Method for calculating the coupled system vibration frequency of a floor with a profiled steel sheet concrete composite floor

Abstract

This invention discloses a method for calculating the vibration frequency of a coupled system of a screen vibration device and a profiled steel sheet concrete composite floor slab, comprising: Step 1, obtaining the influence coefficient parameter ξ of the profiled steel sheet composite floor slab and the equipment foundation on the natural frequency of the floor slab. 1h Step 2: Obtain the parameter η, which is the influence coefficient of the operating frequency of the vibrating screen on the natural frequency of the profiled steel composite floor slab. 1h Step 3: Determine the operating frequency f of the screening and vibrating equipment. hh Step 4: Obtain the coupled natural frequency f of the vibration screen and the profiled steel sheet concrete composite floor slab. 1h This method can accurately assess the impact of the screening and vibration equipment and foundation on the natural frequency of the floor slab, thereby minimizing the possibility of resonance between the screening and vibration equipment and the composite floor slab structure of profiled steel sheet concrete. It avoids problems related to personnel comfort and equipment system operation safety caused by resonance, as well as possible repair and reinforcement issues, and can achieve good environmental and economic benefits.

Description

Technical Field

[0001] This invention relates to the field of vibration and control structure technology, specifically to a method for calculating the vibration frequency of a coupled system of a screen vibration device and a profiled steel sheet concrete composite floor slab. Background Technology

[0002] Currently, scholars both domestically and internationally have conducted extensive research on the problem of vertical vibration of floor slabs. It is well known that resonance caused by vibration source excitation is the root cause of floor slab vibration problems. Resonance between floor slabs and power equipment frequently occurs in engineering projects both domestically and internationally. At best, it hinders normal operation and causes structural cracks; at worst, it damages the main structure, leading to major personal safety accidents, resulting not only in economic losses but also severe social impacts. Resonance typically occurs within vibrating factory buildings, often producing significant noise that can easily cause emotional fluctuations, leading to anxiety, irritability, and other negative emotions, and causing physical harm. Furthermore, vibration can interfere with or completely destroy the function of precision equipment, compromising machining accuracy and surface finish, reducing finished product quality, accelerating component fatigue and wear, shortening the lifespan of equipment and structures, and easily causing large structural deformation and damage, with extremely serious consequences.

[0003] The resonance of corrugated steel sheet concrete composite floor slabs in industrial plants caused by vibrating screens has become particularly prominent in recent years. This is primarily due to two reasons. First, the operating frequency of the vibrating screen and the natural vibration frequency of the floor slab are quite close: in corrugated steel sheet concrete composite floor slab systems with vibrating screens installed, the first-order natural frequency of multi-story frame corrugated steel sheet concrete composite floor slabs is often around 15Hz, while the operating frequency of the vibrating screen is mostly between 10-20Hz, with little difference between the two. Second, conventional vibration control methods mainly calculate the natural frequency of the floor slab and the operating frequency of the vibration source equipment separately, maximizing the difference during equipment procurement and design stages. However, after the vibrating screen's auxiliary equipment base is installed in the corrugated steel sheet concrete composite floor slab system, the coupling of the vibrating equipment and its foundation with the corrugated steel sheet concrete composite floor slab causes significant changes in the local stiffness and strength of the structure, resulting in a large difference in the natural vibration frequency of the floor slab before and after the vibration. Conventional methods to avoid resonance often involve selecting the operating frequency of the vibrating screen as far away as possible from the natural frequency of the floor slab. However, if the difference between the two frequency ranges is small and the vibrating screen and its base are coupled with the profiled steel sheet reinforced concrete composite floor slab, causing a change in the natural frequency of the floor slab, the vibrating screen designed and installed according to this conventional method is very likely to resonate with the natural frequency of the profiled steel sheet reinforced concrete composite floor slab.

[0004] Currently, there is a constant stream of research on the vibration analysis of floor slabs, but most of it focuses on the finite element analysis of the natural frequency of the structure or resonance reinforcement. There is little research on the significant changes in the natural vibration frequency of the coupled system caused by the screen vibration equipment and the base coupled with the profiled steel sheet concrete composite floor slab, and there is a lack of relatively simple and clear calculation methods. It is necessary to further study and clarify these issues. Summary of the Invention

[0005] This invention aims to overcome the shortcomings of the existing technical solutions and proposes a method for calculating the vibration frequency of a coupled system of a screen vibration device and a profiled steel sheet concrete composite floor slab. This method can accurately assess the influence of the screen vibration device and foundation on the natural frequency of the floor slab, thereby minimizing the possibility of resonance between the screen vibration device and the profiled steel sheet concrete composite floor slab structure. This avoids problems related to personnel comfort and equipment system operation safety caused by resonance, as well as possible repair and reinforcement issues, and can achieve good environmental and economic benefits.

