Dynamic modeling and parameter optimization design method of field operation platform with inertia capacity vibration reduction system

Abstract

The invention discloses a method for dynamic modeling and parameter optimization design of a field work platform with an inertia capacity vibration reduction system, including S1: establishing a cone model representing the vertical interaction between foundation soil and an exposed disc foundation, and calculating the vibration impedance of the dynamic interaction between the foundation soil and the outrigger chassis foundation of the field work platform; S2: establishing a motion control equation of a field work platform model with an inertia capacity vibration reduction system considering the SSI effect, and deriving an analytical expression for the amplitude amplification factor; S3: using the H of the displacement amplitude of the work platform as the ∞ norm is the optimization target, and the displacement amplitude of the working platform is H ∞ The norm is the optimization target, and the optimal stiffness and optimal damping of the three inertia damping systems are obtained by genetic algorithm, and the empirical formula suitable for engineering is obtained by least square fitting. The present invention can provide a design method for the vibration reduction design of the field work platform and improve the dynamic stability of its construction operation.

Description

Technical Field

[0001] This invention belongs to the technical field of vibration reduction systems for work platforms, specifically relating to a dynamic modeling and parameter optimization design method for a field work platform with an inertial capacitance vibration reduction system. Background Technology

[0002] Field work platforms, as highly mobile and multifunctional lifting machinery, are widely used in construction sites, maintenance of gates and related hydraulic metal structures, equipment and advertising installation, airport renovation, and high-altitude cleaning. Interference from worker operations or machine vibrations can cause the work platform to vibrate, severely impacting worker stability, comfort, and safety, and reducing operational accuracy. Therefore, vibration reduction design and improved dynamic stability of work platforms are of paramount importance. When field work platforms operate at heights in construction sites, mining areas, and other environments, especially on riverbanks in water conservancy projects, the soft soil interacts dynamically with the platform's outriggers, altering the system's dynamic characteristics. Since vibration reduction design must consider the system's dynamic characteristics, the soil-structure interaction (SSI) effect cannot be ignored in the dynamic modeling and vibration reduction design of field work platforms.

[0003] Dynamic vibration absorbers are a commonly used vibration control structure in engineering practice. The classic Voigt-type dynamic vibration absorber, composed of a spring, damper, and mass block, can effectively reduce the amplitude of the main system and broaden the applicable range of excitation frequencies by adjusting the period of the additional system to be close to the fundamental period of the main system. However, when the working platform bears a large weight, the mass block in the Voigt-type dynamic vibration absorber usually needs to have a larger value to achieve the ideal vibration reduction effect, which greatly reduces the mobility of the field working platform. Summary of the Invention

[0004] The purpose of this invention is to provide a dynamic modeling and parameter optimization design method for field operation platforms with inertial capacitance vibration reduction system, and to solve two problems in the existing field operation platform vibration reduction design: (1) the existing design has brought errors to the calculation of the dynamic characteristics of the main system due to ignoring the SSI effect during field operation; (2) the existing traditional spring-damper-mass block vibration reduction system has reduced the mobility performance of the field operation platform due to its large mass.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] A method for dynamic modeling and parameter optimization design of field operation platforms with inertial capacitance vibration reduction systems includes the following steps:

[0007] S1: Establish a cone model to represent the vertical interaction between the foundation soil and the exposed circular foundation, and calculate the vibration impedance of the dynamic interaction between the foundation soil and the outrigger chassis foundation of the field operation platform.

[0008] S2: Establish the motion control equations of the field operation platform model with inertial capacitance damping system considering SSI effect, and derive the analytical expression of amplitude amplification factor;

[0009] S3: Optimize the parameters of the inertial capacitance vibration reduction system by taking the H∞ norm of the displacement amplitude of the work platform as the optimization target.

[0010] Traditional vibration reduction systems use a spring-damper-mass block configuration. However, literature indicates that a large mass is required for effective vibration reduction, which reduces the mobility of the work platform. Therefore, this invention uses inertial capacitance instead of a mass block. Inertial capacitance, a novel element utilizing the inertia of mass units at both ends to achieve vibration reduction, exhibits a force proportional to the relative acceleration at those ends. Compared to traditional dynamic vibration absorbers, the inertial capacitance mass far exceeds its physical mass, sometimes by tens of times, thus avoiding the large mass of vibration-damping elements in traditional dynamic vibration absorbers. Therefore, this application introduces inertial capacitance into the vibration reduction design of field work platforms, establishing a mechanical model of a field work platform with inertial capacitance vibration reduction system considering the SSI effect. Based on this, the H-axis of the displacement amplitude of the upper structure of the work platform is used as the basis for the design. ∞ Using the norm as the optimization objective, the optimal design parameters for the inertial capacitance vibration reduction system are derived. This invention effectively improves the dynamic stability of field operation platforms while ensuring their mobility.

