CN106285143A - Method for converting TTLCD-eccentric structure into TTMD-eccentric structure - Google Patents

Abstract

The invention discloses a method for converting a TTLCD-eccentric structure into a TTMD-eccentric structure, and belongs to the technical field of seismic resistance, energy consumption and vibration reduction of engineering structures. The method comprises the following steps: obtaining a motion equation of liquid in the TTLCD, and interaction force and moment of the TTLCD and the eccentric structure in the vibration process; obtaining a motion equation, control force and moment of the equivalent TTMD; establishing an eccentric structure dynamic balance equation under the action of an earthquake and a coupling equation of a TTLCD-eccentric structure system and a TTMD-eccentric structure system; and finding out the relation between the TTMD relative displacement and the liquid relative displacement in the TTLCD, and obtaining the relational expression of the mass ratio, the frequency ratio and the damping ratio between the TTLCD-eccentric structural system and the TTMD-eccentric structural system. The method of the invention can quickly and conveniently obtain optimized parameters and numerical simulation, thereby improving the vibration reduction effect of the damper on the eccentric structure.

Description

TTLCD-eccentric structure is converted into the method for TTMD-eccentric structure

Technical field

The present invention relates to engineering structure antidetonation and passive energy dissipation technical field, reverse the damping of frequency modulation fluid column particularly to one Device (Torsional Tuned Liquid Column Damper, TTLCD)-eccentric structure is converted into torsion frequency modulation mass damping The method of device (Torsional Tuned Mass Damper, TTMD)-eccentric structure.

Background technology

It is misaligned, such as central television that eccentric structure is generally building shape variation, architecture quality center and center of rigidity Platform building, center, Shanghai and Shanghai international financial center etc..Center of rigidity is produced by the inertia force acting on mass centre during earthquake Raw torsional moment, causes the heavy damage of structure generation unrepairable.In HAICHENG EARTHQUAKE in 1975, the two of rural power office office building Layer and partial threelayer are arranged asymmetric due to structure and are added the impact of torsion, and west side bottom gable seriously ftractures, and intersection is split Seam reaches 10cm.In Tangshan Earthquake in 1976, many L-shaped planes and other concave planes destroy because of torsion, wherein Tianjin The corner post many places of people printing house are destroyed.In earthquakes in Taiwan in 1999, many asymmetric brick houses and reinforced concrete frame Structure all occurs in that significantly reverses earthquake damage characteristics.In Wenchuan earthquake in 2008, the structural elements of part Tall Buildings is serious Destroy.Traditional design method employed in engineering is to be arranged by adjustment structure and increase torsional rigidity to reduce the torsion of bias Turn reaction, but in building function it has been determined that in the case of, structure arranges that to adjust leeway the least, and increases torsional rigidity and can increase The cross section of component also can increase geological process, so traditional method for designing can not solve eccentric structure well in geological process Under torsional vibration problems.

Structural vibration control technology is considered as the effective means alleviating structural earthquake and Wind Vibration Response.Subtract in building structure Shaking in research, tuned mass damper, TMD (Tuned Mass Damper, TMD) principle is simple, existing frequency ratio and damping ratio optimization Empirical equation, simultaneously dynamic response analysis also can by large-scale finite element procedure carry out numerical simulation i.e. spring with damping in parallel After be connected with quality point again.But designing and producing of this apparatus system is complex, after coming into operation, need regular maintenance.Frequency modulation Column damper (Tuned Liquid Column Damper, TLCD) is to increase knot by the liquid rocked in U/V type pipe The antivibrator of structure, the purpose reaching to reduce structural vibration with this.Be easily installed owing to TLCD has and safeguard, cost is low, can With the advantage that combines etc. with the water supply installation in building, cause the extensive concern of researcher.

It is a kind of for reversing frequency modulation column damper (Torsional Tuned Liquid Column Damper, TTLCD) The effectively suppression pure torsion of eccentric structure or the damping control device of translation-torsion coupled vibration, but the vibration damping that TTLCD is to building Effect is heavily dependent on choosing of parameter.Conventional damper method for optimally designing parameters mainly utilizes random vibration theory And modern control theory, minimum as optimization aim using agent structure displacement root-mean-square and acceleration-root-mean square, be not given Being similar to the optimal parameter design expression formula of TMD, this brings a lot of inconvenience to actual TTLCD design.TTLCD vibration damping The numerical simulation of effect mainly uses MATLAB to program, and MATLAB software exists certain difficulty to the numerical simulation of labyrinth Degree.Due to the expression formula of the existing optimal parameter design of TMD, and finite element program is used easily TTMD vibroshock to be carried out mould Intending, therefore research one is reversed frequency modulation column damper (TTLCD)-eccentric structure system and is converted into torsion tuned mass damper, TMD (TTMD)-eccentric structure system carries out the method for parameter optimization and numerical computations and has great engineering significance.

Summary of the invention

It is not suitable for TTLCD design, and the number of TTLCD effectiveness in vibration suppression to solve conventional damper parameter optimization method The problems such as value simulation difficulty is big, the invention provides the method that TTLCD-eccentric structure is converted into TTMD-eccentric structure, described side Method includes: according to fluid dynamic theory, it is thus achieved that reverse liquid motion equation in frequency modulation column damper；According to momentum and angular motion Amount conservation, it is thus achieved that reverse interaction force and moment that frequency modulation column damper occurs in vibration processes with eccentric structure；Root According to dAlembert principle, it is thus achieved that equivalence is reversed the equation of motion of tuned mass damper, TMD, controlled power and moment；Set up geological process Lower eccentric structure power balance equation, and according to certain vibration shape of single Damper Control eccentric structure, use moda1 decomposition to obtain To generalized coordinates equation, that sets up TTLCD-eccentric structure and TTMD-eccentric structure two system couples equation；In identical excitation Under, find out the relation between liquid relative displacement in TTMD relative displacement and TTLCD, it is thus achieved that TTLCD-eccentric structure system with The relational expression of mass ratio, frequency ratio and damping ratio between TTMD-eccentric structure system.

When the subpoint of tilted tube is A (y_A,z_A, 0) and during angle of inclination beta=pi/2, described torsion frequency modulation column damper Middle liquid motion equation is:

$\stackrel{\·\·}{u}+2{\mathrm{\ζ}}_A{\mathrm{\ω}}_A\stackrel{\·}{u}+{\mathrm{\ω}}_A^{2}u=-{\mathrm{\κ}}_{T0}{\stackrel{\·\·}{u}}_{TT},$

${\mathrm{\κ}}_{T0}=\frac{2A_p}{r_f{L}_{eff}},{\stackrel{\·\·}{u}}_{TT}=r_f\stackrel{\·\·}{\mathrm{\θ}},I_{fx}=m_f{r}_f^2,L_{eff}=2H+\frac{A_H}{A_B}B,{\mathrm{\ω}}_A=\sqrt{\frac{2g}{L_{eff}}}.$

Wherein, I_fxAnd r_fFor TTLCD for eccentric structure barycenter around the rotary inertia of x-axis and the radius of gyration, m_fFor TTLCD The quality of middle liquid；B is the length of the horizontal pipe fluid column of TTLCD；H is the length of the vertical pipeline fluid column of TTLCD；A_BFor The area of section of the horizontal pipe fluid column of TTLCD；A_HArea of section for the vertical pipeline fluid column of TTLCD；U is liquid in TTLCD Body is along relative displacement during vessel wall motion；Ap is the area that the horizontal component of TTLCD comprises；G is acceleration of gravity；For bias Structure barycenter is around the torsion angle acceleration of x-axis；ζ_AAnd ω_AIt is respectively damping ratio and the self-vibration circular frequency of TTLCD of TTLCD；y_AWith z_AY and z direction coordinate for vertical pipeline subpoint A.

Interaction force and moment that described torsion frequency modulation column damper occurs in vibration processes with eccentric structure is:

$F_{C_{M}y}=m_f({\stackrel{\·\·}{v}}_g+\stackrel{\·\·}{v}-{\stackrel{\‾}{\mathrm{\κ}}}_{T3}{\stackrel{\·\·}{u}}_{TT}{z}_A/r_f),F_{C_{M}z}=m_f({\stackrel{\·\·}{w}}_g+\stackrel{\·\·}{w}+{\stackrel{\‾}{\mathrm{\κ}}}_{T3}{\stackrel{\·\·}{u}}_{TT}{y}_A/r_f),{\stackrel{\‾}{\mathrm{\κ}}}_{T3}=\frac{2H}{L_1},$

$M_{C_{M}x}=m_f{r}_f({\stackrel{\·\·}{u}}_{TT}+\frac{{\stackrel{\‾}{\mathrm{\κ}}}_{T3}{y}_A}{r_f}{a}_z-\frac{{\stackrel{\‾}{\mathrm{\κ}}}_{T3}{z}_A}{r_f}{a}_y)+m_f{r}_f{\stackrel{\‾}{\mathrm{\κ}}}_{T0}\stackrel{\·\·}{u},{\stackrel{\‾}{\mathrm{\κ}}}_{T0}={\mathrm{\κ}}_{T0}{L}_{eff}/L_1,L_1=2H+\frac{A_B}{A_H}B.$

Wherein, m_fFor the quality of liquid in TTLCD；B is the length of the horizontal pipe fluid column of TTLCD；H is the perpendicular of TTLCD The length of straight pipeline fluid column；A_BArea of section for the horizontal pipe fluid column of TTLCD；A_HFor TTLCD vertical pipeline fluid column cut Face area；r_fFor TTLCD for eccentric structure barycenter around the radius of gyration of x-axis；U be in TTLCD liquid along during vessel wall motion Relative displacement；WithFor eccentric structure barycenter along the relative displacement acceleration in y and z direction；a_zAnd a_yIt is respectively vertical pipeline to throw Shadow point A is along the relative displacement acceleration in y, z direction；WithFor earthquake along the acceleration in y and z direction.

