Novel tuned mass damper for low-frequency vertical vibration control

Abstract

The invention belongs to the technical field of structural vibration control, and discloses a novel tuned mass damper for low-frequency vertical vibration control. Rigidity elements of the novel tuned mass damper comprise a positive rigidity element composed of a vertical spring and a negative rigidity element composed of a cam, a roller and a transverse spring, the positive rigidity element bears the dead weight of a mass block, and the positive rigidity element and the negative rigidity element are connected in parallel to provide equivalent dynamic rigidity. Compared with a traditional TMD, under the condition of the same mass and tuning frequency, the positive stiffness element has higher stiffness, so that the static deformation and self weight of the vertical spring are remarkably reduced, the requirement of the system for the installation space is effectively reduced, the arrangement flexibility is improved, and the engineering adaptability of the system in the limited space is enhanced; the method is especially suitable for ultralow-frequency vertical vibration control scenes.

Description

Technical Field

[0001] This invention belongs to the field of structural vibration control technology, and relates to a novel tuned mass damper for low-frequency vertical vibration control. Background Technology

[0002] A tuned mass damper (TMD) is a passive device widely used in structural vibration control. It is commonly used in large civil engineering structures such as high-rise buildings, bridges, and offshore platforms to reduce the dynamic response caused by external excitations such as wind, waves, earthquakes, and traffic. In bridge engineering, TMDs are particularly suitable for long bridges with high main girder flexibility and low structural damping, used to control vibrations caused by wind, traffic, or crowds.

[0003] Traditional TMDs consist of a mass block, elastic elements (such as vertically positioned helical springs), and energy-dissipating elements (such as viscous dampers). Their performance depends on the proper tuning of the mass, stiffness coefficient, and damping coefficient to ensure their natural frequency is close to the structure's dominant frequency, thus achieving resonant energy absorption. For mid-to-high frequency vertical vibration control, traditional TMDs are stable and widely used in engineering. However, when controlling low-frequency (e.g., 0.2-0.3Hz range) or ultra-low-frequency (<0.2Hz) vertical vibrations, traditional TMDs face significant technical bottlenecks:

[0004] On the one hand, in order to achieve a lower natural frequency, the stiffness of the TMD needs to be significantly reduced, which leads to a significant increase in the static deformation of the spring, thus placing higher demands on the vertical installation space. On the other hand, in order to ensure that the spring meets the stress requirements under controlled load, the diameter and length of the spring wire need to be increased, resulting in an increase in the mass of the spring, and a corresponding increase in the overall weight, volume and cost of the system, affecting the structural layout and engineering feasibility.

[0005] Let the mass of the TMD be m, its stiffness be k, and its natural frequency be f. The static deformation of the spring under its own weight can be expressed as:

[0006] Δ=mg / k=g / (2πf) 2 (1)

[0007] Therefore, when the natural frequency of the TMD is 0.2Hz, its static deformation is approximately 6.2m; when the frequency drops to 0.1Hz, the static deformation increases to approximately 24.8m. Clearly, this value far exceeds the installation space provided by the structure, limiting the application of traditional TMDs in low-frequency vertical vibration control. Taking long-span bridges as an example, the internal clearance of their box girder is typically only 3-5 meters, which cannot meet the vertical installation space requirements of traditional TMDs.

[0008] Therefore, there is an urgent need to develop a new type of TMD structure that can significantly reduce spring static deformation and spring mass while meeting tuning frequency requirements, and adapt to limited installation space, so as to expand the engineering applicability of TMD in the field of low-frequency and ultra-low-frequency vertical vibration control. Summary of the Invention

[0009] This invention discloses a novel TMD (Transient Dynamic Mechanism) for low-frequency vertical vibration control, primarily addressing the problems of large static deformation of the spring and high structural weight inherent in existing TMDs for such applications. This device effectively reduces the static deformation of the spring and lowers its mass by introducing a negative stiffness mechanism, thereby improving its control efficiency and engineering adaptability in the 0.2-0.3Hz range. Furthermore, the structural design of this invention makes it suitable for vertical vibration control at even lower frequencies (<0.2Hz), expanding the application boundaries of TMDs in ultra-low frequency vertical vibration control.