[0011] Further optimization is needed. The dynamic interaction between the foundation soil and the outrigger chassis of the field operation platform can be described by vibration impedance, which represents the relationship between force and displacement at their interface, i.e., stiffness coefficient and damping coefficient. Although my country's current "Code for Design of Foundations of Power Machinery" recommends stiffness coefficients and damping coefficients characterizing the dynamic interaction between various foundation soils and mechanical equipment foundations based on the accumulation and statistics of a large amount of experimental data, these recommended parameters have significant errors as machine speeds increase and geological conditions become more diverse. In step S1, the model considers the contact surface between the foundation soil and the outrigger chassis of the field operation platform as an exposed disk with radius r0, and replaces the semi-infinite foundation with a truncated semi-infinite elastic cone with a vertex height z0; the shear modulus of the foundation soil is G. s Poisson's ratio is υ, and the shear wave velocity is V. s ;

[0012] Assuming the outrigger chassis experiences a vertical displacement of w0 under a vertical load P0, the vibration impedance of the dynamic interaction between the foundation soil and the outrigger chassis foundation of the field operation platform can be obtained by calculating the wave propagation process using the cone model theory. for:

[0013]

[0014] In the formula, the static stiffness of the exposed circular foundation is... Dimensionless stiffness Dimensionless damping is Dimensionless frequency a0=ωr0 / V s Imaginary unit ω is the characteristic frequency; where the relevant parameters c = 2V s ;

[0015] Therefore, the spring constant K can be obtained. f and damping coefficient C f for:

[0016] K f =N·K s K p (a0) (2)

[0017] -C f =NK s C p (a0)(3) where N is the number of outriggers distributed on the left and right sides of the field operation platform.

[0018] Further optimization is achieved in step S2, where the motion control equations for the field operation platform model containing the inertial capacitance vibration reduction system are established as follows:

[0019] The lower base and upper platform of the field operation platform are simplified as concentrated mass blocks represented by m1 and m2, respectively, and the lifting connection structure on both sides is equivalent to a spring with stiffness k; the connection between the upper platform and the lower base of the operation platform contains inertial volume m. i Spring k d and damping c d The vibration reduction system Y(m) consists of i k d c d );

[0020] The vibration reduction system Y includes the following three forms:

[0021] The first form is: spring k d Damping c d and habitual tolerance m i When three elements are connected in series, it is called a series type.

[0022] The second form is: damping c d and habitual tolerance m i After parallel connection with spring k d Series connection, denoted as hybrid type I;

[0023] The third form is: damping c d and spring k d After parallel connection with inertial capacity m i Series connection, denoted as hybrid type II;

[0024] The upper platform is subjected to a vertical harmonic excitation Fsin(ωt) with frequency ω and amplitude F, where t is time; the degrees of freedom of each node in the vibration reduction system are represented by displacement x. n Let n = 0, 1, 2, 3; according to d'Alembert's principle, the motion control equations of the three field operation platform mechanical models with inertial capacitance damping systems are as follows:

[0025] The motion control equations for a field work platform with a series inertial capacitance damping system are as follows:

[0026]

[0027] The motion control equations for the field operation platform including the hybrid type I inertial capacitance vibration reduction system are as follows:

[0028]

[0029] The motion control equations for the field operation platform including the hybrid type II inertial capacitance vibration reduction system are as follows:

[0030]

[0031] Further optimization is achieved by deriving the analytical expression for the amplitude amplification factor in step S2 as follows:

[0032] Introduce the following parameters: Substituting this into the above motion control equations and performing a Laplace transform, the displacement of the upper platform can be obtained:

[0033]

[0034] Where: i = 1, 2, 3 correspond to the series inertial-capacitive vibration reduction system, the hybrid type I inertial-capacitive system, and the hybrid type II inertial-capacitive system, respectively;

[0035] Equation (7) is further dimensionless, and parameters are defined as follows:

[0036]

[0037] This leads to the analytical expression for the amplitude amplification factor of the upper platform:

[0038]

[0039] The coefficient in the formula is as follows:

[0040] A 11 =-4δξ2λ 4 +2[2δ(μ+ν 2 )ξ2+β(δνξ1+ξ2+δμξ2)]λ 2 -2b(μ+ν 2 )ξ2;

[0041] B 11 =δ(β+8νξ1ξ2)λ 3 -β[δ(μ+ν 2 )+4νξ1ξ2]λ;

[0042] C 11 =4δξ2λ 6 -2{2δ(1+μ+ν 2 )ξ2+β[ξ2+δ(νξ1+ξ2+μξ2)]}λ 4 +2{2sn 2 ξ2+β[(1+μ+ν 2 )ξ2+δν(ξ1+νξ2)]}λ 2 -2bv 2 ξ2;

[0043] D 11 =-δ(β+8νξ1ξ2)λ 5 +{8νξ1ξ2+β[4νξ1ξ2+δ(1+μ+ν 2 +4νξ1ξ2)]}λ 3 -βν(σν+4ξ1ξ2)λ;

