Method for judging internal instability of large-span suspension bridge

Abstract

The invention discloses a method for judging internal instability of a large-span suspension bridge, which belongs to the technical field of bridge engineering and comprises the following steps of: 1, acquiring section parameters and modal parameters of a bridge, and constructing a vertical-torsional coupling dynamic model of a main cable-suspender-main beam system of the large-span suspension bridge; 2, on the basis of bridge section parameters and modal parameters, vertical modal inherent frequencies of all orders and torsional modal inherent frequencies of all orders are calculated; 3, for the combination of any one vertical mode and any one torsional mode, calculating a frequency ratio, and judging whether the frequency ratio falls into a sensitive frequency ratio range of internal instability or not; 4, if the frequency ratio falls into a sensitive frequency ratio range, calculating a critical span interval corresponding to the modal pair according to an internal instability condition; 5, based on the critical span interval of each modal pair, establishing a segmented envelope line of internal instability; and 6, judging the internal instability risk of the bridge according to the subsection envelope line indexes. By the adoption of the method, the vibration risk of the large-span suspension bridge under the non-external resonance condition can be effectively recognized.

Description

Technical Field

[0001] This invention relates to the technical field of bridge engineering, and in particular to a method for identifying internal instability in long-span suspension bridges. Background Technology

[0002] With the rapid development of high-performance materials and construction methods, modern suspension bridges exhibit the characteristics of "large span, high flexibility, and low damping": the main span continues to increase, the natural frequency shifts downward, and the modal frequencies become more concentrated. Mainstream research on bridge vibration has long been based on a mechanical framework dominated by external excitations, such as vortex-induced vibration, buffeting, and vehicle-bridge coupled vibrations caused by traffic loads. This framework typically uses the "coincidence of external excitation frequency and structural frequency" as the triggering condition, i.e., external instability (or resonance), and its response usually decays rapidly after the external excitation is removed.

[0003] However, when the research focuses on ultra-long-span suspension bridge systems with dense modes and rich coupling paths, long-term monitoring and operational data show that even under normal wind conditions, sparse traffic flow, and a lack of significant external disturbances, repetitive vibrations, mode switching, and energy exchange can still be observed. Furthermore, the vibrations can persist for a considerable period after the removal of external excitation. These phenomena suggest that the traditional external resonance assumption alone cannot explain such dynamic responses in ultra-long-span flexible systems; this is likely due to an internal instability mechanism triggered by coincidence or proximity of structural frequencies. Summary of the Invention

[0004] The purpose of this invention is to provide a method for identifying internal instability of long-span suspension bridges. Based on the sensitive frequency ratio range and segmented envelope, it effectively identifies the risk of repeated vibration and delayed response of long-span suspension bridges under non-external resonance conditions caused by mode switching and energy exchange mechanisms.

[0005] To achieve the above objectives, the present invention provides a method for determining internal instability of long-span suspension bridges, comprising the following steps: S1. Obtain the bridge section parameters and modal parameters, and construct a vertical-torsional coupled dynamic model of the main cable-suspender-main beam system of a long-span suspension bridge; S2. Based on the bridge section parameters and modal parameters, calculate the natural frequencies of each vertical modal and each torsional modal. S3. For any combination of vertical and torsional modes, calculate the frequency ratio and determine whether the frequency ratio falls within the sensitive frequency ratio range of internal instability. S4. If the frequency ratio falls within the sensitive frequency ratio range, calculate the critical span interval corresponding to the mode pair based on the internal instability condition. S5. Based on the critical span interval of each mode pair, establish a piecewise envelope of internal instability; S6. Determine the risk of internal instability of the bridge based on the segmented envelope index.

[0006] Preferably, in step S1, the governing equations for the vibration modes of the dynamic model are: ; ; in, This represents the mass per unit length of the main beam. Represents vertical displacement. Represents the vertical bending stiffness of the main beam. Represents the horizontal force of the main cable. Represents the cross-coupling term caused by vertical-torsional interaction. Represents the angle of twist. The polar radius of inertia representing the cross section. Represents the warping stiffness of the cross section. The representative section is the Saint-Venant torsional stiffness. This represents the horizontal distance of the main cable from the center of torsion, which is half of the horizontal spacing of the main cable.

[0007] Preferably, in step S2, the vertical first First-order modal natural frequencies and torsional first-order natural frequencies The natural frequencies of the first mode are obtained by solving the corresponding modal frequency equations: ; ; in, Represents the vertical first First-order modal natural frequencies, Represents the reversal of the first First-order modal natural frequencies, Represents the vertical displacement of the first Normalized mode shape, Represents the twist angle. Normalized mode shape.