[0006] To solve the above-mentioned technical problems, the present invention is achieved through the following technical solution:

[0007] A method for calculating the vibration frequency of a coupled system of a screen vibration device and a profiled steel sheet concrete composite floor slab includes:

[0008] Step 1: Obtain the influence coefficient parameter ξ of the profiled steel sheet composite floor slab and equipment foundation on the natural frequency of the floor slab. 1h ξ 1h The result is obtained by calculation using formula (1):

[0009]

[0010] in l is the width of the profiled steel sheet concrete composite floor slab in the short span direction, h is the total thickness of the profiled steel sheet concrete composite floor slab, l0 is the width of the equipment foundation parallel to the short span direction of the floor slab, and h0 is the thickness of the equipment foundation.

[0011] Step 2: Obtain the influence coefficient parameter η of the operating frequency of the vibrating screen equipment on the natural frequency of the profiled steel composite floor slab. 1h η 1h The result is obtained by formula (2):

[0012]

[0013] in like Then η 1h =0 (Research and analysis results show that when the newly added unit stiffness of the equipment foundation accounts for less than 1 / 4 of the unit width stiffness after coupling the equipment foundation-corrugated steel sheet concrete composite floor slab, the impact of vibrating equipment on the natural frequency of the corrugated steel sheet concrete composite floor slab is small and can be almost ignored); B is the unit width stiffness of the corrugated steel sheet concrete composite floor slab, B s Stiffness per unit width after coupling of equipment foundation and profiled steel sheet concrete composite floor slab;

[0014] Step 3: Determine the operating frequency f of the screening and vibrating equipment. hhTo determine the installation method of the screen vibration equipment support, if the screen vibration equipment base is a spring vibration isolation support, the effect of the screen vibration equipment's operating frequency on the natural frequency of the profiled steel composite floor slab should be negative (i.e., reduced), and this should be denoted as -f. hh If the base of the vibrating screen is a rigid support, the operating frequency of the vibrating screen should have a positive effect (i.e., increase) on the natural frequency of the profiled steel composite floor slab, which is denoted as f. hh ;

[0015] Step 4: Obtain the coupled natural frequency f of the vibration screen and the profiled steel sheet concrete composite floor slab. 1h f 1h The result is obtained by formula (3):

[0016]

[0017] Where f 11 This is the natural first-order vibration frequency of the profiled steel sheet composite floor slab.

[0018] In step 2, the calculation method for the unit width stiffness B of the profiled steel sheet concrete composite floor slab is detailed in 14.4.2 of the "Standard for Design of Steel Structures" (GB50017-2017).

[0019] In step 2, the stiffness per unit width B after coupling of the equipment foundation and the profiled steel sheet concrete composite floor slab is... s The calculation method is as follows:

[0020]

[0021] Where E is the elastic modulus of the steel beam in the composite floor slab of profiled steel sheet and concrete, and n is the ratio of the elastic modulus of steel and concrete after considering concrete creep.

[0022] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0023] This invention proposes for the first time a method for calculating the natural frequency of a screen vibration device-profiled steel sheet concrete composite floor slab, considering the coupling effect between the screen vibration device and its foundation. It comprehensively considers the influence of the foundation height, width, and stiffness, the profiled steel sheet floor slab span, height, and stiffness, and the operating frequency of the screen vibration device to obtain the coupled vibration frequency of the screen vibration device-profiled steel sheet concrete composite floor slab. The calculation method of this invention can further quantitatively calculate the influence of different parameters on the system's natural frequency. Due to the large number of parameters to be considered in the calculation, finite element numerical simulation is used for parametric analysis based on experimental and theoretical analysis. Fitting these data yields the method for calculating the natural frequency of the coupled system. The coupled vibration frequency of the screen vibration device-profiled steel sheet concrete composite floor slab obtained by the calculation method of this invention has high accuracy and small error, avoiding the problem of resonance caused by inaccurate calculation of the natural frequency of the screen vibration device-profiled steel sheet concrete composite floor slab coupled system, where the design operating frequency of the screen vibration device is too close to the system's natural frequency. Compared with existing standards and design manuals, the calculation method of this invention can take into account the influence of the screen vibration equipment and its foundation on the coupled system. Based on experiments and numerical simulations, the calculation method of this invention improves the accuracy of the coupled vibration frequency of the screen vibration equipment-corrugated steel sheet concrete composite floor slab by more than 20%. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the coupling system of the screening and vibration equipment-profiled steel sheet concrete composite floor slab of the present invention.