[0044] A 22 =2s 4 -{β(1+δμ)+2[δ(μ+ν 2 )+4νξ1ξ2]}λ 2 +vn 2 +bm;

[0045] B 22 =-4[δνξ1+(1+δμ)ξ2]λ 3 +2[βνξ1+2(μ+ν 2 )ξ2]λ;

[0046] C 22 =-2s 6 +{β(1+δ+δμ)+2[4νξ1ξ2+δ(1+μ+ν 2 +4νξ1ξ2)]}λ4 -{β[1 + μ + (1 + δ)ν 2 +2ν(δν + 4ξ1ξ2)}λ 2 +βν 2 ;

[0047] D 22 = 4[δξ1 + (1 + δ + δμ)ξ2]λ 5 +2ν(βξ1 + 2νξ2)λ - 2{β(1 + δ)νξ2 + 2[(1 + μ + ν 2 )ξ2 + δν(ξ1 + νξ2)]}λ 3 ;

[0048] A 33 = 2δλ 4 -[β(1 + δμ)+2ν(δν + 4ξ1ξ2)]λ 2 +(βν 2 +βμ);

[0049] B 33 =-4(δνξ1 + ξ2)λ 3 +2[νξ1+(βμ + 2ν 2 )ξ2]λ;

[0050] C 33 =-2δλ 6 +[β(1 + δ + δμ)+2(δ + δν 2 +4νξ1ξ2)]λ 4 -{2ν(δν + 4ξ1ξ2)+β[1 + μ+(1 + δ)ν 2 +4νξ1ξ2]}λ 2 +βν 2 ;

[0051] D 33 = 4(δνξ1 + ξ2)λ 5 +2ν[2νξ2+β(ξ1 + νξ2)]λ - 2{β[(1 + δ)νξ1+(1 + μ)ξ2]-2[δνξ1+(1 + ν 2 )ξ2]}λ 3

[0052] For further optimization, in step S3, taking the H ∞ norm of the displacement amplitude of the upper platform established according to equation (9) as the optimization objective, which can be expressed in mathematical terms as:

[0053] Objective function:

[0054]

[0055] Constraints:

[0056]

[0057] Given a set of inertia-mass ratios δ={δ1,δ2,δ3,……,δ M In the case of}, the above optimization model is solved using a genetic algorithm to obtain a set of corresponding optimal stiffness ratios. and a set of corresponding optimal damping ratios Where M represents the number of types of inertia-mass ratio δ, and M is the highest order of the fitting function with respect to inertia-mass ratio δ, which is a positive integer.

[0058] The optimal stiffness ratio and optimal damping ratio are fitted into empirical formulas suitable for practical engineering as follows:

[0059]

[0060] In the formula, θ m-1 and Let m be the undetermined coefficients to be fitted, where m∈{1,2,3,……,M};

[0061] Based on the principle of least squares, let the sum of squared errors of the coefficients of the optimal stiffness ratio fitting formula and the optimal damping ratio fitting formula be S1 and S2, respectively. To obtain the minimum values ​​of S1 and S2, the partial derivatives of S1 and S2 with respect to each term must be 0. This can be expressed mathematically as follows:

[0062]

[0063] Rearranging equations (12) and (13) into matrix form, we can see the following:

[0064]

[0065] Solving matrices (16) and (17) will yield the unknown coefficients in the fitting empirical formula.

[0066] Compared with the prior art, the present invention has the following beneficial effects:

[0067] 1. In this invention, the dynamic interaction between the foundation soil and the outrigger chassis of the work platform is described by vibration impedance. Three different inertial-capacitive-spring-damped vibration reduction structures are connected between the upper platform and the lower base body, thus forming a mechanical model of the field work platform with an inertial-capacitive vibration reduction system considering the SSI effect. By solving the motion control equations of the corresponding dynamic model, the analytical expression of the amplitude amplification factor of the work platform is obtained. The amplitude of the work platform displacement is expressed as H... ∞Using the norm as the optimization objective, numerical solutions for the optimal stiffness and optimal damping of three inertial capacitive vibration reduction systems were obtained through a genetic algorithm. Empirical formulas applicable to engineering were then derived through least squares fitting. The dynamic interaction between the foundation soil and the outrigger chassis of the field work platform was considered, making the mechanical model of the field work platform more consistent with actual conditions, improving the calculation accuracy of the dynamic characteristics of the field work platform, and laying the foundation for vibration reduction design of work platforms in complex environments.