[0008] Preferably, in step S3, the vertical direction of the bridge is... First-order frequency and torsional first-order frequency The formula for calculating the frequency ratio of the first frequency is: .

[0009] Preferably, in step S3, the sensitive frequency ratio range is established based on an energy transfer index: ; in, Represents the coupling strength, taken as As the threshold for internal instability, where Must meet: ; The sensitive frequency ratio range is Centered on, when When, the first-order approximation is: ; That is, the range of sensitive frequency ratios is .

[0010] Preferably, in step S4, the critical span interval is obtained through the following steps: Calculate the vertical first Step and Torsion Critical span length corresponding to the first mode: ; Within the sensitive frequency ratio range By taking the minimum and maximum values, the critical span range of this mode combination can be obtained. .

[0011] Preferably, in step S5, the segmented envelope index is defined as the statistical value of a given span. The number of mode pairs falling into the critical span interval is calculated using the following formula: ; in, Represents the maximum vertical order. Represents the maximum torsional order. Represents a given span Whether it falls within the critical length range.

[0012] Preferably, in step S6, the segmented envelope index If the bridge is at risk of internal instability, then the segmented envelope index is used to determine this. The higher the value, the greater the potential risk of internal instability.

[0013] Therefore, the present invention employs the above-mentioned method for determining internal instability of long-span suspension bridges, which has the following advantages: (1) In this invention, it is possible to effectively identify the risk of low-frequency vibration and mode conversion caused by the modal coupling of the structure itself, even in the absence of significant external disturbances or when the external frequency is misaligned with the mode (such as normal wind conditions and sparse traffic flow).

[0014] (2) In this invention, the proposed critical span interval provides a quantitative basis for judging whether the span length scale has entered the internal instability, and establishes a clear span-coupling risk mapping.

[0015] (3) In this invention, a segmented envelope is constructed as a unified risk indicator to achieve an integrated measurement of "whether it is unstable" and "instability intensity" under different span lengths.

[0016] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating a method for determining internal instability of a long-span suspension bridge according to the present invention. Figure 2 This is a schematic diagram of the main cable-suspender-main beam provided in an embodiment of the present invention; Figure 3 An energy transfer diagram provided for an embodiment of the present invention. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments 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. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Specific model specifications need to be selected and determined according to the actual specifications of the device, etc. The specific selection calculation method adopts existing technology in the art, and therefore will not be described in detail.

[0019] Example like Figures 1-2 As shown, the present invention provides a method for determining internal instability of a long-span suspension bridge, comprising the following steps: S1. Obtain the bridge section parameters and modal parameters, and construct a vertical-torsional coupled dynamic model of the main cable-suspender-main girder system of the long-span suspension bridge. The governing equations of the dynamic model under antisymmetric vibration modes are: ; ; in, This represents the mass per unit length of the main beam. Represents vertical displacement. Represents the vertical bending stiffness of the main beam. Represents the horizontal force of the main cable. Represents the cross-coupling term caused by vertical-torsional interaction. Represents the angle of twist. The polar radius of inertia representing the cross section. Represents the warping stiffness of the cross section. The representative section is the Saint-Venant torsional stiffness. This represents the horizontal distance of the main cable from the center of torsion, which is half of the horizontal spacing of the main cable.

[0020] S2. Based on the bridge section parameters and modal parameters, calculate the natural frequencies of each vertical modal and each torsional modal. First-order modal natural frequencies and torsional first-order natural frequencies The natural frequencies of the first mode are obtained by solving the corresponding modal frequency equations: ; ; in, Represents the vertical first First-order modal natural frequencies, Represents the reversal of the first First-order modal natural frequencies, Represents the vertical displacement of the first Normalized mode shape, Represents the twist angle. Normalized mode shape.

[0021] S3. For any combination of vertical and torsional modes, calculate the frequency ratio and determine whether the frequency ratio falls within the sensitive frequency ratio range of internal instability. Bridge vertical section First-order frequency and torsional first-order frequency The formula for calculating the frequency ratio of the first frequency is: ; The sensitivity frequency range is established based on the energy transfer rate index: ; in, Represents the coupling strength, taken as As the threshold for internal instability, where Must meet: ; The sensitive frequency ratio range is Centered on, half width approximately ,when When, the first-order approximation is: ; That is, the range of sensitive frequency ratios is .like Figure 3 As shown, The three-dimensional distribution clearly shows that: with Increase, energy transfer degree index ( Approximately "equal width" expansion (total width approximately) ), and when After leaving that range, It rapidly decays to a low level. In engineering, this can be used to implement windowed avoidance: ensuring... (Or, by taking a more conservative coefficient), the risks of passive amplification and long-term response can be effectively reduced.