[0025] Attached reference numerals: 1-Combined steel sheet and concrete floor slab, 2-Equipment foundation, 3-Screening and vibration equipment. Detailed Implementation

[0026] To enable those skilled in the art to better understand the technical solutions of the present invention, preferred embodiments of the present invention are described below in conjunction with specific examples. However, it should be understood that the accompanying drawings are for illustrative purposes only and should not be construed as limiting the scope of this patent. For better illustration of this embodiment, some components in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. For those skilled in the art, it is understandable that some well-known methods for calculating the vibration frequency of a screen vibration device-corrugated steel sheet concrete composite floor slab coupling system and their explanations may be omitted in the drawings. The positional relationships described in the accompanying drawings are for illustrative purposes only and should not be construed as limiting the scope of this patent.

[0027] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments to facilitate a clear understanding of the present invention, but these descriptions do not constitute a limitation on the present invention.

[0028] like Figure 1As shown, this invention provides a coupling system of a screening and vibration device and a profiled steel sheet concrete composite floor slab. This system includes, from bottom to top, a profiled steel sheet concrete composite floor slab 1, a device foundation 2, and a screening and vibration device 3. Wherein, l is the width of the profiled steel sheet concrete composite floor slab in the short span direction, h is the total thickness of the profiled steel sheet concrete composite floor slab, l0 is the width of the device foundation parallel to the short span direction of the floor slab, h0 is the thickness of the device foundation, B is the stiffness per unit width of the profiled steel sheet concrete composite floor slab, and B... s f represents the stiffness per unit width of the coupled equipment foundation-corrugated steel sheet concrete composite floor slab. 11 f is the natural first-order vibration frequency of the profiled steel sheet composite floor slab. hh f is the operating frequency of the screening and vibrating equipment. 1h These are the basic parameters required for calculating the coupled natural frequencies of the screen vibration equipment and the profiled steel sheet concrete composite floor slab.

[0029] First, in step 1, determine the total thickness h and short span l of the profiled steel sheet concrete composite floor slab, the thickness h0 of the equipment foundation, and the width l0 parallel to the short span direction of the floor slab. Calculate the influence coefficient parameter ξ of the additional equipment foundation on the natural frequency of the floor slab. 1h ;

[0030] ξ 1h The result is obtained by calculation using formula (1):

[0031]

[0032] in

[0033] Step 2: Determine the unit width stiffness B of the profiled steel sheet concrete composite floor slab, and the unit width stiffness B after coupling the equipment foundation and the profiled steel sheet concrete composite floor slab. s The influence coefficient parameter η of the working frequency of the vibrating screen equipment on the natural frequency of the profiled steel composite floor slab was calculated. 1h :

[0034] η 1h The result is obtained by formula (2):

[0035]

[0036] in like η 1h =0;

[0037] For details on the calculation method of the unit width stiffness B of the profiled steel sheet concrete composite floor slab, please refer to 14.4.2 of the "Standard for Design of Steel Structures" (GB50017-2017).

[0038] Stiffness per unit width B after coupling of equipment foundation and profiled steel sheet concrete composite floor slab s The calculation method is as follows:

[0039]

[0040] Where E is the elastic modulus of the steel beam in the composite floor slab of profiled steel sheet and concrete, and n is the ratio of the elastic modulus of steel and concrete after considering concrete creep.

[0041] Step 3: Determine the operating frequency f of the screening and vibrating equipment. hh To determine the installation method of the screen vibration equipment support, if the screen vibration equipment base is a spring vibration isolation support, then the effect of the operating frequency of the screen vibration equipment on the natural frequency of the profiled steel composite floor slab should be negative (i.e., reduced), denoted as -f. hh If the base of the vibrating screen is a rigid support, then the operating frequency of the vibrating screen should have a positive effect (i.e., increase) on the natural frequency of the profiled steel composite floor slab, denoted as f. hh .

[0042] Step 4: Determine the natural first-order vibration frequency f of the profiled steel sheet composite floor slab. 11 Combining the relevant influence coefficient ξ obtained in steps 1, 2, and 3 1h η 1h f hh The coupled natural frequency f of the vibrating screen and the profiled steel sheet concrete composite floor slab was calculated. 1h :

[0043] f 1h The result is obtained by formula (3):

[0044]

[0045] Among them (1)

[0046] (2) like η 1h =0,

[0047] (3) If the base of the screen vibration equipment is a spring vibration isolation support, it is denoted as -f hh If the base of the vibrating screen is a rigid support, it is denoted as f. hh .