[0068] 2. By using inertial capacitance elements instead of the mass blocks of traditional dynamic vibration absorbers, the defects of excessive mass of damping elements in traditional dynamic vibration absorbers are avoided. This not only ensures good dynamic stability but also reduces the overall mass of the field work platform containing the vibration damping system, greatly improving mobility. Attached Figure Description

[0069] Figure 1 A dynamic model of a field work platform with inertial capacitance damping system considering SSI effect;

[0070] Figure 2 A schematic diagram of a vibration reduction system containing inertial capacitance; wherein, Figure 2 (a) in the figure represents spring k. d Damping c d and habitual tolerance m i A schematic diagram of a vibration reduction system consisting of three components connected in series; Figure 2 (b) in the diagram represents damping c. d and habitual tolerance m i After parallel connection with spring k d Schematic diagram of a series vibration reduction system; Figure 2 (c) in the figure represents the damping c. d and spring k d After parallel connection with inertial capacity m i Schematic diagram of a series vibration reduction system;

[0071] Figure 3 This is a cone model representing the vertical dynamic interaction between the foundation soil and the exposed circular foundation; where, Figure 3 (a) in the figure represents a cone model under vertical load. Figure 3 (b) The mechanical equivalent model of the cone model;

[0072] Figure 4 This is a comparison chart of empirical formulas and numerical solutions for a series inertial compressive vibration reduction system in medium-hard soil foundations. Figure 4 (a) in the figure shows the relationship between the optimal stiffness ratio and the inertia-mass ratio; Figure 4 (b) in the figure shows the relationship between the optimal damping ratio and the inertia-mass ratio;

[0073] Figure 5 This is a comparison chart of empirical formulas and numerical solutions for a series inertial compressive vibration reduction system on medium-soft soil foundation. Figure 5 (a) in the figure shows the relationship between the optimal stiffness ratio and the inertia-mass ratio; Figure 5 (b) in the figure shows the relationship between the optimal damping ratio and the inertia-mass ratio;

[0074] Figure 6 A comparison diagram of empirical formulas and numerical solutions for a series inertial compressive vibration reduction system on a soft soil foundation is shown. Figure 6 (a) in the figure shows the relationship between the optimal stiffness ratio and the inertia-mass ratio; Figure 6 (b) in the figure shows the relationship between the optimal damping ratio and the inertia-mass ratio;

[0075] Figure 7 This is a comparison diagram of empirical formulas and numerical solutions for a mixed soil-concrete type I inertial compressive vibration reduction system on a medium-hard soil foundation. Figure 7 (a) in the figure shows the relationship between the optimal stiffness ratio and the inertia-mass ratio; Figure 7 (b) in the figure shows the relationship between the optimal damping ratio and the inertia-mass ratio;

[0076] Figure 8 This is a comparison chart of empirical formulas and numerical solutions for a mixed soil-concrete type I inertial-compressive vibration reduction system on a medium-soft soil foundation. Figure 8 (a) in the figure shows the relationship between the optimal stiffness ratio and the inertia-mass ratio; Figure 8 (b) in the figure shows the relationship between the optimal damping ratio and the inertia-mass ratio;

[0077] Figure 9 A comparison diagram of empirical formulas and numerical solutions for a type I inertial compressive vibration reduction system with soil-concrete composite structure on a soft soil foundation is shown. Figure 9 (a) in the figure shows the relationship between the optimal stiffness ratio and the inertia-mass ratio; Figure 9 (b) in the figure shows the relationship between the optimal damping ratio and the inertia-mass ratio;

[0078] Figure 10 This is a comparison chart of empirical formulas and numerical solutions for a mixed soil-concrete type II inertial compressive vibration reduction system on a medium-hard soil foundation. Figure 10 (a) in the figure shows the relationship between the optimal stiffness ratio and the inertia-mass ratio; Figure 10 (b) in the figure shows the relationship between the optimal damping ratio and the inertia-mass ratio;

[0079] Figure 11 This is a comparison chart of empirical formulas and numerical solutions for a mixed soil-concrete type II inertial-compressive vibration reduction system on medium-soft soil foundations. Figure 11 (a) in the figure shows the relationship between the optimal stiffness ratio and the inertia-mass ratio; Figure 11 (b) in the figure shows the relationship between the optimal damping ratio and the inertia-mass ratio;

[0080] Figure 12 A comparison diagram of empirical formulas and numerical solutions for a type II inertial compressive vibration reduction system with soil-soil composite structure on a soft soil foundation is shown. Figure 12 (a) in the figure shows the relationship between the optimal stiffness ratio and the inertia-mass ratio; Figure 12 (b) in the figure shows the relationship between the optimal damping ratio and the inertia-mass ratio;

[0081] Figure 13 Curves showing the variation of amplitude amplification factor with excitation frequency for three field operation platforms with different inertial capacitance vibration reduction systems; Figure 13 (a) in the figure is the curve of the amplitude amplification factor of the field operation platform of the series inertial-capacitive vibration reduction system as a function of the excitation frequency, and the relationship between the optimal stiffness ratio and the inertia-mass ratio. Figure 13 (b) in the figure is the curve of the amplitude amplification factor of the field operation platform of the hybrid type I inertial-capacitive vibration reduction system as a function of the excitation frequency, and the relationship between the optimal stiffness ratio and the inertia-mass ratio. Figure 13 (c) in the figure is the curve of the amplitude amplification factor of the field operation platform of the hybrid type II inertial-capacitive vibration reduction system as a function of the excitation frequency, and the relationship between the optimal stiffness ratio and the inertia-mass ratio. Detailed Implementation

[0082] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0083] This invention proposes a method for dynamic modeling and parameter optimization design of a field work platform with inertial capacitance damping system considering the SSI effect. For example... Figure 1 As shown, the implementation of the present invention will be described in detail below with reference to specific examples, so that the advantages and features of the present invention can be more easily understood by those skilled in the art.