The equation of motion that tuned mass damper, TMD is reversed in described equivalence is:

${\stackrel{\·\·}{u}}^{*}+2{\mathrm{\ζ}}_A^{*}{\mathrm{\ω}}_A^{*}{\stackrel{\·}{u}}^{*}+{\mathrm{\ω}}_A^{*2}{u}^{*}=-{\stackrel{\·\·}{u}}_T^{*},{\mathrm{\ω}}_A^{*}=\sqrt{\frac{k^{*}}{{\stackrel{\‾}{I}}_{C_{M}x}^{*}}},2{\mathrm{\ζ}}_A^{*}{\mathrm{\ω}}_A^{*}=\frac{c^{*}}{{\stackrel{\‾}{I}}_{C_{M}x}^{*}},{\stackrel{\‾}{I}}_{C_{M}x}^{*}=m_A^{*}{r}_A^{*2},{\stackrel{\·\·}{u}}_T^{*}=r_A^{*}\stackrel{\·\·}{\mathrm{\θ}}.$

Control power and moment is:

$F_{C_{M}y}^{*}=-m_A^{*}({\stackrel{\·\·}{v}}_g+\stackrel{\·\·}{v}),F_{C_{M}z}^{*}=-m_A^{*}({\stackrel{\·\·}{w}}_g+\stackrel{\·\·}{w}),M_{C_{M}x}^{*}={\stackrel{\‾}{I}}_{C_{M}x}^{*}({\stackrel{\·\·}{u}}_T^{*}+{\stackrel{\·\·}{u}}^{*})/r_A^{*}$

Wherein,k^*And c^*It is respectively TTMD mass, damping and rigidity；WithFor TTMD for eccentric structure barycenter Rotary inertia and the radius of gyration around x-axis；u^*For TTMD relative displacement；WithFor relative along y with z direction of eccentric structure barycenter Displacement acceleration；WithFor earthquake along the acceleration in y and z direction；For eccentric structure barycenter around the torsion angle acceleration of x-axis；WithIt is respectively damping ratio and the self-vibration circular frequency of TTMD of TTMD.

A TTLCD is placed, when single TTLCD controls the jth vibration shape of eccentric structure, eccentric knot eccentric structure i-th layer The vibration shape j approximate representation that displacement employing in the structure equation of motion, the TTLCD equation of motion and control power is controlled is: v_i=q_j φ_j(3i-2), w_i=q_jφ_j(3i-1), u_Ti=r_Siθ_i=q_jφ_j3i, the equation that couples of described TTLCD-eccentric structure system is:

λ_ij=κ_T0φ_j3ir_fij/r_Si,

${\stackrel{\‾}{\mathrm{\λ}}}_{ij}={\mathrm{\λ}}_{ij}{L}_{eff}/L_1,{\mathrm{\μ}}_j=\frac{m_{fj}}{m_j}{V}_{Tij}^2,V_{Tij}^2=v_{Tij}^2+2{\mathrm{\φ}}_{j3i}{\stackrel{\‾}{\mathrm{\κ}}}_{T3i}(y_{Aij}{\mathrm{\φ}}_{j(3i-1)}-z_{Aij}{\mathrm{\φ}}_{j(3i-2)})/r_{Si},v_{Tij}^2={\mathrm{\φ}}_{j(3i-2)}^2+{\mathrm{\φ}}_{j(3i-1)}^2+{({\mathrm{\φ}}_{j3i}{r}_{fij}/r_{Si})}^2,$ L_Tjy=(m_S+m_fj)φ_j(3i-2)),L_Tjz=(m_S+m_fj)φ_j(3i-1).

The equation that couples of described TTMD-eccentric structure system is:

$\left[\begin{array}{cc}1+{\mathrm{\μ}}_j^{*}& {\mathrm{\λ}}_{ij}^{*}{m}_{Aj}/m_j^{*}\\ {\mathrm{\λ}}_{ij}^{*}& 1\end{array}\right]\left[\begin{array}{c}{\stackrel{\·\·}{q}}_j\\ {\stackrel{\·\·}{u}}^{*}\end{array}\right]+\left[\begin{array}{cc}2{\mathrm{\ζ}}_{Sj}^{*}{\mathrm{\ω}}_{Sj}^{*}& 0\\ 0& 2{\mathrm{\ζ}}_{Aj}^{*}{\mathrm{\ω}}_{Aj}^{*}\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{q}}_j\\ {\stackrel{\·}{u}}^{*}\end{array}\right]+\left[\begin{array}{cc}{\mathrm{\ω}}_{Sj}^{*2}& 0\\ 0& {\mathrm{\ω}}_{Aj}^{*2}\end{array}\right]\left[\begin{array}{c}{q}_j\\ u^{*}\end{array}\right]=-\left[\begin{array}{c}{L}_{Tj}^{*T}/m_j^{*}\\ 0^T\end{array}\right]{\stackrel{\·\·}{\stackrel{\→}{x}}}_g,$

${\mathrm{\μ}}_j^{*}=\frac{m_{Aj}}{m_j^{*}}{v}_{Tij}^{*2},v_{Tij}^{*2}={\mathrm{\φ}}_{j(3i-2)}^2+{\mathrm{\φ}}_{j(3i-1)}^2+{({\mathrm{\φ}}_{j3i}{r}_{Aij}^{*}/r_{Si})}^2,{\mathrm{\λ}}_{ij}^{*}=\frac{r_{Aij}^{*}}{r_{Si}}{\mathrm{\φ}}_{j3i},$

$L_{Tj}^{*T}=\[\begin{array}{ccc}{L}_{Tjy}^{*}& L_{Tjz}^{*}& 0\end{array}\],L_{Tjy}^{*}=(m_S^{*}+m_{Aj}^{*}){\mathrm{\φ}}_{j(3i-2))},L_{Tjz}^{*}=(m_S^{*}+m_{Aj}^{*}){\mathrm{\φ}}_{j(3i-1)}.$

Wherein, μ_j、ζ_Sj、ω_Sj、ζ_AjAnd ω_AjIt is respectively liquid quality and eccentric structure modal mass ratio, bias in TTLCD Structural damping ratio, eccentric structure self-vibration circular frequency, the damping ratio of TTLCD and the natural frequency of vibration of TTLCD；WithIt is respectively TTMD mass and equivalent structure modal mass ratio, equivalent damping ratio, equivalence Structure self-vibration circular frequency, the damping ratio of TTMD and the natural frequency of vibration of TMD；m_fj、m_AjBe respectively liquid in TTLCD quality and TTMD mass；U be in TTLCD liquid along relative displacement during vessel wall motion；u^*For TTMD relative displacement；m_j、It is respectively partially The modal mass of eccentric structure after core structure and equivalence；m_S、It is respectively the floor matter of eccentric structure after eccentric structure and equivalence Amount；r_SiFor eccentric structure around the radius of gyration of x-axis.

Mass ratio, frequency ratio and damping ratio between described TTLCD-eccentric structure system and TTMD-eccentric structure system Relational expression:

${\mathrm{\&mu;}}_j^{*}={\mathrm{\&mu;}}_j\frac{{\mathrm{\&kappa;}}_{T0}{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T0}{(v_{Tj}^{*}/V_{Tj})}^2}{1+{\mathrm{\&mu;}}_j\&lsqb;1-{\mathrm{\&kappa;}}_{T0}{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T0}{(v_{Tj}^{*}/V_{Tj})}^2\&rsqb;}<{\mathrm{\&mu;}}_j,{\mathrm{\&delta;}}_{jopt}=\frac{f_{Aj,opt}}{f_{Sj}}=\frac{{\mathrm{\&delta;}}_{jopt}^{*}}{\sqrt{1+{\mathrm{\&mu;}}_j\&lsqb;1-{\mathrm{\&kappa;}}_{T0}{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T0}{(v_{Tj}^{*}/V_{Tj})}^2\&rsqb;}},{\mathrm{\&zeta;}}_{Aj}={\mathrm{\&zeta;}}_{Aj}^{*}.$

${\mathrm{\&mu;}}_j=\frac{m_{fj}}{m_j}{V}_{Tij}^2,V_{Tij}^2=v_{Tij}^2+2{\mathrm{\&phi;}}_{j3i}{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T3i}(y_{Aij}{\mathrm{\&phi;}}_{j(3i-1)}-z_{Aij}{\mathrm{\&phi;}}_{j(3i-2)})/r_{Si},v_{Tij}^2={\mathrm{\&phi;}}_{j(3i-2)}^2+{\mathrm{\&phi;}}_{j(3i-1)}^2+{({\mathrm{\&phi;}}_{j3i}{r}_{fij}/r_{Si})}^2$

