CN-121980642-A - Suspension bridge dynamic displacement response calculation method based on suspension cable-sling-beam coupling effect and application

CN121980642ACN 121980642 ACN121980642 ACN 121980642ACN-121980642-A

Abstract

A suspension bridge dynamic displacement response calculation method based on suspension cable-sling-beam coupling effect and application thereof take the inertia effect of a main cable and the rigidity influence of a sling in a suspension bridge into consideration, firstly, a mechanical model of suspension cable-sling-beam coupling under the action of a moving vehicle is established, a suspension bridge dynamic response analysis formula is solved, an approximation processing method that vertical dynamic response of the cable and the beam is only excited by an excitation item with similar wavelength is adopted for vertical dynamic response displacement of the cable and the beam in any mode, namely, cable-beam displacement response in any mode is approximately generated only by the excitation item corresponding to the mode, decoupling processing is carried out on a suspension bridge nonlinear dynamic response equation by utilizing the approximation processing method, a coupling frequency formula of a suspension bridge cable-beam coupling system is deduced, and a vertical displacement response analysis formula of the cable and the beam structure under the action of the moving vehicle is constructed, so that the suspension bridge dynamic displacement response is accurately calculated. In the suspension bridge design phase, and in the suspension bridge operation phase.

Inventors

XU HAO
CHEN Jin
YANG YONGBIN

Assignees

重庆大学

Dates

Publication Date: 20260505
Application Date: 20251224

Claims (6)