[0022] S4. If the frequency ratio falls within the sensitive frequency ratio range, then calculate the critical span interval corresponding to this mode pair based on the internal instability condition: Calculate the vertical first Step and Torsion Critical span length corresponding to the first mode: ; Within the sensitive frequency ratio range By taking the minimum and maximum values, the critical span of this modal combination can be obtained. .

[0023] S5. Based on the critical span interval of each mode pair, establish a piecewise envelope for internal instability. The piecewise envelope index is defined as the statistical value of a given span. The number of mode pairs falling into the critical span interval is calculated using the following formula: ; in, Represents the maximum vertical order. Represents the maximum torsional order. Represents a given span Whether it falls within the critical length range.

[0024] S6. Determine the internal instability risk of the bridge based on the segmented envelope index. When the segmented envelope index... If the bridge is at risk of internal instability, then the segmented envelope index is used to determine this. The higher the value, the greater the potential risk of internal instability.

[0025] Therefore, the present invention adopts the above-mentioned method for identifying internal instability of long-span suspension bridges. Based on the sensitive frequency ratio range and segmented envelope, it effectively identifies the risk of repeated vibration and delayed response of long-span suspension bridges under non-external resonance (or non-external instability) conditions caused by mode switching and energy exchange mechanisms.

[0026] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for determining internal instability of a long-span suspension bridge, characterized in that: Includes the following steps: S1. Obtain the bridge section parameters and modal parameters, and construct a vertical-torsional coupled dynamic model of the main cable-suspender-main beam system of a long-span suspension bridge; S2. Based on the bridge section parameters and modal parameters, calculate the natural frequencies of each vertical modal and each torsional modal. S3. For any combination of vertical and torsional modes, calculate the frequency ratio and determine whether the frequency ratio falls within the sensitive frequency ratio range of internal instability. S4. If the frequency ratio falls within the sensitive frequency ratio range, calculate the critical span interval corresponding to the mode pair based on the internal instability condition. S5. Based on the critical span interval of each mode pair, establish a piecewise envelope of internal instability; S6. Determine the risk of internal instability of the bridge based on the segmented envelope index.

2. The method for determining internal instability of a long-span suspension bridge according to claim 1, characterized in that: In step S1, the governing equations for the vibration modes of the dynamic model are: ； ； in, This represents the mass per unit length of the main beam. Represents vertical displacement. Represents the vertical bending stiffness of the main beam. Represents the horizontal force of the main cable. Represents the cross-coupling term caused by vertical-torsional interaction. Represents the angle of twist. The polar radius of inertia representing the cross section. Represents the warping stiffness of the cross section. The representative section is the Saint-Venant torsional stiffness. This represents the horizontal distance of the main cable from the center of torsion, which is half of the horizontal spacing of the main cable.

3. The method for determining internal instability of a long-span suspension bridge according to claim 2, characterized in that: In step S2, the vertical first First-order modal natural frequencies and torsional first-order natural frequencies The natural frequencies of the first mode are obtained by solving the corresponding modal frequency equations: ； ； in, Represents the vertical first First-order modal natural frequencies, Represents the reversal of the first First-order modal natural frequencies, Represents the vertical displacement of the first Normalized mode shape, Represents the twist angle. Normalized mode shape.

4. The method for determining internal instability of a long-span suspension bridge according to claim 3, characterized in that: In step S3, the bridge vertical section... First-order frequency and torsional first-order frequency The formula for calculating the frequency ratio of the first frequency is: 。 5. The method for determining internal instability of a long-span suspension bridge according to claim 4, characterized in that: In step S3, the sensitive frequency ratio range is established based on the energy transfer degree index: ； in, Represents the coupling strength, taken as As the threshold for internal instability, where Must meet: ； The sensitive frequency ratio range is Centered on, when When, the first-order approximation is: ； That is, the range of sensitive frequency ratios is .

6. The method for determining internal instability of a long-span suspension bridge according to claim 5, characterized in that: In step S4, the critical span interval is obtained through the following steps: Calculate the vertical first Step and Torsion Critical span length corresponding to the first mode: ； Within the sensitive frequency ratio range By taking the minimum and maximum values, the critical span range of this mode combination can be obtained. .

7. The method for determining internal instability of a long-span suspension bridge according to claim 6, characterized in that: In step S5, the segmented envelope index is defined as the statistical value of a given span. The number of mode pairs falling into the critical span interval is calculated using the following formula: ； in, Represents the maximum vertical order. Represents the maximum torsional order. Represents a given span Whether it falls within the critical length range.

8. The method for determining internal instability of a long-span suspension bridge according to claim 7, characterized in that: In step S6, the segmented envelope index If the bridge is at risk of internal instability, then the segmented envelope index is used to determine this. The higher the value, the greater the potential risk of internal instability.

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