\frac{\left(i\mathrm{\ω}\right){\mathrm{\μ\Δ}}_{02}}{1+\left(i\mathrm{\ω}\right){\mathrm{\λ}}_{02}}{x}_3=-{\stackrel{\·\·}{x}}_g;$

$\[{\left(i\mathrm{\ω}\right)}^2+\frac{\left(i\mathrm{\ω}\right){\mathrm{\μ}}_{01}{\mathrm{\Δ}}_{01}}{1+\left(i\mathrm{\ω}\right){\mathrm{\λ}}_{01}}+\frac{\left(i\mathrm{\ω}\right){\mathrm{\μ}}_{01}{\mathrm{\Δ}}_{02}}{1+\left(i\mathrm{\ω}\right){\mathrm{\λ}}_{02}}\]x_3-\frac{\left(i\mathrm{\ω}\right){\mathrm{\μ}}_{01}{\mathrm{\Δ}}_{02}}{1+\left(i\mathrm{\ω}\right){\mathrm{\λ}}_{02}}{x}_2-\frac{\left(i\mathrm{\ω}\right){\mathrm{\μ}}_{01}{\mathrm{\Δ}}_{01}}{1+\left(i\mathrm{\ω}\right){\mathrm{\λ}}_{01}}{x}_1=-{\stackrel{\·\·}{x}}_g.$

7. the control method of connected double_towers structure seismic response as claimed in claim 6, it is characterised in that

Described set constraints as: described antivibrator is velocity correlation type energy-dissipating device, set λ₀₁=λ₀₂=0, ξ₁=ξ₂= 0；

Described fundamental vibration governing equation is:

D=a₀(iω)⁵+a₁(iω)⁴+a₂(iω)³+a₃(iω)²+a₄(iω)+a₅；

Wherein, a₀=1；a₁=△₀₁+μ△₀₂+△₀₁μ₀₁+△₀₂μ₀₁；

$a_2={\mathrm{\ω}}_1^2+{\mathrm{\ω}}_2^2+{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}\mathrm{\μ}+{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}+{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ\μ}}_{01};$

$a_3={\mathrm{\Δ}}_{01}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_1^2+{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_1^2+{\mathrm{\Δ}}_{02}{\mathrm{\μ\ω}}_1^2+{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^2+{\mathrm{\Δ}}_{01}{\mathrm{\ω}}_2^2+{\mathrm{\Δ}}_{01}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^2;$

$a_4={\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ\μ}}_{01}{\mathrm{\ω}}_1^2+{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^2+{\mathrm{\ω}}_1^2{\mathrm{\ω}}_2^2;$

$a_5={\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_1^2{\mathrm{\ω}}_2^2+{\mathrm{\Δ}}_{01}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_1^2{\mathrm{\ω}}_2^2;$

α₁=b₁₃(iω)³+b₁₂(iω)²+b₁₁(iω)+b₁₀；Wherein, b₁₃=1；b₁₂=△₀₂μ+△₀₁μ₀₁+△₀₂μ₀₁+△₀₁；

α₂=b₂₃(iω)³+b₂₂(iω)²+b₂₁(iω)+b₂₀, wherein, b₂₃=1；b₂₂=△₀₁+△₀₂μ+△₀₂μ₀₁+△₀₁μ₀₁；

8. the control method of connected double_towers structure seismic response as claimed in claim 7, it is characterised in that

The relative vibration energy of described first high building is

The relative vibration energy of described second high building is

Described average relative vibrational energy formula is:

The average relative vibrational energy of described first high building is

The average relative vibrational energy of described second high building is

And,

Then

Wherein,

$\begin{array}{c}{M}_{52}=b_0^{\′}\left(-a_0{a}_4{a}_5+a_1{a}_4^2+a_2^2{a}_5-a_2{a}_3{a}_4\right)\\ +a_0{b}_1^{\′}\left(-a_2{a}_5+a_3{a}_4\right)\\ +a_0{b}_2^{\′}\left(a_0{a}_5-a_1{a}_4\right)\\ +a_0{b}_3^{\′}\left(-a_0{a}_3+a_1{a}_2\right)\\ +\frac{a_0{b}_4^{\′}}{a_5}\left(-a_0{a}_1{a}_5+a_0{a}_3^2+a_1^2{a}_4-a_1{a}_2{a}_3\right)\end{array};$