[0084] Step 1: Establish a cone model representing the vertical interaction between the foundation soil and the exposed circular foundation, as shown in the figure. Calculate the vibration impedance of the dynamic interaction between the foundation soil and the outrigger base of the field work platform. Among them, Figure 3 (a) in the figure represents a cone model under vertical load. Figure 3 (b) The mechanical equivalent model of the cone model.

[0085] In this embodiment, m1 = 8000 kg, m2 = 3000 kg, r0 = 1.382 m, and k = 0.8 × 10⁻⁶. 8 N / m, N=2. According to the "Code for Seismic Design of Buildings" (GB 50011-2010), the basic parameters (shear wave velocity V) of three typical foundation soils—medium-hard soil, medium-soft soil, and soft soil—are selected. s Soil density ρ s The Poisson's ratio (ν) is shown in Table 1.

[0086] Table 1 Material properties of foundation soil

[0087]

[0088] The natural frequency of the superstructure The stiffness coefficient K of the three foundation soils was obtained. f Damping coefficient C f As shown in Table 2.

[0089] Table 2 Stiffness coefficients K of three types of foundation soil f Damping coefficient C f

[0090]

[0091] Step 2: Establish the motion control equations for the field operation platform model with inertial capacitance damping system considering SSI effect, and derive the analytical expression for the amplitude amplification factor. The lower base body and upper platform of the field operation platform are simplified as concentrated mass blocks represented by m1 and m2, respectively, and the lifting connection structures on both sides are equivalent to springs with stiffness k.

[0092] like Figure 2 As shown, three different types of vibration reduction systems Y(m) containing inertial capacity 3, spring 1, and damping 2 are installed between the upper platform and the lower base of the field operation platform. i k d c d ).in, Figure 2 (a) in the figure represents spring k. d Damping c d and habitual tolerance m i When three elements are connected in series, it is called a series type. Figure 2 (b) in the diagram represents damping c. d and habitual tolerance m i After parallel connection with spring k d Series connection, denoted as hybrid type I; Figure 2 (c) in the figure represents the damping c. d and spring k d After parallel connection with inertial capacity m i Series connection, denoted as hybrid type II.

[0093] The degrees of freedom of each node in the vibration reduction system are represented by displacement x. n (n = 0, 1, 2, 3) represents the system. Based on d'Alembert's principle, the motion control equations for three types of inertial capacitive damping systems can be listed as follows:

[0094] The motion control equations for a field work platform with a series inertial capacitance damping system are as follows:

[0095]

[0096] The motion control equations for the field operation platform including the hybrid type I inertial capacitance vibration reduction system are as follows:

[0097]

[0098] The motion control equations for a field work platform with a series type II inertial capacitance damping system are as follows:

[0099]

[0100] Introduce the following parameters: Substituting into the above kinematic equations and performing a Laplace transform, the displacement law of the upper platform is obtained as follows:

[0101]

[0102] in: The imaginary unit is i, where i = 1, 2, 3 correspond to the series-type inertial-capacitive vibration reduction system, the hybrid type I inertial-capacitive system, and the hybrid type II inertial-capacitive system, respectively.

[0103] Further dimensionless transformation, while defining parameters:

[0104]

[0105] This leads to the analytical expression for the amplitude amplification factor of the upper platform:

[0106]

[0107] The coefficients in the formula are as follows:

[0108] A 11 =-4δξ2λ 4 +2[2δ(μ+ν 2 )ξ2+β(δνξ1+ξ2+δμξ2)]λ 2 -2β(μ+ν 2 )ξ2

[0109] B 11 =δ(β+8νξ1ξ2)λ 3 -β[δ(μ+ν 2 )+4νξ1ξ2]λ

[0110] C 11 =4δξ2λ 6 -2{2δ(1+μ+ν 2 )ξ2+β[ξ2+δ(νξ1+ξ2+μξ2)]}λ 4 +2{2δν 2 ξ2+β[(1+μ+ν 2 )ξ2+δν(ξ1+νξ2)]}λ2 -2bv 2 ξ2

[0111] D 11 =-δ(β+8νξ1ξ2)λ 5 +{8νξ1ξ2+β[4νξ1ξ2+δ(1+μ+ν 2 +4νξ1ξ2)]}λ 3 -βν(σν+4ξ1ξ2)λ

