Rotational inertia double-tuned mass damper parameter optimization method and vibration reduction system

Abstract

The invention discloses a parameter optimization method for a rotary inertia double-tuned mass damper and a vibration reduction system. The parameter optimization method comprises the steps that S1, a main structure motion equation comprising the rotary inertia double-tuned mass damper is constructed; s2, selecting combined variables from a design variable space of the rotary inertia double-tuned mass damper, adopting a genetic simulated annealing algorithm for each combined variable, and optimizing parameters by taking minimization of the maximum acceleration frequency response of a main structure as an objective to obtain an optimal parameter data set; s3, cleaning an optimal parameter data set based on an IQR criterion; s4, constructing a correction factor, and establishing a parameter correction factor nonlinear mapping model through tensor basis function expansion; and S5, multiplying the theoretical closed solution by the parameter correction factor to obtain design parameters of the rotary inertia double-tuned mass damper. Compared with an analytical formula design, the RIDTMD designed by using the corrected formula has the advantages that the vibration reduction efficiency is improved by about 10% at most, and the asymmetric three-peak phenomenon of a core frequency band can be effectively eliminated.

Description

Technical Field

[0001] The present invention relates to the field of civil engineering structure vibration control, and in particular to a rotational inertia dual tuned mass damper parameter optimization method and a vibration reduction system. Background Art

[0002] With the widespread adoption of long-span, lightweight floor structures in public buildings, the comfort issues associated with human-induced vibrations are becoming increasingly prominent. Due to their light weight and low damping ratio, these structures are prone to vertical resonance under human-induced load excitation, which not only interferes with the normal functioning of the building but also poses a potential threat to the physical and mental health of occupants. While tuned mass dampers (TMDs) are widely used for vibration control in current engineering practice, their application has significant drawbacks. Firstly, TMDs require a significant amount of physical mass to achieve their tuning effect, placing stringent demands on the local bearing capacity of the main structure. Secondly, their installation requires a significant amount of building space, which conflicts with the trend toward lightweight design and the spatial constraints of existing building renovations.

[0003] To overcome the mass limitations of TMDs, inertia has been introduced as a new type of inertial element in the field of vibration reduction. It converts linear motion into flywheel rotational motion through transmission mechanisms such as ball screws and rack and pinion gears, generating an apparent inertial force far exceeding its own physical mass (up to thousands of times its physical mass). Based on this, researchers have developed composite devices such as tuned viscous mass dampers (TVMDs) and tuned inertia dampers (TIDs). However, such devices require simultaneous anchoring to the floor slab and adjacent structural layers (or foundations), and long-span floor slabs typically lack reliable lower supports, making their installation unfeasible. Although rotating inertia dual tuned mass dampers (RIDTMDs) and tuned inertia mass systems (TIMSs) can be installed unilaterally on the floor slab without cross-layer anchoring, their theoretical research has primarily focused on displacement control (such as in earthquake and wind-induced vibration scenarios) and is difficult to directly apply to human-induced vibration problems centered on vertical acceleration control.

[0004] While a multi-objective optimization model for human-induced vibration control (TIMS) has been established, explicit parameter expressions are not provided, leading to a complex engineering parameter configuration process. The analytical solution for acceleration control using extended fixed-point theory (RIDTMD) can reduce the physical mass requirement to 80% of the equivalent TMD. However, this theoretical framework ignores the damping characteristics of the primary structure, resulting in an asymmetric three-peak phenomenon in the system's frequency response function within the control frequency band. When the primary structure's damping ratio increases, the RIDTMD's vibration reduction band shifts, the peak response significantly increases, and the actual control effect deviates from theoretical expectations. This flaw stems from the classical fixed-point theory's assumption of zero primary structure damping during derivation. However, the actual damping ratio of concrete floors typically ranges from 2% to 4%, resulting in detuned RIDTMD parameters. Existing technologies have yet to establish a quantitative correction relationship between the primary structure's damping ratio and the RIDTMD parameters, necessitating an optimization design method that incorporates a damping compensation mechanism. Summary of the Invention

[0005] To address the aforementioned shortcomings and deficiencies in existing technologies, the present invention provides a parameter optimization method and vibration reduction system for a rotating inertia dual tuned mass damper (RIDTMD). This method aims to address the asymmetric three-peak frequency response of a rotating inertia dual tuned mass damper (RIDTMD) caused by neglecting the damping of the primary structure. This invention proposes an explicit damping correction factor model that eliminates the frequency response asymmetry while retaining the advantages of single-sided installation and lightweight design.