${\mathrm{\Δ}}_5=a_0^2{a}_5^2-2a_0{a}_1{a}_4{a}_5-a_0{a}_2{a}_3{a}_5+a_0{a}_3^2{a}_4+a_1^2{a}_4^2+a_1{a}_2^2{a}_5-a_1{a}_2{a}_3{a}_4;$

$b_0=b_{13}^2=1;$

$b_1=2b_{11}{b}_{13}-b_{12}^2=-{\mathrm{\μ}}^2{\mathrm{\Δ}}_{02}^2-2{\mathrm{\μ\Δ}}_{02}^2{\mathrm{\μ}}_{01}-{\mathrm{\Δ}}_{01}^2{\mathrm{\μ}}_{01}^2-2{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}^2-{\mathrm{\Δ}}_{02}^2{\mathrm{\μ}}_{01}^2-2{\mathrm{\Δ}}_{01}^2{\mathrm{\μ}}_{01}-{\mathrm{\Δ}}_{01}^2+2{\mathrm{\ω}}_2^2;$

$\begin{array}{c}{b}_2=b_{11}^2-2b_{10}{b}_{12}={\mathrm{\μ}}^2{\mathrm{\μ}}_{01}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2+2{\mathrm{\μ}}^2{\mathrm{\μ}}_{01}{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2+2{\mathrm{\μ\μ}}_{01}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2+{\mathrm{\μ}}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2+2{\mathrm{\μ\μ}}_{01}{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2-2{\mathrm{\μ\μ}}_{01}{\mathrm{\Δ}}_{02}^2{\mathrm{\ω}}_2^2\\ +{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2{\mathrm{\μ}}_{01}^2-2{\mathrm{\μ}}_{01}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\ω}}_2^2-4{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}^2{\mathrm{\ω}}_2^2-2{\mathrm{\Δ}}_{02}^2{\mathrm{\μ}}_{01}^2{\mathrm{\ω}}_2^2-4{\mathrm{\Δ}}_{01}^2{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^2-2{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^2-2{\mathrm{\Δ}}_{01}^2{\mathrm{\ω}}_2^2+{\mathrm{\ω}}_2^4\end{array};$

$b_3=-b_{10}^2=-{\mathrm{\μ}}_{01}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\ω}}_2^4-2{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}^2{\mathrm{\ω}}_2^4-{\mathrm{\Δ}}_{02}^2{\mathrm{\μ}}_{01}^2{\mathrm{\ω}}_2^4-2{\mathrm{\Δ}}_{01}^2{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^4-2{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^4-{\mathrm{\Δ}}_{01}^2{\mathrm{\ω}}_2^4;$

b₄=0； $b_0^{\′}=b_{23}^2=1;$

$b_1^{\′}=2b_{21}{b}_{13}-b_{22}^2=-{\mathrm{\μ}}^2{\mathrm{\Δ}}_{02}^2-2{\mathrm{\μ\Δ}}_{02}^2{\mathrm{\μ}}_{01}-{\mathrm{\Δ}}_{01}^2{\mathrm{\μ}}_{01}^2-2{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}^2-{\mathrm{\Δ}}_{02}^2{\mathrm{\μ}}_{01}^2-2{\mathrm{\Δ}}_{01}^2{\mathrm{\μ}}_{01}-{\mathrm{\Δ}}_{01}^2+2{\mathrm{\ω}}_2^2;$