[0010] The TMD of this invention consists of a mass element, a positive stiffness element, a negative stiffness element, and an energy-dissipating element, wherein the mass element, positive stiffness element, and energy-dissipating element are similar to those of a conventional TMD. The negative stiffness element consists of a cam, a roller, and a leaf spring. By customizing the outer contour shape of the cam, the diameter of the roller, and the stiffness of the leaf spring, the cam-roller-leaf spring can form a negative stiffness element with a constant stiffness coefficient.

[0011] The mass of the mass element is denoted as m, and the stiffness coefficient of the normal stiffness element is denoted as k. p (>0), the stiffness coefficient of a negative stiffness element is denoted as k. n (<0), the viscous damping coefficient of the energy-consuming element is denoted as c.

[0012] The entire weight of the mass element is borne by the positive stiffness element; therefore, the static deformation Δ of the spring in this invention can be calculated using the following formula:

[0013] Δ=mg / k p (2)

[0014] The total dynamic stiffness coefficient of the TMD in this invention is k p +k n Since (>0), its natural frequency f can be calculated using the following formula:

[0015]

[0016] Compared to traditional TMDs, this invention utilizes a positive stiffness element with a higher stiffness value while maintaining consistent quality and tuning frequency. This effectively reduces the static deformation and self-weight of the vertical spring (i.e., the positive stiffness element). For example, when the stiffness of the negative stiffness element satisfies... At that time, the static deformation of the spring in the TMD of this invention is mg / k pFor traditional TMDs, in order to achieve the same tuning frequency, the spring stiffness needs to be reduced to... The static deformation will increase to 5 mg / k p This is equivalent to five times that of the present invention. Due to the increased spring stiffness, the present invention's TMD also has significant advantages in terms of spring mass, volume, layout flexibility, and engineering adaptability.

[0017] The technical solution of the present invention:

[0018] A novel tuned mass damper for low-frequency vertical vibration control includes a vertical spring 1, a mass block 2, a cam 3, a roller 4, a transverse spring 5, a rigid support 6, an energy-dissipating element 7, a rigid rod 8, bolts 9, and a fixing plate 10. The upper end of the vertical spring 1 is fixedly connected to the controlled structure, and the lower end is connected to the mass block 2. Sufficient space is left below the mass block 2 to ensure it can vibrate freely within the designed amplitude range. The cam 3 is installed in the center of the mass block 2 and forms an integral part with it. The roller 4 is supported on the transverse spring 5 and rolls freely along the outer surface of the cam 3. The upper end of the rigid support 6 is fixed to the controlled structure. One end of the transverse spring 5 is fixed to the rigid support 6, and... Its boundary conditions take various forms according to actual needs: one end fixed and the other end unsupported, one end fixed and the other end simply supported, and both ends simply supported; the upper end of the energy dissipation element 7 is connected to the controlled structure, and the lower end is connected to the mass block 2 to achieve energy dissipation; the roller 4 is installed on the other end of the transverse spring 5 through the rigid round rod 8, bolt 9 and fixing plate 10; the specific connection method is as follows: the rigid round rod 8 is inserted into the center hole of the roller 4 and placed in the pre-set slot of the transverse spring 5; the fixing plate 10 is set on both sides of the slot of the transverse spring 5, and the bolt 9 passes through the fixing plate 10 and the transverse spring 5 and is tightened to form a clamping of the rigid round rod 8, thereby realizing the stable fixation of the roller 4 on the transverse spring 5.

[0019] The vertical spring 1 is a helical tension spring made of spring steel wire, and its cross-section is generally circular.

[0020] The mass block 2 is made of steel. The connection position between the mass block 2 and the vertical spring 1 is as close as possible to the bottom surface of the mass block 2, thereby reducing the height occupied by the mass block 2 alone and improving the space utilization rate.