[0006] To achieve the above objectives, the present invention provides a parameter optimization method for a rotating inertia dual tuned mass damper, which comprises the following steps:

[0007] S1: Construct the main structural motion equations including the rotating inertial dual tuned mass damper;

[0008] S2: Select combination variables from the design variable space of the rotating inertia dual tuned mass damper, use the genetic simulated annealing algorithm to optimize the parameters of each combination variable with the goal of minimizing the maximum acceleration frequency response of the main structure, and obtain the optimal parameter data set;

[0009] S3: Clean the optimal parameter data set based on the IQR criterion;

[0010] S4: Construct correction factors and establish a nonlinear mapping model of parameter correction factors through tensor basis function expansion;

[0011] S5: Multiply the theoretical closed-form solution by the parameter correction factor to obtain the design parameter expression of the rotating inertia dual tuned mass damper.

[0012] A further improvement of the present invention is that the main structure motion equation in step S1 is expressed as:

[0013]

[0014] Where: M is the mass of the main structure; C is the stiffness of the main structure; K is the damping of the main structure; m is the tuned mass; k1 is the primary stiffness of the damper; k2 is the secondary stiffness of the damper; c is the damping of the damper; m b is the inertia coefficient of the damper; x(t) is the displacement response of the main structure; x1(t) is the displacement response of the tuned mass; x2(t) is the displacement response of the inertia; and F(t) is the excitation of the main structure.

[0015] A further improvement of the present invention is that in step S2, the design variables include the main structure damping ratio ζ0 and the damper main mass ratio μ; the design parameters to be optimized include the main tuning frequency ratio q, the sub-tuning frequency ratio η, the sub-mass ratio μ b , damping ratio ζ; the expression of the objective function used by the genetic simulated annealing algorithm is:

[0016]

[0017] st0.8≤q≤1.0,1.0≤η≤1.2,

[0018] 0≤μ b ≤2μ,0≤ζ≤0.05

[0019] Where: H(Ω) is the acceleration frequency response function.

[0020] A further improvement of the present invention is that in step S2, combined variables are selected by traversing according to a predetermined step size in the design variable space composed of the main structure damping ratio ζ0∈[0.005,0.05] and the main mass ratio μ∈[0.005,0.05], and each combined variable includes each design variable.

[0021] A further improvement of the present invention is that in step S4:

[0022] The correction factor is defined as:

[0023]

[0024] Where: β P is the parameter correction factor, whose subscript P∈{q,η,μ b ,ζ}; and P CF (μ) are the average values ​​and theoretical closed-form solutions of the optimized design parameters respectively;

[0025] The expression of the parameter correction factor nonlinear mapping model is:

[0026]

[0027] Among them: a P 、b P 、c Pd P 、e P 、g P is the fitting coefficient of the correction factor, which is obtained by global optimization of the Levenberg-Marquardt algorithm based on the optimal parameter data set.

[0028] A further improvement of the present invention is that the design parameters of the rotating inertia dual tuned mass damper in step S5 are expressed as follows:

[0029]

[0030] Where: q corr. is the correction result of the main tuning frequency ratio; η corr. The correction result of this tuning frequency ratio; μ b,corr. is the correction result of the secondary mass ratio; corr. is the correction result of the damping ratio; β q (ζ0,μ),β η (ζ0,μ), β ζ (ζ0,μ) are the correction factors obtained by substituting the nonlinear mapping model of each parameter correction factor into the fitting coefficient.

[0031] The present invention also provides a vibration reduction system, which includes a rotational inertia dual tuned mass damper designed using the above-mentioned rotational inertia dual tuned mass damper parameter optimization method; the rotational inertia dual tuned mass damper is installed in a large-span floor structure to suppress the acceleration response caused by human-induced vibration.

[0032] The advantages of the present invention are as follows:

[0033] (1) A damping correction factor was constructed to dynamically compensate for the damping effect of the main structure, completely eliminating the frequency response asymmetry of the theoretical design formula and effectively reducing the peak acceleration response of the main structure;

[0034] (2) By replacing the traditional iterative optimization method with an explicit parameter expression and covering the full damping range of large-span floor slabs, the design efficiency can be greatly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a schematic diagram of the process of the present invention;

[0036] Figure 2 Schematic diagram of the main structure-RIDTMD model;

[0037] Figure 3 Optimized the flowchart for GSAA;

[0038] Figure 4 Design parameter fitting validation diagram for RIDTMD;

[0039] Figure 5 The figure is a comparison of the frequency response curves of the corrected formula and the analytical formula. DETAILED DESCRIPTION

[0040] The following describes the embodiments of the present invention through specific examples. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments. The details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the following embodiments and features in the embodiments can be combined with each other unless they conflict.

