A method for intelligent monitoring of bending stiffness of a beam based on bending wave transfer function

Abstract

The application discloses a kind of beam bending stiffness intelligent monitoring method based on bending wave transfer function, piezoelectric sensor is connected with high-frequency signal acquisition instrument and gathers elastic wave signal in beam, deduces the transfer characteristics of two kinds of bending waves in beam based on bending wave transfer function: propagation wave and near-field wave, find that the wave velocity and attenuation characteristics of two kinds of bending waves are different, the wave velocity of propagation wave increases with the increase of section stiffness and the propagation characteristics are strong, while the change rule of the wave velocity of near-field wave is complex and extremely easy to attenuate, according to which the vibration excitation device is arranged at a reasonable position, and the vibration excitation device is used to impact the beam body transversely, to excite bending waves. Utilize the attenuation characteristics of near-field wave to filter near-field wave interference, combine wavelet transform to realize accurate identification of bending propagation wave velocity, deduce the relationship between wave velocity and section stiffness using bending wave transfer function, and obtain the real-time change of the section stiffness of the beam by inversion, to realize non-destructive, real-time monitoring of the evolution process of beam bending stiffness.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of engineering structure health detection and monitoring data analysis, and specifically relates to a beam bending stiffness intelligent monitoring method based on bending wave transfer function. BACKGROUND

[0002] Beam members in engineering structures bear transverse loads and are mainly deformed in bending, and are widely used in civil engineering, machinery, aerospace and other fields related to national economy and people's livelihood. The bending stiffness of the beam is an important indicator for evaluating its working performance. Therefore, developing an effective method for detecting and monitoring the bending stiffness of the beam is an important basic work for ensuring the safety of a large number of infrastructure structures in China and improving the management and maintenance level of transportation infrastructure in China.

[0003] Existing beam bending stiffness detection is mostly carried out by load test method, which verifies the deformation capacity of the component under the test load, and then evaluates the bending resistance of the beam structure. For example, the bridge engineering detection field proposes to load the bridge by using vehicles or other counterweights, and measure the deformation value of the bridge under each level of loading condition to evaluate the bending resistance of the bridge (Highway Bridge Load Test Regulations). In addition, measuring the vibration fundamental frequency and mode of the beam member in the structure is also a commonly used method (Urban Bridge Detection and Evaluation Technical Specifications). It is generally believed that the greater the bending stiffness, the higher the structure fundamental frequency. In recent years, the method of identifying bridge modal by mobile testing (Research Progress of Bridge Rapid Testing and Flexibility Identification Based on Mobile Impact Vibration, Tian Yongding, Zhang Jian, Southeast University, Nanjing 211189, Jiangsu) to judge the stiffness of the structure has been widely studied at home and abroad.

[0004] However, the analysis results of the above method often reflect the stiffness performance of the complete structure system, which includes the comprehensive influence of the bending stiffness of the beam itself, the boundary conditions, and the stiffness of the components connected by the beam. The degradation of the cross-sectional stiffness of the beam member is unevenly distributed along the beam length, and the above method cannot further investigate the cross-sectional stiffness at different positions of the beam. Moreover, for large engineering structures, load testing is time-consuming and often needs to interrupt the normal use of the structure, for example, when load testing is performed on a bridge, traffic needs to be closed, and the testing cost is extremely high.

[0005] In view of the two problems that the local bending stiffness of the beam is difficult to accurately evaluate and the detection and monitoring is time-consuming, a beam bending stiffness intelligent monitoring method based on bending wave transfer function is provided, a relationship between the cross-section bending stiffness and the propagation wave velocity which can be propagated for a long distance is established through the bending wave transfer function induced by transverse impact, and the beam bending stiffness is monitored by monitoring the change of the bending wave velocity in the beam. The main features include: 1) the influence of near-field waves is effectively filtered through the study on the attenuation characteristics of two kinds of modal bending waves, and the propagation wave velocity is accurately identified in the test; 2) the detection and real-time monitoring of the local bending stiffness of the target beam section are realized through the correlation analysis of the cross-section bending stiffness and the propagation wave velocity. SUMMARY

[0006] The purpose of the present application is to provide a beam bending stiffness intelligent monitoring method based on bending wave transfer function to solve the problems in the background art.