[0112] A 22 =2s 4 -{β(1+δμ)+2[δ(μ+ν 2 )+4νξ1ξ2]}λ 2 +vn 2 +vm

[0113] B 22 =-4[δνξ1+(1+δμ)ξ2]λ 3 +2[βνξ1+2(μ+ν 2 )ξ2]λ

[0114] C 22 =-2s 6 +{β(1+δ+δμ)+2[4νξ1ξ2+δ(1+μ+ν 2 +4νξ1ξ2)]}λ 4

[0115] -{β[1+μ+(1+δ)ν 2 ]+2ν(σν+4ξ1ξ2)}λ 2 +vn 2

[0116] D 22 =4[δξ1+(1+δ+δμ)ξ2]λ 5 +2ν(βξ1+2νξ2)λ-2{β(1+δ)νξ2+2[(1+μ+ν 2 )ξ2+δν(ξ1+νξ2)]}λ 3

[0117] A 33 =2s 4 -[β(1+σμ)+2ν(σν+4ξ1ξ2)]λ 2 +(bn 2 +bm)

[0118] B 33 =-4(δνξ1+ξ2)λ 3 +2[νξ1+(βμ+2ν 2 )ξ2]λ

[0119] C 33 =-2δλ 6 +[β(1+δ+δμ)+2(δ+δν 2 +4νξ1ξ2)]λ 4 -{2ν(δν+4ξ1ξ2)+β[1+μ+(1+δ)ν 2 +4νξ1ξ2]}λ 2 +βν 2

[0120] D 33 =4(δνξ1+ξ2)λ 5 +2ν[2νξ2+β(ξ1+νξ2)]λ-2{β[(1+δ)νξ1+(1+μ)ξ2]-2[δνξ1+(1+ν 2 )ξ2]}λ 3

[0121] Step 3: Establish the H-axis of the displacement amplitude of the work platform ∞ The norm is used as the optimization objective, and a genetic algorithm is used for numerical solution. The optimization results of the series inertial-compressive vibration reduction system are as follows: Figure 4-6 As shown in Table 3. Among them, Figure 4 This is a comparison chart of empirical formulas and numerical solutions for a series inertial compressive vibration reduction system in medium-hard soil foundations. Figure 4 (a) in the figure shows the relationship between the optimal stiffness ratio and the inertia-mass ratio; Figure 4 (b) in the figure shows the relationship between the optimal damping ratio and the mass-inertia ratio. Figure 5 This is a comparison chart of empirical formulas and numerical solutions for a series inertial compressive vibration reduction system on medium-soft soil foundation. Figure 5 (a) in the figure shows the relationship between the optimal stiffness ratio and the inertia-mass ratio; Figure 5 (b) in the figure shows the relationship between the optimal damping ratio and the mass-inertia ratio. Figure 6 A comparison diagram of empirical formulas and numerical solutions for a series inertial compressive vibration reduction system on a soft soil foundation is shown. Figure 6 (a) in the figure shows the relationship between the optimal stiffness ratio and the inertia-mass ratio; Figure 6 (b) in the figure shows the relationship between the optimal damping ratio and the mass-inertia ratio.

[0122] The optimization results of the hybrid type I inertial-capacitive system are as follows: Figure 7-9 As shown in Table 4. Among them, Figure 7 This is a comparison diagram of empirical formulas and numerical solutions for a mixed soil-concrete type I inertial compressive vibration reduction system on a medium-hard soil foundation. Figure 7 (a) in the figure shows the relationship between the optimal stiffness ratio and the inertia-mass ratio; Figure 7 (b) in the figure shows the relationship between the optimal damping ratio and the mass-inertia ratio. Figure 8 This is a comparison chart of empirical formulas and numerical solutions for a mixed soil-concrete type I inertial-compressive vibration reduction system on a medium-soft soil foundation. Figure 8 (a) in the figure shows the relationship between the optimal stiffness ratio and the inertia-mass ratio; Figure 8 (b) in the figure shows the relationship between the optimal damping ratio and the mass-inertia ratio. Figure 9 A comparison diagram of empirical formulas and numerical solutions for a type I inertial compressive vibration reduction system with soil-concrete composite structure on a soft soil foundation is shown. Figure 9 (a) in the figure shows the relationship between the optimal stiffness ratio and the inertia-mass ratio; Figure 9 (b) in the figure shows the relationship between the optimal damping ratio and the mass-inertia ratio.