[0041] While some exemplary embodiments of the present invention have been described for purposes of illustration, it should be understood that the present invention may be implemented in other ways not specifically shown in the drawings.

[0042] like Figure 1 、 Figure 2 As shown, an embodiment of the present invention provides a method for optimizing parameters of a rotating inertia dual tuned mass damper, wherein the rotating inertia dual tuned mass damper (RIDTMD) is as follows: Figure 2 As shown, it includes a tuned mass block, an inertia container, a main spring, a secondary spring, and a damper. The inertia container converts linear motion into flywheel rotational motion through a transmission mechanism, generating an apparent mass amplification effect. The rotary inertia dual tuned mass damper can be anchored to the floor structure on one side without the need for cross-floor installation.

[0043] like Figure 1 As shown, a method for optimizing parameters of a rotating inertia dual tuned mass damper according to this embodiment specifically includes the following steps:

[0044] S1: Construct the main structural motion equations including the rotating inertial dual tuned mass damper;

[0045] Its expression is:

[0046]

[0047] Where: M is the mass of the main structure; C is the stiffness of the main structure; K is the damping of the main structure; m is the tuned mass; k1 is the primary stiffness of the damper; k2 is the secondary stiffness of the damper; c is the damping of the damper; m b is the inertia coefficient of the damper; x(t) is the displacement response of the main structure; x1(t) is the displacement response of the tuned mass; x2(t) is the displacement response of the inertia; and F(t) is the excitation of the main structure.

[0048] In this embodiment, the main structure of the building is a single degree of freedom system, and the excitation it receives is a simple harmonic load, which is expressed as: F(t) = fsin(ωp t).

[0049] S2: Select combination variables from the design variable space of the rotating inertia dual tuned mass damper, and use the genetic simulated annealing algorithm (GSAA) to optimize the parameters of each combination variable with the goal of minimizing the maximum acceleration frequency response of the main structure to obtain the optimal parameter data set;

[0050] In some embodiments, during the genetic simulated annealing algorithm (GSAA) parameter optimization process, the objective function used is:

[0051]

[0052] st0.8≤q≤1.0,1.0≤η≤1.2,

[0053] 0≤μ b ≤2μ,0≤ζ≤0.05

[0054] Where: H(Ω) is the acceleration frequency response function, which is derived from the main structure motion equation; q is the main tuning frequency ratio of RIDTMD; η is the sub-tuning frequency ratio of RIDTMD; μ b is the secondary mass ratio of RIDTMD; ζ is the damping ratio of RIDTMD; ζ0 is the damping ratio of the main structure; μ is the main mass ratio of RIDTMD. The expressions of the above parameters are:

[0055]

[0056] The design variables include the main structure damping ratio ζ0 and the main mass ratio μ. The design parameters to be optimized include the main tuning frequency ratio q, the sub-tuning frequency ratio η, the sub-mass ratio μ b , damping ratio ζ.

[0057] Genetic simulated annealing algorithm (GSAA) parameters: population size 200, maximum number of iterations 100, selection ratio 0.9, crossover probability 0.9, mutation probability 0.001, initial temperature 100, and annealing rate 0.5.

[0058] A full combination traversal optimization (step size Δ = 0.005) is performed in the design variable space composed of the main structure damping ratio ζ0∈[0.005,0.05] and the main mass ratio μ∈[0.005,0.05]. Each variable combination is optimized 200 times independently to form the optimal parameter data set.

[0059] In some embodiments, by embedding the annealing selection strategy of the Metropolis criterion in the selection, crossover and mutation processes of the genetic algorithm, a hybrid optimization mechanism with both global optimization capabilities and local fine search is formed, which can effectively meet the optimization requirements of the complex parameter space of RIDTMD.