[0007] The present application is realized at least by one of the following technical solutions.

[0008] A beam bending stiffness intelligent monitoring method based on bending wave transfer function, comprising the following steps:

[0009] Step 1, obtaining the bending wave transfer function in the beam considering material damping induced by transverse impact based on wave equation;

[0010] Step 2, analyzing the attenuation characteristics of the bending wave to determine the position of the vibration excitation device;

[0011] Step 3, determining the expected velocity of the bending wave in the beam based on the bending wave transfer function and the relationship between the expected velocity and the cross-section stiffness;

[0012] Step 3, identifying the actual bending wave velocity in the beam through piezoelectric sensing technology and wavelet transform algorithm, and taking the actual bending wave velocity as an index to evaluate the evolution of the cross-section stiffness and monitor the change of the beam cross-section bending stiffness.

[0013] Further, the bending wave transfer function comprises:

[0014] (2) establishing the Timoshenko beam wave equation considering material damping:

[0015]

[0016] Wherein u and are the transverse displacement and rotational displacement of the Timoshenko beam respectively; E, G, p, h, A, I and K are the elastic modulus, shear modulus, density, viscous internal damping coefficient, cross-section area, cross-section moment of inertia and cross-section shear shape coefficient of the beam material respectively; x, N z , C x , C Dand t are the transverse coordinate, the axial pre-stress, the damping coefficient and the time at the position of interest on the beam, respectively; q(x, t) is the external load acting on the beam;

[0017] (2) The above beam wave equation is converted to the frequency domain for solving, and the bending wave transfer function in the frequency domain is obtained:

[0018]

[0019] where ω, i represent the frequency value and the imaginary unit, respectively, and in the formula is the form of the solution of the transverse displacement in the frequency domain in the beam wave equation, k1 and k2 are the bending wave numbers, a1 and a2 are the amplitudes of the propagating wave and the near-field wave transmitted to the left, d1 and d2 are the amplitudes of the propagating wave and the near-field wave transmitted to the right, and the remaining parameters are defined as follows:

[0020] α = EI Z (κAGω 2 η 2 -κAG-N x )

[0021] β = EI Z ωη(2κAG+N x )

[0022]

[0023] For k1:

[0024] g = -α (e + γ) - β (f + δ), h = β (e + γ) - α (f + δ)

[0025] For k2:

[0026] g = α (e - γ) + β (f - δ), h = α (f - δ) - β (e - γ)

[0027] Where:

[0028] γ = -κAGN x +ω 2 (EI Z ρA+ρI Z κAG+ρI Z N x );

[0029] δ = κAGN x ηω-ω 3 (ρI Z κAGη+EI Z ρAη);

[0030] λ = κGρA 2 ω 2- p 2 I Z A w 4 ;

[0031] m = - k G p A 2 w 3 h

[0032]

[0033]

[0034] a = g 2 - d 2 - 4 a l + 4 b m

[0035] b = 2 g d - 4 a m - 4 l b

[0036] Further, the analysis of the attenuation characteristics of the bending wave and the determination of the position of the vibration excitation device include the following steps:

[0037] The wave number k is expressed by a complex number m + ni, m and n are both real numbers, the structural response waveform solution is obtained by inverse Fourier transform of the bending wave transfer function, and the attenuation characteristics of the two types of bending waves, i.e. the propagating wave and the near-field wave, are obtained by the wave number:

[0038]

[0039] wherein u(x, t) is the transverse displacement of the Timoshenko beam, is the solution form of the transverse displacement of the Timoshenko beam in the frequency domain, is the particular solution term of , a1 and a2 are the amplitudes of the propagating wave and the near-field wave transferred to the left, d1 and d2 are the amplitudes of the propagating wave and the near-field wave transferred to the right, m1, n1 are the values of m and n corresponding to the propagating wave, m2 and n2 are the values of m and n corresponding to the near-field wave, x, w and t are respectively the transverse coordinate of the position discussed on the beam, the frequency of the wave and the time, and i is the imaginary unit;