[0021] The mass block 2 is a mass element. The spring group consisting of vertical spring 1 constitutes a positive stiffness element, and the cam 3, roller 4 and horizontal spring 5 constitute a negative stiffness element. The positive stiffness element and the negative stiffness element are connected in parallel to provide equivalent dynamic stiffness.

[0022] The cam 3 is made of stainless steel, and its outer wall arc is formed by high-precision laser cutting. After cutting, it is polished to ensure that the coefficient of friction of the outer wall is as low as possible.

[0023] The roller 4 has high load-bearing capacity, low coefficient of friction and excellent durability.

[0024] The transverse spring 5 is made of steel, and its vertical stiffness is significantly greater than its transverse stiffness, so as to ensure that when the mass block 2 vibrates, the transverse spring 5 only undergoes transverse deformation and does not produce vertical deformation.

[0025] The rigid support 6 is made of steel and has high rigidity and load-bearing capacity.

[0026] The energy-consuming element 7 can be a liquid viscous damper or an eddy current damper, providing linear viscous damping characteristics, and the viscous damping coefficient remains basically stable within the set amplitude range.

[0027] The round rod 8 is made of steel and has high rigidity and load-bearing capacity.

[0028] The bolt 9 is a regular bolt or a high-strength bolt.

[0029] The fixing plate 10 is made of steel.

[0030] The mass block 2 is the mass element of the TMD of the present invention; the spring group composed of vertical spring 1 constitutes the positive stiffness element; the cam 3, roller 4 and horizontal spring 5 constitute the negative stiffness element.

[0031] The mass m and total dynamic stiffness coefficient k of the TMD of this invention are given by [reference to a specific invention]. p +k n The design principles for the viscous damping coefficient c are consistent with those of traditional TMD. Specifically, the mass m is determined based on actual engineering requirements, and then the total stiffness coefficient k is calculated based on the target tuning frequency. On this basis, the vibration control efficiency or robustness is optimized by adjusting the viscous damping coefficient c.

[0032] Based on the available space height for installing the TMD, determine the allowable length of the vertical spring and its static deformation, thereby determining the stiffness coefficient k of the positive stiffness element. p The stiffness coefficient of a negative stiffness element can be obtained from the relationship k. n =kk p The conclusion is as follows.

[0033] The vertical force exerted by the negative stiffness element on mass block 2 is expressed as follows:

[0034] k n x = n·k h (δ+S(x))S ′ (x) (1)

[0035] In the formula, n represents the number of combinations of "cam 3 outer contour - roller 4 - transverse spring 5" in the new type of tuned mass damper, and k hLet S(x) represent the stiffness coefficient of a single transverse spring 5, x be the vertical displacement of mass block 2, δ be the initial compression of transverse spring 5, and S(x) be the trajectory of the center of roller 4. ′ (x) represents the derivative of S(x) with respect to x.

[0036] The trajectory S(x) of the center of the roller 4 is calculated using the following formula:

[0037]

[0038] The motion trajectory S(x) curve of the center of roller 4 is plotted by solving the above formula. The upper and lower limits of the curve are set according to the actual required height of cam 3.

[0039] The outer contour of the cam 3 Calculate using the following formula:

[0040]

[0041] In the formula, r represents the radius of roller 4.

[0042] The beneficial effects of the present invention are as follows: (1) By introducing a negative stiffness mechanism, the static deformation of the spring and the mass of the spring itself are effectively reduced, thereby significantly reducing costs and improving the lightweight level; (2) The present invention significantly reduces the installation space requirements, and is especially suitable for environments where the internal net height of the box girder in a long-span bridge is generally 3-5m, which can meet the space adaptation requirements of ultra-low frequency TMD with a tuning frequency as low as 0.1Hz; (3) The mass of the negative stiffness mechanism is mainly concentrated in cam 3, and cam 3 can be used as part of the effective mass of TMD; (4) The present invention only adds four components, namely cam, roller, transverse spring and rigid support, on the basis of traditional TMD. The overall structure is simple and reliable, and has good engineering feasibility and potential for promotion and application. Attached Figure Description

[0043] Figure 1 This is a novel TMD (Transient Damping) construction diagram for low-frequency vertical vibration control;

[0044] Figure 2 This is a partial structural diagram of the connection between roller 4 and transverse spring 5;

[0045] Figure 3 This is a front view of the connection between roller 4 and transverse spring 5;

[0046] Figure 4 This is a schematic diagram of the working principle of the new TMD.