[0060] like Figure 3 As shown, the genetic simulated annealing algorithm (GSAA) used in this embodiment specifically includes:

[0061] (1) Initialize the population: Randomly generate parameter combinations {q,η,μ b ,ζ};

[0062] (2) Calculate fitness: the objective function value is used as the basis for selection;

[0063] (3) Genetic algorithm operations: selection, crossover, and mutation;

[0064] (4) Embedding Metropolis criterion: with probability e -Δf / T Accept the inferior solution (Δf is the fitness difference, T is the current temperature);

[0065] (5) Cooling update: T k+1 =0.5T k .

[0066] S3: Clean the optimal parameter data set obtained in step S2 based on the IQR criterion; specifically, it includes:

[0067] Calculate the interquartile range IQR = Q3-Q1 of each parameter in the 200 optimization results;

[0068] Outliers outside [Q1-1.5IQR, Q3+1.5IQR] were eliminated.

[0069] IQR criterion cleaning can effectively eliminate the pseudo-convergence phenomenon caused by random initial values ​​in the optimization process, and provide a high-quality data basis for the correction factor coefficient fitting.

[0070] S4: Construct correction factors and establish a nonlinear mapping model of parameter correction factors through tensor basis function expansion: Specifically:

[0071] like Figure 4 As shown, the correction factor is defined as:

[0072]

[0073] Where: β P is the parameter correction factor, whose subscript P∈{q,η,μ b ,ζ}; and P CF (μ) are the average values ​​and theoretical closed-form solutions of the optimized design parameters respectively;

[0074] The expression of the tensor basis function nonlinear mapping model is:

[0075]

[0076] Among them: a P 、b P 、c P d P 、e P 、g P is the correction factor fitting coefficient, and its value is shown in Table 1.

[0077] Table-1 Fitting coefficients

[0078]

[0079] In some embodiments, step S4 performs global fitting based on the Levenberg-Marquardt algorithm, and the goodness of fit of each parameter (R 2 ) are all over 0.9975.

[0080] S5: Multiply the theoretical closed-form solution by the parameter correction factor to obtain the design parameters. The expression of the design parameters is:

[0081]

[0082] Where: q corr. is the correction result of the main tuning frequency ratio; η corr. The correction result of this tuning frequency ratio; μ b,corr. is the correction result of the secondary mass ratio; corr. is the correction result of the damping ratio; β q (ζ0,μ),β η (ζ0,μ), β ζ (ζ0,μ) are the correction factors obtained by substituting the nonlinear mapping model of the parameter correction factor into the fitting coefficients corresponding to the coefficients to be optimized. For example, substitute the parameter q in the first row of Table-1 into β P From the expression of (ζ0,μ), we can get β d (ζ0,μ).

[0083] In step S5, the parameter correction factor can make up for the deficiency of the theoretical closed-form solution that does not consider the damping of the main structure, and provides an explicit expression that is convenient for engineering application.

[0084] In a specific example, a 10 m × 6 m prestressed concrete beam-string floor has a first-order modal frequency of 3.489 Hz, a mass of 8583 kg, and a damping ratio of 0.05. The design objective is to suppress vertical vibrations induced by a single-person jumping excitation (see Xiong and Chen, 2018 for the power spectrum model).

[0085] 1. RIDTMD parameter optimization process:

[0086] Set the main mass ratio μ = 0.05.

[0087] Substitute into the correction formula to calculate:

[0088] β q =1.00+6.70×0.05×0.05-0.40×0.05 2 -5.00×0.05 2 =1.0032

[0089] q=1 / (1+0.05) 0.5 ×1.0032=0.9759×1.0032=0.9791

[0090] β η =1.00+0.24×0.05+0.30×0.05 2 +4.00×0.05 2 =1.0228

[0091] η=(1+0.05) / (1-0.05)×1.0228=1.1053×1.0228=1.1304

[0092] β μb =1.00+2.00×0.05+25.00×0.05×0.05-5.40×0.05 2 =1.1490

[0093] μ b =2×0.05×(1-0.05) / (1+0.05) 2 ×1.1490=0.0862×1.1490=0.0990

[0094] β ζ =0.88+8.00×0.050=1.2800

[0095] ζ=((10 / 3-3 / 20×0.05)×0.05 3 / (1+0.05) 3 ) 0.5 ×1.2800=0.0190×1.2800=0.0243

[0096] 2. Vibration reduction effect verification

[0097] Install the RIDTMD at the center of the floor (the most unfavorable response point).