[0040] From the above formula, the amplitude attenuation expressions of the two types of bending waves are respectively and

[0041] The amplitude attenuation rates of the propagating wave and the near-field wave can be obtained by substituting the structural parameters into the amplitude attenuation expressions, and the position of the transverse force impact is determined, and the distance between the vibration excitation device and the piezoelectric sensor is set as l c , so as to ensure that the influence of the near-field wave at the position of the piezoelectric sensor can be ignored, i.e.

[0042] Further, the determination of the flexural wave expected speed based on the flexural wave transfer function in the beam and its relationship with the cross-sectional stiffness comprises the following steps:

[0043] The propagation wave theoretical speed c is obtained from the structural response waveform solution t :

[0044]

[0045] The theoretical wave speed can be obtained according to the above formula, and it is found that the wave speed monotonically increases with the increase of the cross-sectional flexural stiffness.

[0046] Further, the cross-sectional stiffness includes the cross-sectional size and the cross-sectional material elastic modulus, which can effectively comprehensively reflect the cross-sectional stiffness comprehensive performance of the tested beam segment.

[0047] Further, the actual flexural wave speed in the beam is determined by the step 3 to determine the position of the vibration excitation device, the piezoelectric sensor is connected to the high-frequency signal acquisition instrument to obtain the time history signal of the wave response in the beam, and the wavelet transform is used to identify the actual propagation speed c of the flexural propagation wave a .

[0048] Further, the actual flexural propagation wave propagation speed is compared and analyzed with the theoretical wave speed to evaluate the actual flexural stiffness of the beam member:

[0049] c a ≥ c t , the actual cross-sectional flexural stiffness of the beam is better than the design stiffness, c a is the actual propagation speed of the flexural propagation wave, c t is the theoretical wave speed of the propagation wave;

[0050] c a < c t , the actual cross-sectional flexural stiffness of the beam is weaker than the design stiffness;

[0051] And the change of c a is monitored in real time to obtain the evolution process of the cross-sectional flexural stiffness, and the change of the cross-sectional stiffness is monitored through the change of the wave speed.

[0052] Further, the piezoelectric sensor is arranged in the form of being embedded in the beam or being pasted on the surface of the steel beam, and only the acquisition instrument needs to be connected during monitoring. If a sensor is damaged due to aging, it can be directly replaced without affecting the test results, and there is no need to recalibrate.

[0053] Further, the piezoelectric sensor is arranged in the form of being embedded in the beam or being pasted on the surface of the steel beam, and only the acquisition instrument needs to be connected during monitoring. If a sensor is damaged due to aging, it can be directly replaced without affecting the test results, and there is no need to recalibrate.

[0054] 1Further, the piezoelectric sensor is embedded in the beam at a fixed interval along the beam length.

[0055] Compared with the prior art, the application has the following beneficial effects:

[0056] 1、The application can establish the correlation between the bending wave velocity and the cross-section bending stiffness through the bending wave transfer function, measure the bending wave velocity, identify the local bending stiffness of the beam segment between the transverse load impact position and the piezoelectric sensor, and recognize the transverse load impact position.

[0057] 2、The application analyzes the attenuation characteristics of the two bending waves through the bending wave transfer function, further determines the shortest distance between the impact load and the piezoelectric sensor to filter the influence of the near-field wave, and realizes the accurate measurement of the wave velocity of the target bending wave.

[0058] 3、The application proposes that the two types of bending waves in the beam have attenuation and propagation characteristics, and can be used to optimize the current elastic wave-based structure defect detection.