[0123] The optimization results of the hybrid type II inertial-capacitive system are as follows: Figure 10-12 As shown in Table 5. Among them, Figure 10 This is a comparison chart of empirical formulas and numerical solutions for a mixed soil-concrete type II inertial compressive vibration reduction system on a medium-hard soil foundation. Figure 10 (a) in the figure shows the relationship between the optimal stiffness ratio and the inertia-mass ratio; (b) in the figure shows the relationship between the optimal damping ratio and the inertia-mass ratio. Figure 11 The figure shows a comparison of empirical formulas and numerical solutions for a mixed soil-conductivity type II vibration reduction system for medium-soft soil foundations. In the figure, 11(a) is the relationship between the optimal stiffness ratio and the inertia-mass ratio. Figure 11 (b) in the figure shows the relationship between the optimal damping ratio and the mass-inertia ratio. Figure 12 A comparison diagram of empirical formulas and numerical solutions for a type II inertial compressive vibration reduction system with soil-soil composite structure on a soft soil foundation is shown. Figure 12 (a) in the figure shows the relationship between the optimal stiffness ratio and the inertia-mass ratio; Figure 12 (b) in the figure shows the relationship between the optimal damping ratio and the mass-inertia ratio.

[0124] Table 3

[0125]

[0126] Table 4

[0127]

[0128] Table 5

[0129]

[0130] Using the least squares method, the optimal stiffness ratio and optimal damping ratio obtained from Tables 3, 4, and 5 are fitted with formulas to obtain empirical formulas applicable to engineering projects, as shown in Tables 6, 7, and 8.

[0131] In practical engineering calculations, the interaction effect between the soil and the outrigger chassis is generally not considered when calculating field operation platforms; that is, the soil is treated as a rigid foundation. However, the model of this invention introduces K... f and C f The value of is taken into account the interaction between the soil and the foundation. The effect after its introduction is... Figure 13It can be seen that: without considering the SSI effect, the foundation is rigid; considering the SSI effect, the influence of foundation soils with different hardness levels on the vibration reduction effect can be observed. Among these, Figure 13 (a) in the figure is the curve of the amplitude amplification factor of the field operation platform of the series inertial capacitance vibration reduction system as a function of the excitation frequency; Figure 13 (b) in the figure is the curve of the amplitude amplification factor of the field operation platform of the hybrid type I inertial capacitive system as a function of the excitation frequency; Figure 13 (c) in the figure represents the curve of the amplitude amplification factor of the field operation platform of the hybrid type II inertial capacitive system as a function of the excitation frequency.

[0132] Table 6 Optimal Solution of Series-Type Inertial Compressive Vibration Reduction System

[0133]

[0134] Table 7 Optimal Solution of Hybrid Type I Inertial Compressive Vibration Reduction System

[0135]

[0136] Table 8 Optimal Solution of Hybrid Type II Inertial Compressive Vibration Reduction System

[0137]

[0138]