${\mathrm{\&mu;}}_j^{*}=\frac{m_{Aj}}{m_j^{*}}{v}_{Tij}^{*2},v_{Tij}^{*2}={\mathrm{\&phi;}}_{j(3i-2)}^2+{\mathrm{\&phi;}}_{j(3i-1)}^2+{({\mathrm{\&phi;}}_{j3i}{r}_{Aij}^{*}/r_{Si})}^2,{\mathrm{\&lambda;}}_{ij}^{*}=\frac{r_{Aij}^{*}}{r_{Si}}{\mathrm{\&phi;}}_{j3i},$

${\mathrm{\&kappa;}}_{T0}=\frac{2A_p}{r_f{L}_{eff}},{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T0}={\mathrm{\&kappa;}}_{T0}{L}_{eff}/L_1,L_1=2H+\frac{A_B}{A_H}B.$

Wherein, μ_j、f_Sj、ζ_AjAnd f_Aj,optIt is respectively liquid quality and eccentric structure modal mass ratio, eccentric knot in TTLCD The optimal natural frequency of vibration of the structure natural frequency of vibration, the damping ratio of TTLCD and TTLCD； It is respectively TTMD mass and equivalence Structural modal mass ratio, the damping ratio of TTMD and TMD and eccentric structure optimum frequency ratio；m_fj、m_AjIt is respectively liquid in TTLCD Quality and TTMD mass；m_j、It is respectively the modal mass of eccentric structure after eccentric structure and equivalence；r_SiFor eccentric structure around The radius of gyration of x-axis.

Described eccentric structure is frame structure, shear wall structure or frame-shear wall and framed-tube structure.

Described moda1 decomposition need to be under the conditions of eccentric structure be in elastic deformation stage.

The invention provides a kind of method making and carrying out TTLCD parameter optimization in aforementioned manners, including: as single TTLCD When controlling certain vibration shape of eccentric structure, use moda1 decomposition to obtain generalized coordinates equation, TTLCD-eccentric structure system is turned Turning to TTMD-eccentric structure system, the equation that couples comparing this two system obtains two mass of system ratios, frequency ratio and damping ratio Relational expression, utilizes Den Hartog formula to obtain reversing the parameters optimization of frequency modulation column damper；When structure arranges multiple TTLCD Time, write the equation of motion of TTLCD-eccentric structure as state space equation form, by each for structure degree of freedom seismic response The little object function J that is turned to, and call fminsearch order in optimization toolbox by MATLAB programming, Den Hartog joins Number optimal value is as initial value so that function J is rapidly achieved minima, so that the parameter of each TTLCD is the most reasonable.

Present invention also offers a kind of method making and carrying out TTLCD-eccentric structure finite element numerical simulation in aforementioned manners, Comprise determining that in TTLCD, liquid quality and structural eigenvector normalization modal mass obtain mass ratio and TTMD mass and equivalence knot Structure modal mass ratio, thus obtain arranging TTMD oscillator quality；By changing eccentric structure density of material, adjust structural eigenvector and return One changes modal mass.

The method that the TTLCD-eccentric structure that the present invention provides is converted into TTMD-eccentric structure, its derivation is succinct, thing Reason clear concept；The method using the present invention can obtain TTLCD parameters optimization quickly and easily, and by can easy Numerical-Mode The TTMD intended realizes TTLCD and controls to analyze to the vibration damping of structure, can be easy to structural engineer and directly design TTLCD vibration insulating system, Utilize business finite element program that TTLCD-structural system is carried out numerical simulation.

Accompanying drawing explanation

Fig. 1 is the organigram that prior art reverses frequency modulation column damper；

Fig. 2 is the equivalent TTMD that the embodiment of the present invention is installed on eccentric structure；

Fig. 3 is the schematic diagram that embodiment of the present invention TTLCD-eccentric structure is converted into TTMD-eccentric structure；

Fig. 4 is the embodiment of the present invention Single Storey Eccentric Buildings x direction relative torsion displacement time-histories reaction (ElCentro of 0.1g Ripple, π/4, α=3)；

Fig. 5 is that Acceleration time course reaction (0.1g is definitely reversed in embodiment of the present invention Single Storey Eccentric Buildings x direction ElCentro ripple, π/4, α=3)；

Fig. 6 is embodiment of the present invention Single Storey Eccentric Buildings x direction relative torsion displacement time-histories reaction (the sky tunami of 0.1g, α =3 π/4)；

Fig. 7 is that the Acceleration time course reaction (Tianjin of 0.1g is definitely reversed in embodiment of the present invention Single Storey Eccentric Buildings x direction Ripple, π/4, α=3)；

Fig. 8 is embodiment of the present invention Single Storey Eccentric Buildings x direction relative torsion displacement time-histories reaction (the Tangshan ripple of 0.1g, α =3 π/4)；

Fig. 9 is that the Acceleration time course reaction (Tangshan of 0.1g is definitely reversed in embodiment of the present invention Single Storey Eccentric Buildings x direction Ripple, π/4, α=3)；

Figure 10 is 4 layers of eccentric structure x direction RMS torsional displacement of the embodiment of the present invention and acceleration.

Detailed description of the invention

Below in conjunction with the accompanying drawings and embodiment, technical solution of the present invention is further described.

See Fig. 3, the method that the TTLCD-eccentric structure that the embodiment of the present invention provides is converted into TTMD-eccentric structure, bag Include following steps:

Step S1: according to fluid dynamic theory, it is thus achieved that reverse liquid motion side in frequency modulation column damper (TTLCD) Journey.

Reverse frequency modulation column damper (TTLCD) as it is shown in figure 1, be made up of the rigidity tubing string equipped with liquid, tubing string Cross section can be square, circular or other shapes.B and H is the length of fluid column (one section of horizontal pipe and two sections of tilted tubes), its Corresponding area of section is respectively A_BAnd A_H；β is inclination angle, u be in TTLCD liquid along relative displacement during vessel wall motion.This resistance The horizontal component of Buddhist nun's device is designed to closed conduct, and the area Ap bi-directional symmetrical comprised is in mass centre C_M, concrete shape can be fitted Answer architectural plane.

In rigid conduit system, the ideal fluid equation of motion under geological process is set up by generalized Bernoulli equation,

$\underset{1^{\&prime;}}{\overset{2^{\&prime;}}{\&Integral;}}a\&CenterDot;e_t^{\&prime;}{\mathrm{ds}}^{\&prime;}=-g(x_2-x_1)---\left(1\right)$

In formula (1), a is the absolute acceleration of liquid motion, e ' in TTLCD_tRepresent the tangential direction of liquid motion, gravity Acceleration g, fluid density ρ, x₂-x₁Difference in height for free surface.Therefore, under seismic stimulation, when the subpoint of tilted tube For A (y_A,z_A, 0) and during angle of inclination beta=pi/2, in TTLCD, liquid motion equation is:

$\stackrel{\&CenterDot;\&CenterDot;}{u}+2{\mathrm{\&zeta;}}_A{\mathrm{\&omega;}}_A\stackrel{\&CenterDot;}{u}+{\mathrm{\&omega;}}_A^{2}u=-{\mathrm{\&kappa;}}_{T0}{\stackrel{\&CenterDot;\&CenterDot;}{u}}_{TT},$

${\mathrm{\&kappa;}}_{T0}=\frac{2A_p}{r_f{L}_{eff}},{\stackrel{\&CenterDot;\&CenterDot;}{u}}_{TT}=r_f\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}},I_{fx}=m_f{r}_f^2,L_{eff}=2H+\frac{A_H}{A_B}B,{\mathrm{\&omega;}}_A=\sqrt{\frac{2g}{L_{eff}}}.---\left(2\right)$

Wherein, I_fxAnd r_fFor TTLCD for eccentric structure barycenter around the rotary inertia of x-axis and the radius of gyration, m_fFor TTLCD The quality of middle liquid；B is the length of the horizontal pipe fluid column of TTLCD；H is the length of the vertical pipeline fluid column of TTLCD；A_BFor The area of section of the horizontal pipe fluid column of TTLCD；A_HArea of section for the vertical pipeline fluid column of TTLCD；U is liquid in TTLCD Body is along relative displacement during vessel wall motion；Ap is the area that the horizontal component of TTLCD comprises；G is acceleration of gravity；For bias Structure barycenter is around the torsion angle acceleration of x-axis；ζ_AAnd ω_AIt is respectively damping ratio and the self-vibration circular frequency of TTLCD of TTLCD；y_AWith z_AY and z direction coordinate for vertical pipeline subpoint A.

Step S2: according to momentum and the conservation of angular momentum, it is thus achieved that it is mutual that TTLCD and eccentric structure occur in vibration processes Active force and moment.