[0047] Figure 5 This is the front view of cam 3;

[0048] Figure 6This is a schematic diagram showing the relationship between the outer contour of cam 3 and the center motion trajectory of roller 4;

[0049] Figure 7 5. Schematic diagram of a transverse spring with one end fixed and the other end unrestrained;

[0050] Figure 8 Schematic diagram 5 of a transverse spring that is fixed at one end and simply supported at the other end;

[0051] Figure 9 This is a schematic diagram of a simply supported transverse spring at both ends.

[0052] In the diagram: 1. Spring, 2. Mass block, 3. Cam, 4. Roller, 5. Lateral spring, 6. Rigid support, 7. Energy dissipating element, 8. Rigid rod, 9. Bolt, 10. Fixing plate, L represents the length of 5. Lateral spring, k p Represents the positive stiffness coefficient, k n This represents the negative stiffness coefficient. Detailed Implementation

[0053] The specific embodiments of the present invention will be described in detail below with reference to the technical solutions and accompanying drawings.

[0054] like Figure 1-3 As shown, a novel TMD for low-frequency vertical vibration control mainly includes a vertical spring 1, a mass block 2, a cam 3, a roller 4, a transverse spring 5, a rigid support 6, an energy-dissipating element 7, a rigid rod 8, bolts 9, and a fixing plate 10. The upper end of the vertical spring 1 is fixedly connected to the controlled structure, and the lower end is connected to the mass block 2. Sufficient space is left below the mass block 2 to ensure it can vibrate freely within a specified amplitude range. The cam 3 is installed in the center of the mass block 2 and forms an integral part with it. The roller 4 is supported on the transverse spring 5 and can roll freely along the outer surface of the cam 3. The upper end of the rigid support 6 is fixed to the controlled structure. The transverse spring 5 is installed on the rigid support 6, and its boundary conditions can take various forms according to actual needs, such as one end fixed and the other end unsupported, or one end fixed and the other end unsupported. Simply supported, simply supported at both ends, etc.; the upper end of the energy-consuming element 7 is connected to the controlled structure, and the lower end is connected to the mass block 2 to achieve energy dissipation; the roller 4 is installed on the transverse spring 5 through the rigid round rod 8, bolt 9 and fixing plate 10; the specific connection method is as follows: the rigid round rod 8 is inserted into the center hole of the roller 4 and placed in the pre-set slot of the transverse spring 5; the fixing plate 10 is set on both sides of the slot of the transverse spring 5, and the bolt 9 passes through the fixing plate 10 and the transverse spring 5 and is tightened to form a clamping of the rigid round rod 8, thereby realizing the stable fixation of the roller 4 on the transverse spring 5.

[0055] Mass block 2 is the mass element of the TMD of this invention; the spring assembly consisting of vertical spring 1 constitutes the positive stiffness element; cam 3, roller 4, and transverse spring 5 constitute the negative stiffness element. The mass of the mass element is denoted as m, and the stiffness coefficient of the positive stiffness element is denoted as k.p (>0), the stiffness coefficient of a negative stiffness element is denoted as k. n (<0), the viscous damping coefficient of the energy-consuming element is denoted as c.

[0056] like Figure 2 As shown, in this invention, the weight of the mass element is entirely borne by the normal stiffness element; therefore, its static spring deformation can be expressed as: Δ1=mg / k p Positive stiffness element and negative stiffness element are connected in parallel to jointly provide the system's equivalent dynamic stiffness k = k p +k n The corresponding natural frequency is: Under the premise that the mass m and the tuning frequency f are consistent, compared with the traditional TMD structure, this invention introduces a negative stiffness mechanism to make the stiffness k of the positive stiffness element... p The corresponding increase significantly reduces its static deformation and mass. Due to the increased vertical spring stiffness, the TMD of this invention also offers significant advantages in terms of spring mass, volume, layout flexibility, and engineering adaptability.