$\begin{array}{c}{b}_2^{\′}=b_{21}^2-2b_{20}{b}_{22}={\mathrm{\μ}}^2{\mathrm{\μ}}_{01}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2+2{\mathrm{\μ}}^2{\mathrm{\μ}}_{01}{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2+2{\mathrm{\μ\μ}}_{01}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2+{\mathrm{\μ}}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2\\ +2{\mathrm{\μ\μ}}_{01}{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2-2{\mathrm{\μ\μ}}_{01}{\mathrm{\Δ}}_{02}^2{\mathrm{\ω}}_2^2+{\mathrm{\Δ}}_{01}^2{\mathrm{\Δ}}_{02}^2{\mathrm{\μ}}_{01}^2-2{\mathrm{\μ}}_{01}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\ω}}_2^2-4{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}^2{\mathrm{\ω}}_2^2\\ -2{\mathrm{\Δ}}_{02}^2{\mathrm{\μ}}_{01}^2{\mathrm{\ω}}_2^2-4{\mathrm{\Δ}}_{01}^2{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^2-2{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^2-2{\mathrm{\Δ}}_{01}^2{\mathrm{\ω}}_2^2+{\mathrm{\ω}}_2^4\end{array};$

$b_3^{\′}=-b_{20}^2=-{\mathrm{\μ}}_{01}^2{\mathrm{\Δ}}_{01}^2{\mathrm{\ω}}_2^4-2{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}^2{\mathrm{\ω}}_2^4-{\mathrm{\Δ}}_{02}^2{\mathrm{\μ}}_{01}^2{\mathrm{\ω}}_2^4-2{\mathrm{\Δ}}_{01}^2{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^4-2{\mathrm{\Δ}}_{01}{\mathrm{\Δ}}_{02}{\mathrm{\μ}}_{01}{\mathrm{\ω}}_2^4-{\mathrm{\Δ}}_{01}^2{\mathrm{\ω}}_2^4;$

b′₄=0.

9. the control method of connected double_towers structure seismic response as claimed in claim 8, it is characterised in that to described first The average relative vibrational energy of high building and described second high building carries out target control, determines zero-frequency damping ratio χ of described antivibrator Analytic solutions, including:

Set the damped coefficient of described antivibrator than η=△₀₂/△₀₁, the zero-frequency damping ratio χ=△ of described antivibrator₀₁/2ω₁= c₀₁/2m₁ω₁；

By m₁=μm₂、△₀₂=η △₀₁、ω₁=△₀₁/ 2 χ and ω₂=β ω₁=β △₀₁/ 2 χ substitute into described first tower The average relative vibrational energy in building and the average relative vibrational energy of described second high building, draw described first high building and the second tower The Mean Oscillation energy in building is structural parameters μ, μ₀₁, η, β, χ and △₀₁Function:

M₅₁=h₆₁(ημμ₀₁β)χ⁶+h₄₁(ημμ₀₁β)χ⁴+h₂₁(ημμ₀₁β)χ²+h₀₁(ημμ₀₁β)；

M₅₂=h₆₂(ημμ₀₁β)χ⁶+h₄₂(ημμ₀₁β)χ⁴+h₂₂(ημμ₀₁β)χ²+h₀₂(ημμ₀₁β)；

2a₀△₅=g₄(△₀₁ημμ₀₁β)χ⁴+g₂(△₀₁ημμ₀₁β)χ²+g₀(△₀₁ημμ₀₁β)；

Described target control includes: make the Mean Oscillation energy of described first high buildingMinimum；Make the average of described second high building Vibrational energyMinimum；Make described first high building and the grand mean vibrational energy of described second high buildingMinimum；

According to described target control, determine that passive coupling unit optimizes design equation；

The analytic solutions that design equation i.e. can determine that zero-frequency damping ratio χ of described antivibrator are optimized according to described passive coupling unit.

10. the control method of connected double_towers structure seismic response as claimed in claim 9, it is characterised in that

Described passive coupling unit optimizes design equation:

Or

k₁₀(ημμ₀₁β)χ¹⁰+k₈(ημμ₀₁β)χ⁸+k₆(ημμ₀₁β)χ⁶+k₄(ημμ₀₁β)χ⁴+k₂(ημμ₀₁β)χ²+k₀(ημμ₀₁β)=0；

Wherein, k () is μ, μ₀₁, the function of η, β；

The analytic solutions of zero-frequency damping ratio χ of described antivibrator are and described first high building and the mass ratio μ of described second high building, institute State the mass ratio μ of vestibule and described first high building₀₁, damping ratio η of described antivibrator, described first high building and described second high building Value relevant for frequency ratio β.