[0139] The above description is merely an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. Dynamic modeling and parameter optimization design method of field operation platform with inertia damping system, characterized in that: The steps include: S1: Establish a cone model to represent the vertical interaction between the foundation soil and the exposed disc foundation, and calculate the vibration impedance of the dynamic interaction between the foundation soil and the outrigger chassis foundation of the field operation platform; The model regards the contact surface between the foundation soil and the outrigger chassis as an exposed circular disk with a radius of r0, and uses a truncated semi-infinite elastic cone with a vertex height of z0 to replace the semi-infinite foundation; the shear modulus of the foundation soil is G s , Poisson's ratio is υ, and the shear wave velocity is V s ; Assuming that the vertical displacement of the outrigger chassis under the action of the vertical load P0 is w0, the vibration impedance of the dynamic interaction between the foundation soil and the outrigger chassis foundation of the field operation platform can be obtained by calculating its wave propagation process through the cone model theory: for: In the formula, the static stiffness of the disk foundation is Dimensionless stiffness The dimensionless damping is Dimensionless frequency a0 = ωr0 / Vs, imaginary unit ω is the characteristic frequency; the relevant parameters c=2V s ; From this, we can get the spring coefficient K f and the damping coefficient C f for: K f =N·K s K p (a0) (2) C f =N·K s C p (a0) (3) Wherein, N is the number of outriggers distributed on the left and right sides of the field operation platform; S2: Establish the motion control equation of the field operation platform model with inertia damping system considering SSI effect, and derive the analytical expression of amplitude amplification factor; The process of establishing the motion control equation of the field operation platform model with inertia damping system is as follows: The lower base body and upper platform of the field work platform are simplified as concentrated mass blocks represented by m1 and m2 respectively, and the lifting connection structure on both sides is equivalent to a spring with a stiffness of k; the connection between the upper platform and the lower base body of the work platform contains an inertia m i 、Spring k d and damping c d The vibration reduction system Y(m i , k d , c d ); The vibration reduction system Y includes the following three forms: The first form is: spring k d , damping c d and habitual capacity i The three are connected in series, which is recorded as series type; The second form is: Damping c d and habitual capacity i After parallel connection with spring k d Series connection, recorded as hybrid type I; The third form is: Damping c d and spring k d After parallel connection, the inertia m i connected in series, recorded as mixed type II; The upper platform is subjected to the vertical simple harmonic excitation Fsin(ωt) with a frequency of ω and an amplitude of F, where t is time; the degrees of freedom of each node of the vibration reduction system are expressed by displacement x n Indicates that n = 0, 1, 2, 3; according to the D'Alembert principle, the motion control equations of the mechanical models of three field operation platforms with inertia damping systems are as follows: The motion control equation of the field operation platform with a series inertia damping system is: The motion control equation of the field operation platform including the hybrid type I inertia damping system is: The motion control equation of the field operation platform including the hybrid type II inertia damping system is: The process of deriving the analytical expression for the amplitude amplification factor is as follows: Introduce the following parameters: Substitute it into the above motion control equation and solve it after Laplace transform to get the displacement of the upper platform: Where: i=1, 2, 3 correspond to the series inertia capacity vibration reduction system, the hybrid type I inertia capacity system, and the hybrid type II inertia capacity system respectively; Formula (7) is further dimensionless, and the parameters are defined: Then the analytical expression of the amplitude amplification factor of the upper platform is obtained: The coefficients in the formula are as follows: A 11 =-4δξ2λ 4 +2[2δ(μ+ν 2 )ξ2+β(δνξ1+ξ2+δμξ2)]λ 2 -2b(μ+ν 2 )ξ2; B 11 =δ(β+8νξ1ξ2)λ 3 -β[δ(μ+ν 2 )+4νξ1ξ2]λ; C 11 =4δξ2λ 6 -2{2δ(1+μ+ν 2 )ξ2+β[ξ2+δ(νξ1+ξ2+μξ2)]}λ 4 +2{2sn 2 ξ2+β[(1+μ+ν 2 )ξ2+δν(ξ1+νξ2)]}λ 2 -2bv 2 ξ2; D 11 =-δ(β+8νξ1ξ2)λ 5 +{8νξ1ξ2+β[4νξ1ξ2+δ(1+μ+ν 2 +4νξ1ξ2)]}λ 3 -βν(σν+4ξ1ξ2)λ; A 22 =2s 4 -{β(1+δμ)+2[δ(μ+ν 2 )+4νξ1ξ2]}λ 2 +vn 2 +bm; B 22 =-4[δνξ1+(1+δμ)ξ2]λ 3 +2[βνξ1+2(μ+ν 2 )ξ2]λ; C 22 =-2s 6 +{β(1+δ+δμ)+2[4νξ1ξ2+δ(1+μ+ν 2 +4νξ1ξ2)]}λ 4 -{β[1+μ+(1+δ)ν 2 ]+2ν(σν+4ξ1ξ2)}λ 2 +vn 2 ; D 22 =4[δξ1+(1+δ+δμ)ξ2]λ 5 +2ν(βξ1+2νξ2)λ-2{β(1+δ)νξ2+2[(1+μ+ν 2 )ξ2+δν(ξ1+νξ2)]}λ 3 ; A 33 =2s 4 -[β(1+σμ)+2ν(σν+4ξ1ξ2)]λ 2 +(bn 2 +bm); B 33 =-4(δνξ1+ξ2)λ 3 +2[νξ1+(βμ+2ν 2 )ξ2]λ; C 33 =-2s 6 +[β(1+δ+δμ)+2(δ+δν 2 +4νξ1ξ2)]λ 4 -{2ν(σν+4ξ1ξ2)+β[1+μ+(1+σ)ν 2 +4νξ1ξ2]}λ 2 +vn 2 ; D 33 =4(δνξ1+ξ2)λ 5 +2ν[2νξ2+β(ξ1+νξ2)]λ-2{β[(1+δ)νξ1+(1+μ)ξ2]-2[δνξ1+(1+ν 2 )ξ2]}λ 3 ; S3: The displacement amplitude of the working platform H ∞ The norm is taken as the optimization target, and the parameters of the inertia vibration reduction system are optimized.

2. The method for dynamic modeling and parameter optimization design of a field work platform with an inertia damping system according to claim 1 is characterized in that: In step S3, the upper platform displacement amplitude H is established according to formula (9): ∞ The norm is the optimization goal, which can be expressed in mathematical language as follows: Objective function: Constraints: Given a set of inertia ratios δ = {δ1, δ2, δ3, ..., δ M }, the above optimization model is solved by using genetic algorithm to obtain a set of corresponding optimal stiffness ratios. And a corresponding set of optimal damping ratios Wherein, M represents the number of types of inertia ratio δ, which is a positive integer; The optimal stiffness ratio and optimal damping ratio are fitted into empirical formulas suitable for actual engineering as follows: In the formula, θ m-1 and are the unknown coefficients to be fitted, m∈{1,2,3,…,M}; Based on the principle of least squares method, let the sum of squares of the coefficient errors of the optimal stiffness ratio fitting formula and the optimal damping ratio fitting be S1 and S2 respectively. In order to obtain the minimum values ​​of S1 and S2, the partial derivatives of S1 and S2 on each equation must be 0, which can be expressed in mathematical language as follows: Arrange equations (12) and (13) and rewrite them into matrix form as follows: By solving matrices (16) and (17), we can obtain the unknown coefficients in the fitting empirical formula.

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