1. A suspension bridge dynamic displacement response calculation method based on suspension cable-sling-beam coupling effect is characterized in that the inertia effect of a main cable and the rigidity influence of a sling in a suspension bridge are considered, and a mechanical model of suspension cable-sling-beam coupling under the action of a moving vehicle is firstly established; Solving a dynamic response analytic formula of the suspension bridge, wherein the vertical dynamic response displacement of the cable and the beam adopts an approximate processing method that the vertical dynamic response of the cable and the beam is only excited by excitation items with similar wavelengths under any mode, namely the cable and the beam displacement response under any mode is approximately generated only by the excitation items corresponding to the mode; And (3) decoupling the nonlinear dynamic response equation of the suspension bridge by using the approximation processing method, deducing a coupling frequency formula of a cable-beam coupling system of the suspension bridge, constructing a vertical displacement response analysis formula of the cable and beam structure under the action of the load of the moving vehicle, and accurately calculating the dynamic displacement response of the suspension bridge.
2. A suspension bridge dynamic displacement response calculation method based on suspension cable-beam coupling action as claimed in claim 1, comprising: 1. the mechanical model establishment stage of suspension rope-sling-beam coupling: S1, establishing a suspension bridge motion differential equation The method comprises the steps of constructing a suspension bridge as a theoretical model of a suspension rope-sling-beam, wherein two main ropes of the suspension bridge are equivalently simulated into a parabolic rope with elastic modulus E c , cross-sectional area A c , equivalent unit length mass M c and initial sag y 0 , slings of connecting ropes and the beam are simplified into continuous infinite mass-free springs with unit length equivalent stiffness of k, a bridge deck adopts Euler-Bernoulli beams with main span length L, unit length mass M b and bending stiffness E b I b , the mass of a vehicle body is far smaller than that of the suspension bridge, the inertia effect of the vehicle body is ignored, the moving vehicle body is simplified into a moving load F with speed v, and a vertical vibration response motion equation (formulas (48 and (49)) of the ropes and the beams of the system is established as follows: Where u c and u b represent the vertical displacement response of the cable (c) and beam (b) under the action of the moving vehicle, respectively, δ is a dirac function, x is the on-bridge position of the moving vehicle (x=vt), t is the movement time of the moving vehicle, points (·) and prime (') represent the derivation of the movement time t and the position x of the moving vehicle, respectively, and y c is the initial shape function of the cable, expressed as: T is the initial horizontal tension of the rope under the constant load state of the suspension bridge, and the calculation mode is as follows: g is the gravitational acceleration and Δt is the increment of the horizontal tension of the cable under moving load: where Δl is defined as the effective length of the cable deformation under force, expressed as: 2. calculating the coupling frequency of the cable and the beam: S2, calculating coupling frequency of asymmetric mode lower cable beam For an asymmetric mode (e=2, 4,.), e (even) is an asymmetric (even) mode order, based on a mode superposition method, by solving eigenvalues of formulas (48) and (49), an expression of an e-th order cable-beam coupling circle frequency ω bc,e can be obtained: Wherein Liang Fenliang frequencies ω bh , cable component frequencies ω ch , and cable component frequencies ω h are respectively expressed as: the case of taking the minus sign in formula (54) is defined herein as minus frequency The case of taking the plus sign is defined as the plus frequency Expressed as: S3, calculating coupling frequency of cable beam under symmetrical mode For symmetric modes (o=1, 3,.,) o (odd) is the symmetric (odd) mode order, the suspension bridge coupling frequency in this case solving the eigenvalues of equations (48) and (49), i.e., the eigenvalues of equations (48) and (49) are written as: Wherein K o is the rigidity matrix of the suspension bridge under the symmetrical mode, M o is the mass matrix, omega bc,o is the coupling circle frequency of the suspension bridge of the o-th order under the symmetrical mode, and the corresponding subtracting frequency is Sum and add frequency to Obtaining the coupling frequency of the suspension bridge under the symmetrical mode by solving the characteristic equation (58); 3. and (3) a cable and beam vibration response identification stage: s4, identifying vibration response of asymmetric mode lower cable beam In an asymmetric mode (e=2, 4.)) the suspension bridge is in linear motion, and the vertical displacement vibration responses (formulas (12) and (13)) of the e-th lower cable u c,e and the beam u b,e are obtained by solving the suspension bridge motion differential equation formulas (48) and (49): the coefficient containing subscript e (even) is an asymmetric (even) mode parameter, expressed as S5, identifying symmetrical mode lower cable-beam vibration response For the solution of the vertical displacement vibration response of the cable u c,o and the beam u b,o in the symmetrical mode (o=1, 3.), decoupling the nonlinear dynamic response equations (formulas (48) and (49)) of the suspension bridge, and constructing a vertical displacement response analysis formula of the cable and beam structure under the action of the moving vehicle, wherein the first two-order symmetrical mode is exemplified by (o=1, 3), and the vertical displacement vibration response of the lower cable u c,o and the beam u b,o in the o-th order is expressed as follows: The coefficient containing the subscript o (odd) is a symmetric (odd) mode lower parameter; other coefficients in the theoretical solution of the vertical displacement of the cable are expressed as: other coefficients in the theoretical solution of the vertical displacement of the beam are expressed as: Wherein the coefficients are expressed as: The vertical displacement dynamic response of the S6 cable u c and the beam u b is composed of two modal (symmetric mode of S4 and asymmetric mode of S5) analytical solutions, namely: u c (x,t)＝u c,e (x,t)+u c,o (x,t) (42) u b (x,t)＝u b,e (x,t)+u b,o (x,t) (43)。
3. use of a suspension bridge dynamic displacement response calculation method based on suspension cable-beam coupling according to claim 1 or 2, characterized in that the solution of the vertical displacement response of the cable and the beam under moving load provides a reference for the structural design of the suspension bridge during the suspension bridge design stage.
4. An application of the suspension bridge dynamic displacement response calculation method based on the suspension cable-sling-beam coupling effect according to claim 1 or 2 is characterized in that in the suspension bridge operation stage, based on the cable-beam vertical displacement response, the suspension bridge material parameter is substituted to serve as a health state reference, and the suspension bridge dynamic displacement response calculation method is compared with an actual bridge monitoring result to provide a judgment standard for judging the health condition of the suspension bridge.
5. The application of the suspension bridge dynamic displacement response calculation method based on the suspension rope-sling-beam coupling effect according to claim 3, wherein in the suspension bridge design stage, a reference is provided for the suspension bridge structural design based on the vertical displacement vibration response analysis solutions of the S4 rope u c,e and the beam u b,e and the vertical displacement vibration response analysis solutions of the S5 rope u c,o and the beam u b,o .
6. The application of the suspension bridge dynamic displacement response calculation method based on the suspension cable-sling-beam coupling effect according to claim 4, wherein in the suspension bridge operation stage, based on the vertical displacement dynamic response theoretical solution of the S6 cable u c and the beam u b , the method is used for substituting the suspension bridge material parameters as health state references, comparing with the actual bridge monitoring results and providing a judgment standard for judging the health condition of the suspension bridge.