[0057] In practical applications, to improve system response sensitivity and ensure stable system operation, the outer wall surface of cam 3 should be machined as smoothly as possible, and roller 4 should be made of a material with the lowest possible rolling friction coefficient.

[0058] The parameter design method of the TMD of this invention is described in detail below:

[0059] (1) The mass m and the total dynamic stiffness coefficient k of the TMD of this invention are k p +k n The design principles for the viscous damping coefficient c are consistent with those of traditional TMD. Specifically, the mass m is determined based on actual engineering requirements, and then the total stiffness coefficient k is calculated based on the target tuning frequency. On this basis, the vibration control efficiency or robustness is optimized by adjusting the viscous damping coefficient c.

[0060] (2) Based on the available space height for installing the TMD, first determine the allowable length of the vertical spring and its static deformation, thereby determining the stiffness k of the positive stiffness element. p The stiffness of a negative stiffness element can be determined by the relationship k. n =kk p The conclusion is as follows.

[0061] (3) Figure 1 As shown, the potential energy during the vibration process of the TMD in this invention can be expressed as:

[0062]

[0063] In the formula, n represents the number of combinations of "cam 3 outer contour - roller 4 - transverse spring 5" in the system. Figure 1In the case where n=4, the number of combinations can be changed accordingly (n) and k. h δ represents the stiffness coefficient of a single transverse spring 5, x is the vertical displacement of mass block 2, δ is the initial compression of transverse spring 5, and S(x) is the trajectory of the center point of roller 4.

[0064] (4) Differentiating equation (4) with respect to x, we get:

[0065] F(x) = k p x+n·k h (δ+S(x))S ′ (x) (5)

[0066] In the formula, F(x) is the total vertical force exerted on mass block 2 by the positive stiffness element and the negative stiffness element.

[0067] (5) Let S(0) = 0, then S(x) can be solved by the following formula:

[0068]

[0069] (6) The vertical force exerted by the negative stiffness element on mass block 2 can be expressed as:

[0070] k n x=F(x)-k p x = n·k h (δ+S(x))S ′ (x) (7)

[0071] (7) Substituting equation (7) into equation (6), we get:

[0072]

[0073] (8) Outer contour line of cam 3 Calculate using the following formula:

[0074]

[0075] For the definitions of the symbols in the formula, please refer to [link / reference]. Figure 4 r represents the radius of roller 4.

[0076] (9) When the boundary condition of the transverse spring 5 is that one end is fixed and the other end is unconstrained, the roller 4 is located at the unconstrained end of the transverse spring 5, such as... Figure 7 As shown, the stiffness coefficient of the transverse spring 5 can be calculated using the following formula:

[0077]

[0078] In the formula, E is the elastic modulus of the transverse spring, I is the moment of inertia of the transverse spring section, and L is the total length of the transverse spring.

[0079] When the boundary condition of the transverse spring 5 is that one end is fixed and the other end is simply supported, the roller 4 is located at the transverse spring 5. Place, such as Figure 8 As shown, the stiffness coefficient of the transverse spring 5 can be calculated using the following formula:

[0080]

[0081] In the formula b = La.

[0082] When the boundary condition of the transverse spring 5 is simply supported at both ends, the roller 4 is located at the midpoint of the transverse spring 5, as shown below. Figure 9 As shown, the stiffness coefficient of the transverse spring 5 can be calculated using the following formula:

[0083]

[0084] The above description is merely a preferred embodiment of the present invention and should not be considered as any limitation thereof. Any equivalent changes, modifications, or improvements made by those skilled in the art to the above embodiments when utilizing the technical solutions of the present invention should be considered as falling within the protection scope of the present invention.