[0059] 4、The application is simple and convenient, and can realize real-time monitoring of the local bending stiffness of the target beam segment without using time-consuming and expensive means such as load test. BRIEF DESCRIPTION OF DRAWINGS

[0060] Figure 1 It is a layout of measurement points and load impact points of an engineering beam model in the embodiment of the application;

[0061] Figure 2 It is a Timoshenko beam dynamics theory model considering material damping established in the embodiment of the application;

[0062] Figure 3 It is an analysis result graph of the bending wave attenuation characteristics in the embodiment of the application;

[0063] Figure 4 It is an analysis result graph of the bending wave velocity in the embodiment of the application;

[0064] Figure 5 It is a flowchart of the real-time monitoring method of the beam bending stiffness based on the bending wave transfer function proposed by the application. DETAILED DESCRIPTION

[0065] The technical solutions in the embodiments of the application will be described clearly and completely below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are only part of the embodiments of the application, not all the embodiments. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the application.

[0066] Embodiment 1

[0067] The present invention provides an intelligent monitoring method for beam flexural stiffness based on the flexural wave transfer function. The method comprises the following steps: obtaining the flexural wave transfer function in a beam induced by transverse impact and taking material damping into account based on the wave equation; analyzing the attenuation characteristics and expected propagation velocity of the flexural wave; identifying the actual flexural wave velocity in the beam through piezoelectric sensing technology and a wavelet transform algorithm; and evaluating the cross-sectional stiffness evolution as an indicator. The principle of the present invention is as follows: theoretical analysis reveals the influence of the propagation characteristics of near-field waves in a beam on the accuracy of wave velocity measurement; utilizing the difference in the attenuation characteristics of near-field waves and propagating waves, rationally setting the distance between the piezoelectric sensor and the vibration excitation device, eliminating the influence of the near-field waves, and achieving accurate measurement of the propagating wave velocity; based on the derivation of the flexural wave transfer function and the monotonic positive correlation between the propagating wave velocity and the cross-sectional stiffness, the method achieves real-time health monitoring of the beam cross-sectional flexural stiffness by accurately measuring the flexural wave velocity.

[0068] like Figure 5 As shown, the embodiment of the present invention provides an intelligent monitoring method for beam bending stiffness based on bending wave transfer function, comprising the following steps:

[0069] Step 1: Obtain the bending wave transfer function in the beam with material damping induced by transverse impact based on the wave equation

[0070] (11) Establish the Timoshenko beam wave equation considering material damping:

[0071]

[0072] where υ and are the lateral displacement and rotational displacement of the Timoshenko beam respectively; E, G, ρ, η, A, I z and κ are the elastic modulus, shear modulus, density, viscous internal damping coefficient, beam cross-sectional area, section moment of inertia and section shear shape factor of the beam material, respectively; x, N x 、C D and t are the horizontal coordinate of the discussed position on the beam, axial preload, damping coefficient and time respectively; q(x,t) is the external load acting on the beam.

[0073] (12) The above beam wave equation is converted to the frequency domain and solved to obtain the solution of the bending wave transfer function in the frequency domain:

[0074]

[0075] Among them, i Represent the frequency value and imaginary unit respectively, where is the frequency-domain solution of the lateral displacement in the beam wave equation, k1 and k2 are the bending wave numbers, a1 and a2 are the amplitudes of the propagating wave and the near-field wave transmitted to the left, and d1 and d2 are the amplitudes of the propagating wave and the near-field wave transmitted to the right. The remaining parameters are defined as follows:

[0076] a = EI Z (κAGω 2 η 2 -κAG-N x )

[0077] b = EI Z ωη(2κAG+N x )

[0078]

[0079] For k1:

[0080] g = -a(e + g) - b(f + d), h = b(e + g) - a(f + d)

[0081] For k2:

[0082] g = a(e - g) + b(f - d), h = a(f - d) - b(e - g)

[0083] Where:

[0084] g = -κAGN x +ω 2 (EI Z ρA+ρI Z κAG+ρI Z N x );

[0085] d = κAGN x ηω-ω 3 (ρI Z κAGη+EI Z ρAη);

[0086] l = κGρA 2 ω 2 -ρ 2 I Z Aω 4 ;

[0087] m = -κGρA 2 ω 3 η;

[0088]