[0098] Input the power spectrum of a single-person jumping load and calculate the root mean square acceleration (RMS) of the floor:

[0099]

[0100] Frequency response curve comparison Figure 5 As shown:

[0101] Analytical formula: There are three asymmetric peaks at Ω = 0.875, 1.035, and 1.0225 (low on the left and high on the right)

[0102] After correction using the method of this embodiment, the amplitudes of the three peaks are symmetrical, and the main peak is reduced by 9.75%.

[0103] The above embodiments are merely illustrative of the principles and effects of the present invention and are not intended to limit the present invention. Anyone skilled in the art may modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by one of ordinary skill in the art without departing from the spirit and technical principles disclosed herein are intended to be covered by the claims of the present invention.

Claims

1. A method for optimizing the parameters of a rotating inertia dual tuned mass damper, comprising the following steps: S1: Construct the main structural motion equations including the rotating inertial dual tuned mass damper; S2: Select combination variables from the design variable space of the rotating inertia dual tuned mass damper, use the genetic simulated annealing algorithm to optimize the parameters of each combination variable with the goal of minimizing the maximum acceleration frequency response of the main structure, and obtain the optimal parameter data set; S3: Clean the optimal parameter data set based on the IQR criterion; S4: Construct correction factors and establish a nonlinear mapping model of parameter correction factors through tensor basis function expansion; S5: Multiply the theoretical closed-form solution by the parameter correction factor to obtain the design parameter expression of the rotating inertia dual tuned mass damper.

2. The method for optimizing parameters of a rotating inertia dual tuned mass damper according to claim 1, wherein: The expression of the main structure motion equation in step S1 is: Where: M is the mass of the main structure; C is the stiffness of the main structure; K is the damping of the main structure; m is the tuned mass; k1 is the primary stiffness of the damper; k2 is the secondary stiffness of the damper; c is the damping of the damper; m b is the inertia coefficient of the damper; x(t) is the displacement response of the main structure; x1(t) is the displacement response of the tuned mass; x2(t) is the displacement response of the inertia; and F(t) is the excitation of the main structure.

3. The method for optimizing parameters of a rotating inertia dual tuned mass damper according to claim 2, wherein: In step S2, the design variables include the main structure damping ratio ζ0 and the damper main mass ratio μ; the design parameters to be optimized include the main tuning frequency ratio q, the secondary tuning frequency ratio η, the secondary mass ratio μ b , damping ratio ζ; the objective function expression used by the genetic simulated annealing algorithm is: st0.8≤q≤1.0,1.0≤η≤1.2, 0≤μ b ≤2μ,0≤ζ≤0.05 Where: H(Ω) is the acceleration frequency response function.

4. The method for optimizing parameters of a rotating inertia dual tuned mass damper according to claim 3, wherein: In step S2, combination variables are selected in the design variable space composed of the main structure damping ratio ζ0∈[0.005,0.05] and the main mass ratio μ∈[0.005,0.05] according to a predetermined step size, and each combination variable includes each design variable.

5. The method for optimizing parameters of a rotating inertia dual tuned mass damper according to claim 3, wherein: In step S4: The correction factor is defined as: Where: β P is the parameter correction factor, whose subscript P∈{q,η,μ b ,ζ}; and P CF (μ) are the average values ​​and theoretical closed-form solutions of the optimized design parameters respectively; The expression of the parameter correction factor nonlinear mapping model is: Among them: a P 、b P 、c P d P 、e P 、g P is the fitting coefficient of the correction factor, which is obtained by global optimization of the Levenberg-Marquardt algorithm based on the optimal parameter data set.

6. The method for optimizing parameters of a rotating inertia dual tuned mass damper according to claim 5, wherein: The expressions of the design parameters of the rotating inertia dual tuned mass damper in step S5 are: Where: q corr. is the correction result of the main tuning frequency ratio; η corr. The correction result of this tuning frequency ratio; μ b,corr. is the correction result of the secondary mass ratio; corr. is the correction result of the damping ratio; β q (ζ0,μ),β η (ζ0,μ), β ζ (ζ0,μ) are the correction factors obtained by substituting the nonlinear mapping model of each parameter correction factor into the fitting coefficient.

7. A vibration reduction system, characterized in that: It comprises a rotational inertia dual tuned mass damper designed using the rotational inertia dual tuned mass damper parameter optimization method described in claims 1 to 6; the rotational inertia dual tuned mass damper is installed in a large-span floor structure to suppress the acceleration response caused by human-induced vibration.

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