[0048] Specific implementation examples are as follows:

[0049] The profiled steel sheet concrete composite floor slab has a short span width (l) of 2500mm and a total thickness (h) of 150mm. The equipment foundation, parallel to the short span, has a width (l0) of 1200mm and a thickness (h0) of 200mm. The unit width stiffness (B) of the profiled steel sheet concrete composite floor slab is 3.2 × 10⁻⁶. 16 Nmm 2 The stiffness per unit width B of the equipment foundation-corrugated steel sheet concrete composite floor slab after coupling s 4.8×10 16 Nmm 2 f 11 The natural first-order vibration frequency of the profiled steel sheet composite floor slab is 15Hz. hh The operating frequency of the screening and vibration equipment is 18Hz, and the foundation of the screening and vibration equipment is a rigid support.

[0050] The natural frequencies of the coupled system of the vibrating screen equipment and the profiled steel sheet concrete composite floor slab were calculated using the method of this invention. The results were compared with those obtained from the "Steel Structure Design Manual" and finite element numerical simulation, as shown in Table 1. The calculation of the natural frequencies considering the effect of the vibrating screen equipment and the profiled steel sheet concrete composite floor slab coupling system is highly significant, greatly improving the accuracy of the composite floor slab's natural frequencies and effectively preventing resonance. Calculating the natural frequencies of the vibrating screen equipment and profiled steel sheet concrete composite floor slab coupling system according to this invention is safer and more accurate, and the results are in good agreement with actual values.

[0051] Table 1. Calculation of Natural Frequency of Vibration Equipment for Corrugated Steel Sheet Concrete Composite Floor Slabs

[0052]

[0053] This invention provides a method for calculating the vibration frequency of a coupled system of a vibrating screen and a profiled steel sheet concrete composite floor slab. It primarily considers the coupling effect of the vibrating screen and its foundation on the composite floor slab. Through experimental and numerical simulation analysis, a method for calculating the natural frequency of the floor slab considering the coupling effect is proposed, replacing the traditional method that only considers the natural frequency of the floor slab itself. This method provides a more accurate calculation of the natural vibration properties of the composite floor slab with the vibrating screen and its foundation. It allows for better selection of the vibrating screen's operating frequency during the design phase, minimizing the need to avoid the floor slab's natural frequency and preventing resonance problems. This method for calculating the vibration frequency of the coupled system of the vibrating screen and its foundation fully considers the influence of multiple factors, including the vibrating screen, its foundation, and the composite floor slab. It can accurately assess the impact of the vibrating screen and its foundation on the floor slab's natural frequency, thereby minimizing the possibility of resonance between the vibrating screen and the composite floor slab structure. This avoids issues related to personnel comfort, equipment system safety, and potential repair and reinforcement problems caused by resonance, resulting in significant environmental and economic benefits.

[0054] The above description is merely a preferred embodiment of the present invention, but the present invention is not limited to the specific embodiments described above. Those skilled in the art can make various modifications, additions, or substitutes with similar methods without departing from the principles of the present invention, and these should also be considered within the scope of protection of the present invention.

Claims

1. A method for calculating the vibration frequency of a coupled system of a screen vibration device and a profiled steel sheet concrete composite floor slab, characterized in that, include: Step 1: Obtain the influence coefficient parameter ξ of the profiled steel sheet composite floor slab and equipment foundation on the natural frequency of the floor slab. 1h ξ 1h The result is obtained by calculation using formula (1): in l is the width of the profiled steel sheet concrete composite floor slab in the short span direction, h is the total thickness of the profiled steel sheet concrete composite floor slab, l0 is the width of the equipment foundation parallel to the short span direction of the floor slab, and h0 is the thickness of the equipment foundation. Step 2: Obtain the influence coefficient parameter η of the operating frequency of the vibrating screen equipment on the natural frequency of the profiled steel composite floor slab. 1h η 1h The result is obtained by formula (2): in like Then η 1h =0; B is the stiffness per unit width of the profiled steel sheet concrete composite floor slab, B s Stiffness per unit width after coupling of equipment foundation and profiled steel sheet concrete composite floor slab; Step 3: Determine the operating frequency f of the screening and vibrating equipment. hh Determine the installation method of the screen vibration equipment support. If the screen vibration equipment base is a spring vibration isolation support, it is denoted as -f. hh If the base of the vibrating screen is a rigid support, it is denoted as f. hh ; Step 4: Obtain the coupled natural frequency f of the vibration screen and the profiled steel sheet concrete composite floor slab. 1h f 1h The result is obtained by formula (3): Where f 11 This is the natural first-order vibration frequency of the profiled steel sheet composite floor slab.

2. The method for calculating the vibration frequency of the coupled system of screen vibration equipment and profiled steel sheet concrete composite floor slab as described in claim 1, characterized in that: In step 2, the stiffness per unit width B after coupling of the equipment foundation and the profiled steel sheet concrete composite floor slab is... s The calculation method is as follows: Where E is the elastic modulus of the steel beam in the composite floor slab of profiled steel sheet and concrete, and n is the ratio of the elastic modulus of steel and concrete after considering concrete creep.

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