Claims

1. A novel tuned mass damper for low-frequency vertical vibration control, characterized in that, The novel tuned mass damper includes a vertical spring (1), a mass block (2), a cam (3), a roller (4), a transverse spring (5), a rigid support (6), and an energy-dissipating element (7); The upper end of the vertical spring (1) is fixedly connected to the controlled structure, and the lower end is connected to the mass block (2); there is enough space below the mass block (2) to ensure that it can vibrate freely within the designed amplitude range; the cam (3) is installed in the center of the mass block (2) and is integrated with it; one end of the transverse spring (5) is fixed on the rigid support (6), and the other end is equipped with a roller (4), which rolls freely along the outer surface of the cam (3); the upper end of the rigid support (6) is fixed to the controlled structure; the upper end of the energy dissipation element (7) is connected to the controlled structure, and the lower end is connected to the mass block (2) to achieve energy dissipation.

2. The novel tuned mass damper according to claim 1, characterized in that, The novel tuned mass damper also includes a rigid round rod (8), bolts (9) and a fixing plate (10). The roller (4) is installed on the other end of the transverse spring (5) through the rigid round rod (8), bolts (9) and fixing plate (10). The rigid round rod (8) passes through the center hole of the roller (4) and is placed in the pre-set slot of the transverse spring (5). The fixing plate (10) is set on both sides of the slot of the transverse spring (5). The bolts (9) pass through the fixing plate (10) and the transverse spring (5) and are tightened to form a clamping of the rigid round rod (8), thereby realizing the stable fixation of the roller (4) on the transverse spring (5).

3. The novel tuned mass damper according to claim 1, characterized in that, One end of the transverse spring (5) is fixed to the rigid support (6), and its boundary conditions take various forms according to actual needs: one end is fixed and the other end is unsupported, one end is fixed and the other end is simply supported, and both ends are simply supported.

4. The novel tuned mass damper according to claim 1, characterized in that, The mass block (2) is a mass element. The spring group consisting of the vertical spring (1) constitutes a positive stiffness element, and the cam (3), roller (4) and horizontal spring (5) constitute a negative stiffness element. The positive stiffness element and the negative stiffness element are connected in parallel to provide equivalent dynamic stiffness.

5. The novel tuned mass damper according to claim 1, characterized in that, The vertical stiffness of the transverse spring (5) is greater than its transverse stiffness.

6. The novel tuned mass damper according to claim 1, characterized in that, The energy-consuming element (7) is selected from liquid viscous dampers or electric eddy current dampers.

7. The novel tuned mass damper according to claim 4, characterized in that, The mass of the mass block (2) is m, and the total dynamic stiffness coefficient is k = k p +k n The design principle of the viscous damping coefficient c is consistent with that of the traditional tuned mass damper; based on the space height for installing the new tuned mass damper, the allowable length of the vertical spring (1) and its static deformation are determined, thereby determining the stiffness coefficient k of the positive stiffness element. p The stiffness coefficient of a negative stiffness element is given by the relationship k. n =kk p The conclusion is as follows.

8. The novel tuned mass damper according to claim 4, characterized in that, The vertical force exerted by the negative stiffness element on the mass block (2) is expressed as follows: k n x=n·k h (δ+S(x))S ′ (x) (1) In the formula, n represents the number of combinations of "cam (3) outer contour - roller (4) - transverse spring (5)" in the new tuned mass damper, and k h Let S(x) represent the stiffness coefficient of a single transverse spring (5), x be the vertical displacement of the mass block (2), δ be the initial compression of the transverse spring (5), and S(x) be the trajectory of the center of the roller (4). ′ (x) represents the derivative of S(x) with respect to x.

9. The novel tuned mass damper according to claim 8, characterized in that, The trajectory S(x) of the center of the roller (4) is calculated by the following formula: The motion trajectory S(x) curve of the center of the roller (4) is plotted by solving the above formula. The upper and lower limits of the curve are set according to the actual required height of the cam (3).

10. The novel tuned mass damper according to claim 9, characterized in that, The outer contour of the cam (3) Calculate using the following formula: In the formula, r represents the radius of the roller (4).

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