$F_{C_{M}y}=m_f({\stackrel{\&CenterDot;\&CenterDot;}{v}}_g+\stackrel{\&CenterDot;\&CenterDot;}{v}-{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T3}{\stackrel{\&CenterDot;\&CenterDot;}{u}}_{TT}{z}_A/r_f),F_{C_{M}z}=m_f({\stackrel{\&CenterDot;\&CenterDot;}{w}}_g+\stackrel{\&CenterDot;\&CenterDot;}{w}+{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T3}{\stackrel{\&CenterDot;\&CenterDot;}{u}}_{TT}{y}_A/r_f),{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T3}=\frac{2H}{L_1},$

$M_{C_{M}x}=m_f{r}_f({\stackrel{\&CenterDot;\&CenterDot;}{u}}_{TT}+\frac{{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T3}{y}_A}{r_f}{a}_z-\frac{{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T3}{z}_A}{r_f}{a}_y)+m_f{r}_f{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T0}\stackrel{\&CenterDot;\&CenterDot;}{u},{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T0}={\mathrm{\&kappa;}}_{T0}{L}_{eff}/L_1,L_1=2H+\frac{A_B}{A_H}B.---\left(3\right)$

Wherein, m_fFor the quality of liquid in TTLCD；B is the length of the horizontal pipe fluid column of TTLCD；H is the perpendicular of TTLCD The length of straight pipeline fluid column；A_BArea of section for the horizontal pipe fluid column of TTLCD；A_HFor TTLCD vertical pipeline fluid column cut Face area；r_fFor TTLCD for eccentric structure barycenter around the radius of gyration of x-axis；U be in TTLCD liquid along during vessel wall motion Relative displacement；WithFor eccentric structure barycenter along the relative displacement acceleration in y and z direction；a_zAnd a_yIt is respectively vertical pipeline to throw Shadow point A is along the relative displacement acceleration in y, z direction；WithFor earthquake along the acceleration in y and z direction.

In actual applications, eccentric structure can be frame structure, shear wall structure or frame-shear wall and framed-tube structure.

Step S3: according to dAlembert principle, it is thus achieved that equivalence reverse tuned mass damper, TMD the equation of motion, control power and Moment.

Reverse the torsion tuned mass damper, TMD of frequency modulation column damper equivalence as in figure 2 it is shown, include that bi-directional symmetrical is in knot Structure mass centre equally distributed tuning quality block, viscous damper and torsionspring,WithFor TTMD, bias is tied Structure barycenter is around the rotary inertia of x-axis and the radius of gyration.Two antivibrator equivalence principles are to have identical torsion angle under identical excitation, The i.e. torsion angle of flooring.

The TTMD equation of motion is:

${\stackrel{\&CenterDot;\&CenterDot;}{u}}^{*}+2{\mathrm{\&zeta;}}_A^{*}{\mathrm{\&omega;}}_A^{*}{\stackrel{\&CenterDot;}{u}}^{*}+{\mathrm{\&omega;}}_A^{*2}{u}^{*}=-{\stackrel{\&CenterDot;\&CenterDot;}{u}}_T^{*},{\mathrm{\&omega;}}_A^{*}=\sqrt{\frac{k^{*}}{{\stackrel{\&OverBar;}{I}}_{C_{M}x}^{*}}},2{\mathrm{\&zeta;}}_A^{*}{\mathrm{\&omega;}}_A^{*}=\frac{c^{*}}{{\stackrel{\&OverBar;}{I}}_{C_{M}x}^{*}},{\stackrel{\&OverBar;}{I}}_{C_{M}x}^{*}=m_A^{*}{r}_A^{*2},{\stackrel{\&CenterDot;\&CenterDot;}{u}}_T^{*}=r_A^{*}\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}.$

Control power and moment are

$F_{C_{M}y}^{*}=-m_A^{*}({\stackrel{\&CenterDot;\&CenterDot;}{v}}_g+\stackrel{\&CenterDot;\&CenterDot;}{v}),F_{C_{M}z}^{*}=-m_A^{*}({\stackrel{\&CenterDot;\&CenterDot;}{w}}_g+\stackrel{\&CenterDot;\&CenterDot;}{w}),M_{C_{M}x}^{*}={\stackrel{\&OverBar;}{I}}_{C_{M}x}^{*}({\stackrel{\&CenterDot;\&CenterDot;}{u}}_T^{*}+{\stackrel{\&CenterDot;\&CenterDot;}{u}}^{*})/r_A^{*}---\left(4\right)$

Wherein,k^*And c^*It is respectively TTMD mass, damping and rigidity；WithFor TTMD for eccentric structure barycenter Rotary inertia and the radius of gyration around x-axis；u^*For TTMD relative displacement；WithFor relative along y with z direction of eccentric structure barycenter Displacement acceleration；WithFor earthquake along the acceleration in y and z direction；For eccentric structure barycenter around the torsion angle acceleration of x-axis；WithIt is respectively damping ratio and the self-vibration circular frequency of TTMD of TTMD.

Step S4: set up eccentric structure power balance equation under geological process, and tie according to single Damper Control bias Certain vibration shape of structure, uses moda1 decomposition to obtain generalized coordinates equation, sets up TTLCD-eccentric structure and TTMD-eccentric structure two System couple equation.

Under geological process, eccentric structure power balance equation is:WhereinWithTable Show the mass matrix of eccentric structure, damping matrix and stiffness matrix,For ground motion horizontal acceleration during earthquake,Represent structure displacement, speed and acceleration column vector relative to ground,For earthquake location vector.

Consider that structure is in elastic deformation stage under little shake effect, places a TTLCD eccentric structure i-th layer, when Single TTLCD controls the jth vibration shape of eccentric structure, the displacement in the eccentric structure equation of motion, the TTLCD equation of motion and control power The vibration shape j approximate representation that employing is controlled is: v_i=q_jφ_j(3i-2), w_i=q_jφ_j(3i-1), u_Ti=r_Siθ_i=q_jφ_j3i, set up The equation that couples of TTLCD-eccentric structure system is:

$\left[\begin{array}{cc}1+{\mathrm{\&mu;}}_j& {\stackrel{\&OverBar;}{\mathrm{\&lambda;}}}_{ij}{m}_{fj}/m_j\\ {\mathrm{\&lambda;}}_{ij}& 1\end{array}\right]\left[\begin{array}{c}{\stackrel{\&CenterDot;\&CenterDot;}{q}}_j\\ \stackrel{\&CenterDot;\&CenterDot;}{u}\end{array}\right]+\left[\begin{array}{cc}2{\mathrm{\&zeta;}}_{Sj}{\mathrm{\&omega;}}_{Sj}& 0\\ 0& 2{\mathrm{\&zeta;}}_{Aj}{\mathrm{\&omega;}}_{Aj}\end{array}\right]\left[\begin{array}{c}{\stackrel{\&CenterDot;}{q}}_j\\ \stackrel{\&CenterDot;}{u}\end{array}\right]+\left[\begin{array}{cc}{\mathrm{\&omega;}}_{Sj}^2& 0\\ 0& {\mathrm{\&omega;}}_{Aj}^2\end{array}\right]\left[\begin{array}{c}{q}_j\\ u\end{array}\right]=-\left[\begin{array}{c}{L}_{Tj}^T/m_j\\ 0^T\end{array}\right]{\stackrel{\&CenterDot;\&CenterDot;}{\stackrel{\&RightArrow;}{x}}}_g,{\mathrm{\&lambda;}}_{ij}={\mathrm{\&kappa;}}_{T0}{\mathrm{\&phi;}}_{j3i}{r}_{fij}/r_{Si},$

${\stackrel{\&OverBar;}{\mathrm{\&lambda;}}}_{ij}={\mathrm{\&lambda;}}_{ij}{L}_{eff}/L_1,{\mathrm{\&mu;}}_j=\frac{m_{fj}}{m_j}{V}_{Tij}^2,V_{Tij}^2=v_{Tij}^2+2{\mathrm{\&phi;}}_{j3i}{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T3i}(y_{Aij}{\mathrm{\&phi;}}_{j(3i-1)}-z_{Aij}{\mathrm{\&phi;}}_{j(3i-2)})/r_{Si},v_{Tij}^2={\mathrm{\&phi;}}_{j(3i-2)}^2+{\mathrm{\&phi;}}_{j(3i-1)}^2+{({\mathrm{\&phi;}}_{j3i}{r}_{fij}/r_{Si})}^2,$

$L_{Tj}^T=\&lsqb;\begin{array}{ccc}{L}_{Tjy}& L_{Tjz}& 0\end{array}\&rsqb;,L_{Tjy}=(m_S+m_{fj}){\mathrm{\&phi;}}_{j(3i-2))},L_{Tjz}=(m_S+m_{fj}){\mathrm{\&phi;}}_{j(3i-1)}.---\left(5\right)$

Equally a TTMD is set eccentric structure i-th layer and controls the jth vibration shape, the side of coupling of TTMD-eccentric structure system Cheng Wei:

$\left[\begin{array}{cc}1+{\mathrm{\&mu;}}_j^{*}& {\mathrm{\&lambda;}}_{ij}^{*}{m}_{Aj}/m_j^{*}\\ {\mathrm{\&lambda;}}_{ij}^{*}& 1\end{array}\right]\left[\begin{array}{c}{\stackrel{\&CenterDot;\&CenterDot;}{q}}_j\\ {\stackrel{\&CenterDot;\&CenterDot;}{u}}^{*}\end{array}\right]+\left[\begin{array}{cc}2{\mathrm{\&zeta;}}_{Sj}^{*}{\mathrm{\&omega;}}_{Sj}^{*}& 0\\ 0& 2{\mathrm{\&zeta;}}_{Aj}^{*}{\mathrm{\&omega;}}_{Aj}^{*}\end{array}\right]\left[\begin{array}{c}{\stackrel{\&CenterDot;}{q}}_j\\ {\stackrel{\&CenterDot;}{u}}^{*}\end{array}\right]+\left[\begin{array}{cc}{\mathrm{\&omega;}}_{Sj}^{*2}& 0\\ 0& {\mathrm{\&omega;}}_{Aj}^{*2}\end{array}\right]\left[\begin{array}{c}{q}_j\\ u^{*}\end{array}\right]=-\left[\begin{array}{c}{L}_{Tj}^{*T}/m_j^{*}\\ 0^T\end{array}\right]{\stackrel{\&CenterDot;\&CenterDot;}{\stackrel{\&RightArrow;}{x}}}_g,$

${\mathrm{\&mu;}}_j^{*}=\frac{m_{Aj}}{m_j^{*}}{v}_{Tij}^{*2},v_{Tij}^{*2}={\mathrm{\&phi;}}_{j(3i-2)}^2+{\mathrm{\&phi;}}_{j(3i-1)}^2+{({\mathrm{\&phi;}}_{j3i}{r}_{Aij}^{*}/r_{Si})}^2,{\mathrm{\&lambda;}}_{ij}^{*}=\frac{r_{Aij}^{*}}{r_{Si}}{\mathrm{\&phi;}}_{j3i},---\left(6\right)$

$L_{Tj}^{*T}=\&lsqb;\begin{array}{ccc}{L}_{Tjy}^{*}& L_{Tjz}^{*}& 0\end{array}\&rsqb;,L_{Tjy}^{*}=(m_S^{*}+m_{Aj}^{*}){\mathrm{\&phi;}}_{j(3i-2))},L_{Tjz}^{*}=(m_S^{*}+m_{Aj}^{*}){\mathrm{\&phi;}}_{j(3i-1)}.$

Wherein, μ_j、ζ_Sj、ω_Sj、ζ_AjAnd ω_AjIt is respectively liquid quality and eccentric structure modal mass ratio, bias in TTLCD Structural damping ratio, eccentric structure self-vibration circular frequency, the damping ratio of TTLCD and the natural frequency of vibration of TTLCD；WithIt is respectively TTMD mass and equivalent structure modal mass ratio, equivalent damping ratio, equivalence Structure self-vibration circular frequency, the damping ratio of TTMD and the natural frequency of vibration of TMD；m_fj、m_AjBe respectively liquid in TTLCD quality and TTMD mass；U be in TTLCD liquid along relative displacement during vessel wall motion；u^*For TTMD relative displacement；m_j、It is respectively partially The modal mass of eccentric structure after core structure and equivalence；m_S、It is respectively the floor matter of eccentric structure after eccentric structure and equivalence Amount；r_SiFor eccentric structure around the radius of gyration of x-axis；r_fijFor TTLCD for eccentric structure barycenter around the radius of gyration of x-axis.

In actual applications, moda1 decomposition need to be under the conditions of eccentric structure be in elastic deformation stage.

Step S5: under identical excitation, finds out the pass between liquid relative displacement in TTMD relative displacement and TTLCD System, it is thus achieved that the relation of mass ratio, frequency ratio and damping ratio between TTLCD-eccentric structure system and TTMD-eccentric structure system Formula.

Contrast TTLCD-eccentric structure system and TTMD-eccentric structure system, find out TTMD relative displacement u^*And TTLCD Relation between middle liquid relative displacement u, contrast equation (2) and (4) the right are allowed to identical excitationSelectWithObtain u^*=u/ κ_T0, bring formula (5) and public affairs into simultaneously Formula (6) couples the 2nd equation in equation, and contrast left-hand component obtains Bring conclusions into formula (5) obtain with the 1st equation coupling in equation of formula (6):

$\frac{{\mathrm{\&mu;}}_j{\mathrm{\&kappa;}}_{T0}}{(1+{\mathrm{\&mu;}}_j)V_{Tij}^2}=\frac{{\mathrm{\&mu;}}_j^{*}}{{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T0}(1+{\mathrm{\&mu;}}_j^{*})v_{Tij}^{*2}},\frac{1}{1+{\mathrm{\&mu;}}_j}{\mathrm{\&omega;}}_{Sj}^2=\frac{1}{1+{\mathrm{\&mu;}}_j^{*}}{\mathrm{\&omega;}}_{Sj}^{*2},\frac{1}{1+{\mathrm{\&mu;}}_j}2{\mathrm{\&zeta;}}_{Sj}{\mathrm{\&omega;}}_{Sj}=\frac{1}{1+{\mathrm{\&mu;}}_j^{*}}2{\mathrm{\&zeta;}}_{Sj}^{*}{\mathrm{\&omega;}}_{Sj}^{*}.---\left(7\right)$

Comparison equation (5), (6) thus obtain the matter between TTLCD-eccentric structure system and TTMD-eccentric structure system Amount ratio, frequency ratio and the relational expression of damping ratio:

${\mathrm{\&mu;}}_j^{*}={\mathrm{\&mu;}}_j\frac{{\mathrm{\&kappa;}}_{T0}{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T0}{(v_{Tj}^{*}/V_{Tj})}^2}{1+{\mathrm{\&mu;}}_j\&lsqb;1-{\mathrm{\&kappa;}}_{T0}{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T0}{(v_{Tj}^{*}/V_{Tj})}^2\&rsqb;}<{\mathrm{\&mu;}}_j,{\mathrm{\&delta;}}_{jopt}=\frac{f_{Aj,opt}}{f_{Sj}}=\frac{{\mathrm{\&delta;}}_{jopt}^{*}}{\sqrt{1+{\mathrm{\&mu;}}_j\&lsqb;1-{\mathrm{\&kappa;}}_{T0}{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T0}{(v_{Tj}^{*}/V_{Tj})}^2\&rsqb;}},{\mathrm{\&zeta;}}_{Aj}={\mathrm{\&zeta;}}_{Aj}^{*}.$

${\mathrm{\&mu;}}_j=\frac{m_{fj}}{m_j}{V}_{Tij}^2,V_{Tij}^2=v_{Tij}^2+2{\mathrm{\&phi;}}_{j3i}{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T3i}(y_{Aij}{\mathrm{\&phi;}}_{j(3i-1)}-z_{Aij}{\mathrm{\&phi;}}_{j(3i-2)})/r_{Si},v_{Tij}^2={\mathrm{\&phi;}}_{j(3i-2)}^2+{\mathrm{\&phi;}}_{j(3i-1)}^2+{({\mathrm{\&phi;}}_{j3i}{r}_{fij}/r_{Si})}^2$

${\mathrm{\&mu;}}_j^{*}=\frac{m_{Aj}}{m_j^{*}}{v}_{Tij}^{*2},v_{Tij}^{*2}={\mathrm{\&phi;}}_{j(3i-2)}^2+{\mathrm{\&phi;}}_{j(3i-1)}^2+{({\mathrm{\&phi;}}_{j3i}{r}_{Aij}^{*}/r_{Si})}^2,{\mathrm{\&lambda;}}_{ij}^{*}=\frac{r_{Aij}^{*}}{r_{Si}}{\mathrm{\&phi;}}_{j3i},$

${\mathrm{\&kappa;}}_{T0}=\frac{2A_p}{r_f{L}_{eff}},{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T0}={\mathrm{\&kappa;}}_{T0}{L}_{eff}/L_1,L_1=2H+\frac{A_B}{A_H}B.---\left(8\right)$

Wherein, μ_j、f_Sj、ζ_AjAnd f_Aj,optIt is respectively liquid quality and eccentric structure modal mass ratio, eccentric knot in TTLCD The optimal natural frequency of vibration of the structure natural frequency of vibration, the damping ratio of TTLCD and TTLCD； Be respectively TTMD mass with etc. Efficient construction modal mass ratio, the damping ratio of TTMD and TMD and eccentric structure optimum frequency ratio；m_fj、m_AjIt is respectively liquid in TTLCD The quality of body and TTMD mass；m_j、It is respectively the modal mass of eccentric structure after eccentric structure and equivalence；r_SiFor eccentric structure The radius of gyration around x-axis.

The optimum frequency of TTLCD compares δ_joptReduction compared with TTMD, but optimum damping ratio ζ_joptConstant.

It should be understood that symbol identical in each mathematical formulae that the present embodiments relate to all represents identical containing Justice, therefore some mathematical formulae does not carries out repeat specification to the implication of same-sign.Only use it addition, couple some symbol in equation In representing mathematical relationship, symbol itself is without physical meaning.