[0089] a = g 2 - d 2 -4al + 4b m

[0090] b = 2gd - 4am - 4lb

[0091] Step 2: Analyze the attenuation characteristics of the bending wave to determine the position of the vibration excitation device;

[0092] The wave number k is expressed by a complex number m+ni, m and n are both real numbers, the structural response waveform solution is obtained by inverse Fourier transform of the bending wave transfer function, and the attenuation characteristics of the two types of bending waves, i.e., the propagating wave and the near-field wave, are obtained by the wave number:

[0093]

[0094] wherein υ(x, t) is the transverse displacement of the Timoshenko beam, is the solution form of the transverse displacement of the Timoshenko beam in the frequency domain, is a particular solution of , a1 and a2 are the amplitudes of the propagating wave and the near-field wave transmitted to the left, d1 and d2 are the amplitudes of the propagating wave and the near-field wave transmitted to the right, m1, n1, m2 and n2 are the values of m and n corresponding to the propagating wave and the near-field wave respectively, x, ω and t are the transverse coordinate of the position discussed on the beam, the frequency of the wave and the time respectively, and i is the imaginary unit.

[0095] From the above formula, the amplitude attenuation expressions of the two types of bending waves are respectively and

[0096] The structural parameters are substituted into the amplitude attenuation expressions to obtain the amplitude attenuation rates of the propagating wave and the near-field wave, and the transverse force impact position is determined, the distance between the vibration excitation device and the piezoelectric sensor is set as l c , so as to ensure that the influence of the near-field wave at the position of the piezoelectric sensor can be ignored, i.e.,

[0097] Step 3: determining the expected speed of the bending wave in the beam based on the bending wave transfer function and the relationship between the speed and the cross-sectional stiffness;

[0098] The theoretical wave speed c t of the propagating wave can be obtained from the structural response waveform solution:

[0099]

[0100] According to the above formula, the theoretical wave speed can be obtained, and it is found that the wave speed monotonously increases with the increase of the cross-sectional bending stiffness.

[0101] Step 4: identifying the actual bending wave speed in the beam through the piezoelectric sensing technology and the wavelet transform algorithm, and taking the speed as an index to evaluate the evolution of the cross-sectional stiffness

[0102] (41) The position of the vibration excitation device is determined through step 2, the piezoelectric sensor is connected to the high-frequency signal acquisition instrument to obtain the time history signal of the wave response in the beam, and the actual propagating speed c a of the bending wave is identified through wavelet transform.

[0103] (42)The measured bending propagation wave propagation speed is compared with the theoretical wave speed to analyze and judge the actual bending stiffness of the beam member:

[0104] c a ≥c t , the actual cross-section bending stiffness of the beam is better than the design stiffness,

[0105] c a <c t , the actual cross-section bending stiffness of the beam is weaker than the design stiffness,

[0106] and monitor the change of c a , to obtain the evolution process of the cross-section bending stiffness.

[0107] Embodiment 2

[0108] A system for realizing the bending wave transfer function-based beam bending stiffness intelligent monitoring method of embodiment 1 comprises a vibration excitation device, a piezoelectric sensor, and a high-frequency signal acquisition instrument. The piezoelectric sensor is embedded in the beam at a fixed interval along the length direction of the beam. The vibration excitation device impacts the beam body transversely. The piezoelectric sensor is connected to the high-frequency signal acquisition instrument to collect elastic wave signals in the beam. Based on the bending wave transfer function, the transfer characteristics of two types of bending waves in the beam, i.e., propagation waves and near-field waves, are derived. It is found that the wave speeds and attenuation characteristics of the two types of bending waves are different. The wave speed of the propagation wave increases with the increase of the cross-section stiffness and the propagation characteristics are strong, while the variation law of the wave speed of the near-field wave is complex and the near-field wave is extremely easy to attenuate. Accordingly, the vibration excitation device is arranged at a reasonable position, and the vibration excitation device is used to impact the beam body transversely to excite bending waves. The attenuation characteristics of the near-field wave are used to filter the near-field wave interference. The wave speed of the bending propagation wave is accurately identified by combining the wavelet transform. The wave speed and cross-section stiffness relationship is derived by using the bending wave transfer function, and the real-time change of the cross-section stiffness of the beam is inversely obtained. This method not only considers the difference in the propagation characteristics of the two types of bending waves, i.e., the near-field wave and the propagation wave, in the actual engineering beam structure, but also uses the corresponding relationship between the cross-section stiffness and the bending wave speed. Therefore, the method has high accuracy and strong operability, and effectively realizes the nondestructive and real-time monitoring of the evolution process of the beam bending stiffness.