Description

Suspension bridge dynamic displacement response calculation method based on suspension cable-sling-beam coupling effect and application Technical Field The invention belongs to the technical field of bridge health monitoring and detection, and particularly relates to a suspension bridge dynamic displacement response calculation method based on suspension cable-sling-beam coupling effect and application thereof. Background The bridge is used as a key hub of a transportation engineering system, is an important infrastructure for supporting national economic development and promoting regional culture blending, and the structural safety of the bridge is always the core of industry attention. During service, the bridge is subject to a series of adverse factors such as material performance degradation, overload use, natural disasters and the like, so that the health status problem of the bridge is more and more severe, and once the bridge has accidents, the bridge can not only lead to paralysis of a traffic network and disturbance of normal transportation order, but also cause huge economic loss and even threaten life safety. Therefore, the establishment of an efficient bridge structure health monitoring mechanism, the timely identification of potential hidden danger and the adoption of targeted measures to prolong the service life of the bridge structure health monitoring mechanism become a core problem to be solved urgently in the current bridge engineering field. The suspension bridge has become the preferred bridge type of the large-span bridge which spans wide river and deep valley because of the advantages of large span, light dead weight, high strength and the like. However, the large span characteristic of the suspension bridge significantly complicates the dynamic behavior thereof, and the excitation of wind load, high-speed driving load, earthquake action, temperature change and the like is extremely easy to cause the suspension bridge to generate significant deformation and vibration. The remarkable deformation not only affects the travelling comfort and safety, but also accelerates the structural fatigue damage under the long-term action, even possibly causes catastrophic instability, and seriously threatens the service safety and durability of the suspension bridge. Therefore, the dynamic vibration characteristics of the suspension bridge are accurately identified, and an efficient and reliable analysis method is established, so that the method has great engineering significance for realizing scientific management and maintenance of the whole life cycle, preventing potential disasters, guaranteeing operation safety and prolonging the service life. At present, the technology development of software and hardware in the field of dynamic response analysis of suspension bridges is that the core support is still a theoretical analysis model of the suspension bridge. The suspension bridge theoretical analysis model is widely studied due to the advantages of strong universality, clear physical concept, simple calculation and the like. The main rope is used as a core bearing member of the suspension bridge, bears the load of the bridge deck, traffic and pedestrians on the bridge deck, and transmits the load to the bridge tower and the anchorage. The slings serve as vertical connecting members to effectively transfer deck loads to the main ropes. Although the action of the main rope and the sling is of paramount importance, to simplify the theoretical analysis, most previous studies have assumed that the vertical displacements of the main rope and the beam are identical, and generally neglecting the inertial effect of the main rope and the stiffness contribution of the sling. For a suspension bridge, the dynamic characteristics of the suspension bridge need to be studied, and not only the rope-beam coupling effect, but also the influence of the rigidity of the sling need to be considered. However, there is no theoretical model in the prior art that can identify the suspension bridge displacement response taking into account the cable-to-beam coupling effect. The invention comprises the following steps: aiming at the defects in the prior art, the invention provides a suspension bridge dynamic displacement response calculation model taking the cable-beam coupling effect into consideration based on a suspension cable-sling-beam coupling theory and application thereof. The method comprises the following steps: the invention establishes a mechanical model of suspension cable-sling-beam coupling under the action of a moving vehicle in consideration of cable-beam coupling effect, is used for analyzing the vertical displacement dynamic response of suspension cable bridge cable and beam, and the theoretical system fully considers the inertia effect of a main cable and the rigidity effect of sling in a suspension bridge and provides reference for the technical development of software and hardware in the field of suspens