Embodiments provide a kind of side using above-mentioned TTLCD-eccentric structure to be converted into TTMD-eccentric structure Method, the method carrying out TTLCD parameter optimization:

Den Hartog derive at first eccentric structure under the conditions of undamped by simple harmonic quantity External Force Acting time, additional TMD Optimal damping ratio and optimal frequency ratios so that the displacement response amplification coefficient of eccentric structure is minimum in the range of frequency domain,

${\mathrm{\&delta;}}_{jopt}^{*}=\frac{f_{Aj,opt}}{f_{Sj}^{*}}=\frac{1}{1+{\mathrm{\&mu;}}_j^{*}},{\mathrm{\&zeta;}}_{jopt}^{*}=\sqrt{\frac{3{\mathrm{\&mu;}}_j^{*}}{8(1+{\mathrm{\&mu;}}_j^{*})}}---\left(9\right)$

Equation (9) similarly suitable eccentric structure is under simple harmonic quantity ground acceleration effect, and absolute acceleration amplification coefficient reaches Minima.The tuned frequency of antivibrator designs than the optimization with damping ratio and includes two steps: 1) when considering that single TTLCD controls During certain vibration shape of eccentric structure, use moda1 decomposition to obtain generalized coordinates equation, TTLCD-eccentric structure system is converted into TTMD-eccentric structure system, the equation that couples comparing this two system obtains two mass of system ratios, frequency ratio and the relation of damping ratio Formula, utilizes Den Hartog formula to obtain reversing the parameters optimization of frequency modulation column damper.TTLCD Optimal damping ratio is equal to TTMD Optimal damping ratio, i.e.TTLCD optimal frequency ratios can obtain from formula (8).2) when structure arranges multiple TTLCD, it is necessary to Consider the impact of other vibration shapes neighbouring, write the equation of motion of TTLCD-eccentric structure as state space equation form, by structure Each degree of freedom seismic response minimizes as object function, i.e.Z in formula_S Represent the state parameter of eccentric structure,For positive semi-definite weight matrix,For excitation vector,By Lyapunov algebra matrixAnswer.Calling fminsearch order in optimization toolbox by MATLAB programming, Den Hartog parameter is excellent Change value is as initial value so that function J is rapidly achieved minima, so that the parameter of each TTLCD is the most reasonable.

The embodiment of the present invention additionally provides a kind of side using above-mentioned TTLCD-eccentric structure to be converted into TTMD-eccentric structure Method, the method carrying out TTLCD-eccentric structure finite element numerical simulation:

TTMD system includes quality system, damping system and spring system, uses point/line mass or straight in SAP2000 Connecing employing entity quality to be simulated, spring system can be attached with link unit, and selects Damper unit, input damping The stiffness K of device and damping C.

TTLCD equivalent conversion is that TTMD carries out numerical simulation, including two steps: 1) first determine liquid matter in TTLCD Amount and structural eigenvector normalization modal mass obtain mass ratio μ_j, obtain TTMD mass and equivalent structure mould further according to formula (9) State mass ratioThus obtain arranging TTMD oscillator quality；2) due in TTLCD liquid quality some as additional mass Acting on eccentric structure, structural eigenvector normalization modal mass changes.This quality can be by changing eccentric structure material Density and other attributes and geometric attribute without changing material are adjusted.

It is expanded on further, below by two application examples, the method utilizing the embodiment of the present invention, obtains TTLCD optimum Parameter and finite element numerical simulation.

Application example 1: this embodiment is chosen a monolayer bias frame structure and studied, it is assumed that floor quality is 16 × 10³Kg, physical dimension is a=8m, b=4m.Stiffness coefficient in y, z direction is k_y=340.20kN/m and k_z=125.21kN/ M, an extra stiffness k '_y=3402kN/m and k '_zThe eccentric throw of=1252.1kN/m (elevator in such as Practical Project) is e_y= e_z=1m, structural damping uses Rayleigh damping, and the frequency of structure three first order mode is 1.38,1.82 and 2.86Hz.At floor Placing a TTLCD control structure first vibration mode being suitable for flat shape, in TTLCD, the quality of water is 500kg, and structure the first rank shake Type normalization modal mass is 16000kg, and mass ratio isTTLCD is obtained according to parameter optimization method Excellent frequency and damping ratio are 1.23Hz and 7.59%, TTLCD is converted into TTMD and obtains the quality of TTMD, rigidity and damped coefficient Respectively being 327kg, 225.34kN/m and 44.56kN s/m, structural modal quality becomes 16437Kg.It is respectively adopted peak value For ElCentro, Tianjin and the Tangshan Earthquake ripple accelerogram of 0.1g as input, and by its angle of incidence be respectively 0 °, 15 °, 30 °, until 180 ° calculate various working, are used SAP2000 to be simulated the TTMD after converting.Fig. 4～Fig. 9 is incident angle α During=3 π/4, the relative torsion displacement in x direction and the definitely reaction of torsion Acceleration time course.Sap2000 simulation TTMD is used to calculate The structural response obtained almost is completely superposed, therefore from number with the time-history curves using the method for MATLAB simulation TTLCD to obtain The angle that value calculates, demonstrates reasonability and the feasibility of the method further, thus obtains the correctness of theoretical derivation process And stringency.

Application example 2: this example is chosen one or four layers of eccentric frame structure Design on Vibration Control and carried out, and every layer of structure quality is 16×10³Kg, y, the rigidity in z-axis direction are respectively k_yi=1508.5kN/m and k_zi=536.68kN/m.One extra stiffness k '_yi =18.10 × 10³KN/m and k '_zi=6.44 × 10³The eccentric throw of kN/m is e_y=e_z=1m, structural damping uses Rayleigh Damping, the frequency 1.08,1.41 and 2.23Hz of first three first order mode of structure.Two rank before 2 TTLCD carry out control structure are placed at top layer The vibration shape, in TTLCD, the quality of water is 1400kg.TTLCD optimal frequency and damping ratio difference is obtained according to parameter optimization method For 0.97Hz, 1.25Hz and 7.2%, 2.06%.TTLCD is converted into TTMD obtain the quality of TTMD be respectively 15318kg and 1463kg, rigidity is respectively 652kN/m and 109kN/m, damped coefficient 20.2kN s/m and 14.74kN s/m.The ground of model Vibrations input uses peak value to be the ElCentro seismic wave of 0.1g, and by its angle of incidence be respectively 0 °, 15 °, 30 ° until 180 ° Calculating various working, Figure 10 is each layer maximum displacement and acceleration when being π/4, α=3, it can be seen that use Sap2000 to simulate TTMD Calculated structural response almost fits like a glove with the result using the method for MATLAB simulation TTLCD to obtain.

By above-mentioned 2 application examples it can be seen that can be by being converted into TTMD structure for arranging the structural system of TTLCD System carries out parameter optimization and can directly use finite element software to carry out numerical analysis.

The method that the TTLCD-eccentric structure that the embodiment of the present invention provides is converted into TTMD-eccentric structure, its derivation Succinctly, clear physics conception；The method using the present invention can obtain TTLCD parameters optimization quickly and easily, and by holding Easily the TTMD of numerical simulation realizes TTLCD and controls to analyze to the vibration damping of structure, can be easy to structural engineer and directly design TTLCD and subtract Vibrating system, utilizes business finite element program that TTLCD-structural system is carried out numerical simulation.

Particular embodiments described above, has been carried out the purpose of the present invention, technical scheme and beneficial effect the most in detail Describe in detail bright, be it should be understood that the specific embodiment that the foregoing is only the present invention, be not limited to the present invention, all Within the spirit and principles in the present invention, any modification, equivalent substitution and improvement etc. done, should be included in the guarantor of the present invention Within the scope of protecting.

Claims (10)

1. the method that a TTLCD-eccentric structure is converted into TTMD-eccentric structure, it is characterised in that described method includes: root According to fluid dynamic theory, it is thus achieved that reverse liquid motion equation in frequency modulation column damper；According to momentum and the conservation of angular momentum, obtain Interaction force and moment that frequency modulation column damper occurs in vibration processes must be reversed with eccentric structure；According to reaching bright Bel Principle, it is thus achieved that equivalence is reversed the equation of motion of tuned mass damper, TMD, controlled power and moment；Set up eccentric structure under geological process Power balance equation, and according to certain vibration shape of single Damper Control eccentric structure, use moda1 decomposition to obtain generalized coordinates Equation, that sets up TTLCD-eccentric structure and TTMD-eccentric structure two system couples equation；Under identical excitation, find out Relation between liquid relative displacement in TTMD relative displacement and TTLCD, it is thus achieved that TTLCD-eccentric structure system is eccentric with TTMD- The relational expression of mass ratio, frequency ratio and damping ratio between structural system.