[0109] Embodiment 3

[0110] Next, a simply supported beam is combined as a numerical example to verify the feasibility and implementation of the method of the present application.

[0111] As shown in Figure 1 , a steel box beam simply supported beam structure with a length of 30 m is used. A concentrated load q(x, t) is used to simulate the vibration excitation device. A piezoelectric sensor is embedded at an interval l c = 5 m, and a connecting line is led out to connect the high-frequency signal acquisition instrument. The present application includes the following processes:

[0112] The vibration excitation device excites a bending wave in the steel box beam at a frequency of 100 Hz, the vibration equation of the beam under the impact load is established according to the above step one, as shown in Figure 2 The transmission function of the bending wave is derived, and the propagating wave (wave number k1) and the near-field wave (wave number k2) are distinguished, and it can be found that the propagating wave and the near-field wave both have propagation characteristics and attenuation characteristics. Figure 2 (a) is a beam member subjected to transverse impact; Figure 2 (b) is the force balance of a Timoshenko beam element; Figure 2 (c) is the deformation-internal force relationship considering the K-V damping theory.

[0113] According to the above step two, the attenuation expressions of the propagating wave and the near-field wave are studied, the amplitude of the load impact position is taken as the unit amplitude, and the distance from the load impact position is x, and the calculated amplitudes of the propagating wave and the near-field wave are as shown in Figure 3 . Figure 3 The near-field wave amplitude is difficult to identify after propagating for 10m, and can be ignored through reasonable parameter setting of the wavelet transform algorithm. Therefore, l c = 10m, the piezoelectric signal sensor with a distance of more than 10m from the impact position is selected as the test signal source, and the monitored beam section is ensured to be between the piezoelectric sensor and the vibration excitation device. The bending stiffness of the beam section is monitored according to this principle.

[0114] According to the above step three, the theoretical speed of the propagating wave can be obtained, as shown in Figure 4 The transmission speed increases with the increase of the section stiffness, Figure 4 (a) is the influence of the material elastic modulus on the wave speed; Figure 4 (b) is the influence of the section revolution radius on the wave speed.

[0115] According to step 4, through the high sensitivity measurement of the piezoelectric sensor, combined with the wavelet transform algorithm to filter the interference of the small amplitude such as the near-field wave, the time of the propagating wave from the excitation position to the piezoelectric sensor is identified, and then the measured wave speed is calculated according to the distance between the piezoelectric sensor and the vibration excitation device. The measured wave speed is compared with the theoretical wave speed, the section bending stiffness is identified, and the evolution of the section bending stiffness of the beam is monitored through long-term observation of the wave speed.

[0116] After adopting the above technical scheme, the nondestructive monitoring of the local beam section stiffness can be realized, the technical gap in this field is filled, the measurement process is simple and the operability is strong, long-term application can be realized after the piezoelectric sensor is laid in the early stage, the cost is low, and the measurement method is suitable for various fields such as civil engineering, aerospace, instrument manufacturing, etc.

[0117] The above merely describes preferred specific embodiments of the present application, but the protection scope of the present application is not limited thereto, and any person skilled in the art, according to the technical solution and inventive concept of the present application, makes equivalent replacement or change within the technical range disclosed by the present application, which should be covered within the protection scope of the present application.