2. the method that TTLCD-eccentric structure as claimed in claim 1 is converted into TTMD-eccentric structure, it is characterised in that when The subpoint of tilted tube is A (y_A,z_A, 0) and during angle of inclination beta=pi/2, liquid motion in described torsion frequency modulation column damper Equation is:

$\stackrel{\&CenterDot;\&CenterDot;}{u}+2{\mathrm{\&zeta;}}_A{\mathrm{\&omega;}}_A\stackrel{\&CenterDot;}{u}+{\mathrm{\&omega;}}_A^{2}u=-{\mathrm{\&kappa;}}_{T0}{\stackrel{\&CenterDot;\&CenterDot;}{u}}_{TT},$

${\mathrm{\&kappa;}}_{T0}=\frac{2A_p}{r_f{L}_{eff}},{\stackrel{\&CenterDot;\&CenterDot;}{u}}_{TT}=r_f\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}},I_{fx}=m_f{r}_f^2,L_{eff}=2H+\frac{A_H}{A_B}B,{\mathrm{\&omega;}}_A=\sqrt{\frac{2g}{L_{eff}}}.$

Wherein, I_fxAnd r_fFor TTLCD for eccentric structure barycenter around the rotary inertia of x-axis and the radius of gyration, m_fFor liquid in TTLCD The quality of body；B is the length of the horizontal pipe fluid column of TTLCD；H is the length of the vertical pipeline fluid column of TTLCD；A_BFor TTLCD The area of section of horizontal pipe fluid column；A_HArea of section for the vertical pipeline fluid column of TTLCD；U is liquid edge pipe in TTLCD Relative displacement during wall motion；Ap is the area that the horizontal component of TTLCD comprises；G is acceleration of gravity；For eccentric structure matter The heart is around the torsion angle acceleration of x-axis；ζ_AAnd ω_AIt is respectively damping ratio and the self-vibration circular frequency of TTLCD of TTLCD；y_AAnd z_AIt is perpendicular Y and the z direction coordinate of straight pipeline subpoint A.

3. the method that TTLCD-eccentric structure as claimed in claim 2 is converted into TTMD-eccentric structure, it is characterised in that institute State and reverse the interaction force that occurs in vibration processes with eccentric structure of frequency modulation column damper and moment is:

$F_{C_{M}y}=m_f({\stackrel{\&CenterDot;\&CenterDot;}{v}}_g+\stackrel{\&CenterDot;\&CenterDot;}{v}-{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T3}{\stackrel{\&CenterDot;\&CenterDot;}{u}}_{TT}{z}_A/r_f),F_{C_{M}z}=m_f({\stackrel{\&CenterDot;\&CenterDot;}{w}}_g+\stackrel{\&CenterDot;\&CenterDot;}{w}+{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T3}{\stackrel{\&CenterDot;\&CenterDot;}{u}}_{TT}{y}_A/r_f),{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T3}=\frac{2H}{L_1},$

$M_{C_{M}x}=m_f{r}_f({\stackrel{\&CenterDot;\&CenterDot;}{u}}_{TT}+\frac{{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T3}{y}_A}{r_f}{a}_z-\frac{{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T3}{z}_A}{r_f}{a}_y)+m_f{r}_f{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T0}\stackrel{\&CenterDot;\&CenterDot;}{u},{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T0}={\mathrm{\&kappa;}}_{T0}{L}_{eff}/L_1,L_1=2H+\frac{A_B}{A_H}B.$

Wherein, m_fFor the quality of liquid in TTLCD；B is the length of the horizontal pipe fluid column of TTLCD；H is the vertical pipeline of TTLCD The length of fluid column；A_BArea of section for the horizontal pipe fluid column of TTLCD；A_HFace, cross section for the vertical pipeline fluid column of TTLCD Long-pending；r_fFor TTLCD for eccentric structure barycenter around the radius of gyration of x-axis；U is relative along during vessel wall motion of liquid in TTLCD Displacement；WithFor eccentric structure barycenter along the relative displacement acceleration in y and z direction；a_zAnd a_yIt is respectively vertical pipeline subpoint A Relative displacement acceleration along y, z direction；WithFor earthquake along the acceleration in y and z direction.

4. the method that TTLCD-eccentric structure as claimed in claim 3 is converted into TTMD-eccentric structure, it is characterised in that institute The equation of motion stating equivalence torsion tuned mass damper, TMD is:

${\stackrel{\&CenterDot;\&CenterDot;}{u}}^{*}+2{\mathrm{\&zeta;}}_A^{*}{\mathrm{\&omega;}}_A^{*}{\stackrel{\&CenterDot;}{u}}^{*}+{\mathrm{\&omega;}}_A^{*2}{u}^{*}=-{\stackrel{\&CenterDot;\&CenterDot;}{u}}_T^{*},{\mathrm{\&omega;}}_A^{*}=\sqrt{\frac{k^{*}}{{\stackrel{\&OverBar;}{I}}_{C_{M}x}^{*}}},2{\mathrm{\&zeta;}}_A^{*}{\mathrm{\&omega;}}_A^{*}=\frac{c^{*}}{{\stackrel{\&OverBar;}{I}}_{C_{M}x}^{*}},{\stackrel{\&OverBar;}{I}}_{C_{M}x}^{*}=m_A^{*}{r}_A^{*2},{\stackrel{\&CenterDot;\&CenterDot;}{u}}_T^{*}=r_A^{*}\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}.$

Control power and moment is:

$F_{C_{M}y}^{*}=-m_A^{*}({\stackrel{\&CenterDot;\&CenterDot;}{v}}_g+\stackrel{\&CenterDot;\&CenterDot;}{v}),F_{C_{M}z}^{*}=-m_A^{*}({\stackrel{\&CenterDot;\&CenterDot;}{w}}_g+\stackrel{\&CenterDot;\&CenterDot;}{w}),M_{C_{M}x}^{*}={\stackrel{\&OverBar;}{I}}_{C_{M}x}^{*}({\stackrel{\&CenterDot;\&CenterDot;}{u}}_T^{*}+{\stackrel{\&CenterDot;\&CenterDot;}{u}}^{*})/r_A^{*}$

Wherein,k^*And c^*It is respectively TTMD mass, damping and rigidity；WithFor TTMD for eccentric structure barycenter around x The rotary inertia of axle and the radius of gyration；u^*For TTMD relative displacement；WithFor eccentric structure barycenter along the phase para-position in y and z direction Move acceleration；WithFor earthquake along the acceleration in y and z direction.Speed；Accelerate around the torsion angle of x-axis for eccentric structure barycenter Degree；WithIt is respectively damping ratio and the self-vibration circular frequency of TTMD of TTMD.

5. the method that TTLCD-eccentric structure as claimed in claim 4 is converted into TTMD-eccentric structure, it is characterised in that Eccentric structure i-th layer place a TTLCD, when single TTLCD control eccentric structure the jth vibration shape, the eccentric structure equation of motion, The vibration shape j approximate representation that displacement employing in the TTLCD equation of motion and control power is controlled is: v_i=q_jφ_j(3i-2), w_i=q_j φ_j(3i-1), u_Ti=r_Siθ_i=q_jφ_jxi, the equation that couples of described TTLCD-eccentric structure system is:

$\left[\begin{array}{cc}1+{\mathrm{\&mu;}}_j& {\stackrel{\&OverBar;}{\mathrm{\&lambda;}}}_{ij}{m}_{fj}/m_j\\ {\mathrm{\&lambda;}}_{ij}& 1\end{array}\right]\left[\begin{array}{c}{\stackrel{\&CenterDot;\&CenterDot;}{q}}_j\\ \stackrel{\&CenterDot;\&CenterDot;}{u}\end{array}\right]+\left[\begin{array}{cc}2{\mathrm{\&zeta;}}_{Sj}{\mathrm{\&omega;}}_{Sj}& 0\\ 0& 2{\mathrm{\&zeta;}}_{Aj}{\mathrm{\&omega;}}_{Aj}\end{array}\right]\left[\begin{array}{c}{\stackrel{\&CenterDot;}{q}}_j\\ \stackrel{\&CenterDot;}{u}\end{array}\right]+\left[\begin{array}{cc}{\mathrm{\&omega;}}_{Sj}^2& 0\\ 0& {\mathrm{\&omega;}}_{Aj}^2\end{array}\right]\left[\begin{array}{c}{q}_j\\ u\end{array}\right]=-\left[\begin{array}{c}{L}_{Tj}^T/m_j\\ 0^T\end{array}\right]{\stackrel{\&CenterDot;\&CenterDot;}{\stackrel{\&RightArrow;}{x}}}_g,{\mathrm{\&lambda;}}_{ij}={\mathrm{\&kappa;}}_{T0}{\mathrm{\&phi;}}_{j3i}{r}_{fij}/r_{Si},$

${\stackrel{\&OverBar;}{\mathrm{\&lambda;}}}_{ij}={\mathrm{\&lambda;}}_{ij}{L}_{eff}/L_1,{\mathrm{\&mu;}}_j=\frac{m_{fj}}{m_j}{V}_{Tij}^2,V_{Tij}^2=v_{Tij}^2+2{\mathrm{\&phi;}}_{j3i}{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T3i}(y_{Aij}{\mathrm{\&phi;}}_{j(3i-1)}-z_{Aij}{\mathrm{\&phi;}}_{j(3i-2)})/r_{Si},v_{Tij}^2={\mathrm{\&phi;}}_{j(3i-2)}^2+{\mathrm{\&phi;}}_{j(3i-1)}^2+{({\mathrm{\&phi;}}_{j3i}{r}_{fij}/r_{Si})}^2,$

$L_{Tj}^T=\left[\begin{array}{ccc}{L}_{Tjy}& L_{Tjz}& 0\end{array}\right],L_{Tjy}=(m_S+m_{fj}){\mathrm{\&phi;}}_{j\left(3i-2\right))},L_{Tjz}=(m_S+m_{fj}){\mathrm{\&phi;}}_{j(3i-1)}.$

The equation that couples of described TTMD-eccentric structure system is:

$\left[\begin{array}{cc}1+{\mathrm{\&mu;}}_j^{*}& {\mathrm{\&lambda;}}_{ij}^{*}{m}_{Aj}/m_j^{*}\\ {\mathrm{\&lambda;}}_{ij}^{*}& 1\end{array}\right]\left[\begin{array}{c}{\stackrel{\&CenterDot;\&CenterDot;}{q}}_j\\ {\stackrel{\&CenterDot;\&CenterDot;}{u}}^{*}\end{array}\right]+\left[\begin{array}{cc}2{\mathrm{\&zeta;}}_{Sj}^{*}{\mathrm{\&omega;}}_{Sj}^{*}& 0\\ 0& 2{\mathrm{\&zeta;}}_{Aj}^{*}{\mathrm{\&omega;}}_{Aj}^{*}\end{array}\right]\left[\begin{array}{c}{\stackrel{\&CenterDot;}{q}}_j\\ {\stackrel{\&CenterDot;}{u}}^{*}\end{array}\right]+\left[\begin{array}{cc}{\mathrm{\&omega;}}_{Sj}^{*2}& 0\\ 0& {\mathrm{\&omega;}}_{Aj}^{*2}\end{array}\right]\left[\begin{array}{c}{q}_j\\ u^{*}\end{array}\right]=-\left[\begin{array}{c}{L}_{Tj}^{*T}/m_j^{*}\\ 0^T\end{array}\right]{\stackrel{\&CenterDot;\&CenterDot;}{\stackrel{\&RightArrow;}{x}}}_g,$

${\mathrm{\&mu;}}_j^{*}=\frac{m_{Aj}}{m_j^{*}}{v}_{Tij}^{*2},v_{Tij}^{*2}={\mathrm{\&phi;}}_{j(3i-2)}^2+{\mathrm{\&phi;}}_{j(3i-1)}^2+{({\mathrm{\&phi;}}_{j3i}{r}_{Aij}^{*}/r_{Si})}^2,{\mathrm{\&lambda;}}_{ij}^{*}=\frac{r_{Aij}^{*}}{r_{Si}}{\mathrm{\&phi;}}_{j3i},$

$L_{Tj}^{*T}=\left[\begin{array}{ccc}{L}_{Tjy}^{*}& L_{Tjz}^{*}& 0\end{array}\right],L_{Tjy}^{*}=(m_S^{*}+m_{Aj}^{*}){\mathrm{\&phi;}}_{j\left(3i-2\right))},L_{Tjz}^{*}=(m_S^{*}+m_{Aj}^{*}){\mathrm{\&phi;}}_{j(3i-1)}.$

Wherein, μ_j、ζ_Sj、ω_Sj、ζ_AjAnd ω_AjIt is respectively liquid quality and eccentric structure modal mass ratio, eccentric structure in TTLCD Damping ratio, eccentric structure self-vibration circular frequency, the damping ratio of TTLCD and the natural frequency of vibration of TTLCD；WithIt is respectively TTMD mass and equivalent structure modal mass ratio, equivalent damping ratio, equivalent structure self-vibration circular frequency, TTMD Damping ratio and the natural frequency of vibration of TMD；m_fj、m_AjIt is respectively quality and the TTMD mass of liquid in TTLCD；U is liquid in TTLCD Along relative displacement during vessel wall motion；u^*For TTMD relative displacement；m_j、It is respectively eccentric structure after eccentric structure and equivalence Modal mass；m_S、It is respectively the floor quality of eccentric structure after eccentric structure and equivalence；r_SiFor eccentric structure returning around x-axis Turn radius.

6. the method that TTLCD-eccentric structure as claimed in claim 5 is converted into TTMD-eccentric structure, it is characterised in that institute State the relational expression of mass ratio, frequency ratio and damping ratio between TTLCD-eccentric structure system and TTMD-eccentric structure system:

${\mathrm{\&mu;}}_j^{*}={\mathrm{\&mu;}}_j\frac{{\mathrm{\&kappa;}}_{T0}{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T0}{\left(v_{Tj}^{*}/V_{Tj}\right)}^2}{1+{\mathrm{\&mu;}}_j\&lsqb;1-{\mathrm{\&kappa;}}_{T0}{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T0}{\left(v_{Tj}^{*}/V_{Tj}\right)}^2\&rsqb;}<{\mathrm{\&mu;}}_j,{\mathrm{\&delta;}}_{jopt}=\frac{f_{Aj,opt}}{f_{Sj}}=\frac{{\mathrm{\&delta;}}_{jopt}^{*}}{\sqrt{1+{\mathrm{\&mu;}}_j\&lsqb;1-{\mathrm{\&kappa;}}_{T0}{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T0}{\left(v_{Tj}^{*}/V_{Tj}\right)}^2\&rsqb;}},{\mathrm{\&zeta;}}_{Aj}={\mathrm{\&zeta;}}_{Aj}^{*}.$

${\mathrm{\&mu;}}_j=\frac{m_{fj}}{m_j}{V}_{Tij}^2,V_{Tij}^2=v_{Tij}^2+2{\mathrm{\&phi;}}_{j3i}{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T3i}(y_{Aij}{\mathrm{\&phi;}}_{j(3i-1)}-z_{Aij}{\mathrm{\&phi;}}_{j(3i-2)})/r_{Si},v_{Tij}^2={\mathrm{\&phi;}}_{j(3i-2)}^2+{\mathrm{\&phi;}}_{j(3i-1)}^2+{({\mathrm{\&phi;}}_{j3i}{r}_{fij}/r_{Si})}^2,$

${\mathrm{\&mu;}}_j^{*}=\frac{m_{Aj}}{m_j^{*}}{v}_{Tij}^{*2},v_{Tij}^{*2}={\mathrm{\&phi;}}_{j(3i-2)}^2+{\mathrm{\&phi;}}_{j(3i-1)}^2+{({\mathrm{\&phi;}}_{j3i}{r}_{Aij}^{*}/r_{Si})}^2,{\mathrm{\&lambda;}}_{ij}^{*}=\frac{r_{Aij}^{*}}{r_{Si}}{\mathrm{\&phi;}}_{j3i},$

${\mathrm{\&kappa;}}_{T0}=\frac{2A_p}{r_f{L}_{eff}},{\stackrel{\&OverBar;}{\mathrm{\&kappa;}}}_{T0}={\mathrm{\&kappa;}}_{T0}{L}_{eff}/L_1,L_1=2H+\frac{A_B}{A_H}B.$

Wherein, μ_j、f_Sj、ζ_AjAnd f_Aj,optIn respectively TTLCD, liquid quality is with eccentric structure modal mass ratio, eccentric structure certainly The optimal natural frequency of vibration of vibration frequency, the damping ratio of TTLCD and TTLCD； It is respectively TTMD mass and equivalent structure Modal mass ratio, the damping ratio of TTMD and TTMD and eccentric structure optimum frequency ratio；m_fj、m_AjIt is respectively the matter of liquid in TTLCD Amount and TTMD mass；m_j、It is respectively the modal mass of eccentric structure after eccentric structure and equivalence；r_SiFor eccentric structure around x-axis The radius of gyration.

7. the method that TTLCD-eccentric structure as claimed in claim 1 is converted into TTMD-eccentric structure, it is characterised in that institute Stating eccentric structure is frame structure, shear wall structure or frame-shear wall and framed-tube structure.

8. the method that TTLCD-eccentric structure as claimed in claim 1 is converted into TTMD-eccentric structure, it is characterised in that institute Stating moda1 decomposition need to be under the conditions of eccentric structure be in elastic deformation stage.

9. one kind uses the method that method described in claim 1 carries out TTLCD parameter optimization, it is characterised in that including: when single When TTLCD controls certain vibration shape of eccentric structure, moda1 decomposition is used to obtain generalized coordinates equation, by TTLCD-eccentric structure body System is converted into TTMD-eccentric structure system, and the equation that couples comparing this two system obtains two mass of system ratios, frequency ratio and damping The relational expression of ratio, utilizes Den Hartog formula to obtain reversing the parameters optimization of frequency modulation column damper；When structure arranges multiple During TTLCD, write the equation of motion of TTLCD-eccentric structure as state space equation form, each for structure degree of freedom is rung Should minimize as object function J, and call fminsearch order in optimization toolbox, Den by MATLAB programming Hartog parameter optimization value is as initial value so that function J is rapidly achieved minima, so that the parameter of each TTLCD is more For rationally.

10. use the method that method described in claim 1 carries out TTLCD-eccentric structure finite element numerical simulation, its feature Be, comprise determining that in TTLCD liquid quality and structural eigenvector normalization modal mass obtain mass ratio and TTMD mass with etc. Efficient construction modal mass ratio, thus obtain arranging TTMD oscillator quality；By changing eccentric structure density of material, adjust structure and shake Type normalization modal mass.