Claims

1. A method for intelligent monitoring of flexural stiffness of a beam based on bending wave transfer function, characterized by, The method comprises the following steps: Step 1, obtaining a transverse impact-induced bending wave transfer function in a beam considering material damping based on a wave equation; The bending wave transfer function comprises: (1) establishing a Timoshenko beam wave equation considering material damping: where u and are the transverse displacement and the rotational displacement of the Timoshenko beam, respectively; E, G, p, h, A, I z and K are the elastic modulus, the shear modulus, the density, the viscous internal damping coefficient, the beam cross-sectional area, the cross-sectional moment of inertia and the cross-sectional shear shape coefficient of the beam material, respectively; x, N x , C D and t are the horizontal coordinate of the position under discussion on the beam, the axial pre-stress, the damping coefficient and the time, respectively; q(x, t) is the external load acting on the beam; (2) converting the above beam wave equation to the frequency domain for solving to obtain a solution of the bending wave transfer function in the frequency domain: where ω, i denote the frequency value and the imaginary unit, respectively, in which is the form of the solution of the transverse displacement in the frequency domain in the beam wave equation, k1, k2 are the bending wave numbers, a1, a2 are the amplitudes of the propagating wave and near-field wave, which propagate to the left, d1, d2 are the amplitudes of the propagating wave and near-field wave, which propagate to the right, and the remaining parameters are defined as follows: α = EI Z (κAGω 2 η 2 -κAG-N x ) β = EI Z ωη(2κAG+N x ) For k1: g = -a(e + g) - b(f + d), h = b(e + g) - a(f + d) For k2: g = a(e - g) + b(f - d), h = a(f - d) - b(e - g) Wherein: γ = -κAGN x + ω 2 (EI Z ρA+ρI Z κAG+ρI Z N x ); δ = κAGN x ηω-ω 3 (ρI Z κAGη+EI Z ρAη) λ = κGρA 2 ω 2 -ρ 2 I Z Aω 4 ; μ = -κGρA 2 ω 3 η; b = 2gd - 4am - 4lb; Step 2, analyzing the attenuation characteristics of the bending wave to determine the position of the vibration excitation device; specifically comprising the following steps: The wave number k is expressed by a complex number m + ni, m and n are both real numbers, the inverse Fourier transform of the bending wave transfer function is performed to obtain a structure response waveform solution, and the attenuation characteristics of the two types of bending waves, i.e., the propagating wave and the near-field wave, are obtained by the wave number: wherein is the transverse displacement of a Timoshenko beam, is the form of solution of the transverse displacement of a Timoshenko beam in the frequency domain, is is the particular solution of the equation, a1, a2 are the amplitudes of the propagating wave and near-field wave transmitted to the left, d1, d2 are the amplitudes of the propagating wave and near-field wave transmitted to the right, m1, n1 are the values of the m and n corresponding to the propagating wave, m2, n2 are the values of the m and n corresponding to the near-field wave, respectively, x, ω and t are the transverse coordinate of the position discussed on the beam, the frequency of the wave and the time, respectively, and i is the imaginary unit. The amplitude attenuation expressions of the two types of bending waves are respectively and The structural parameters are substituted into the amplitude attenuation expression to obtain the amplitude attenuation rate of the propagating wave and the near-field wave, and the position of the lateral force impact is determined according to the amplitude attenuation rate. The distance between the vibration excitation device and the piezoelectric sensor is defined as l c to ensure that the influence of the near-field wave at the position of the piezoelectric sensor can be ignored, that is, Step 3, determining the expected bending wave speed based on the bending wave transfer function in the beam and the relationship between the expected bending wave speed and the cross-sectional stiffness; Step 4, identifying the actual bending wave speed in the beam by a piezoelectric sensing technology and a wavelet transform algorithm, and taking the actual bending wave speed as an index to evaluate the cross-sectional stiffness evolution and monitor the change of the bending stiffness of the beam cross section.

2. The method of claim 1, wherein, Determining the expected bending wave speed based on the bending wave transfer function in the beam and the relationship between the expected bending wave speed and the cross-sectional stiffness comprises the following steps: The structural response waveform solution yields the propagating wave theory wave speed c t : According to the above formula, the theoretical wave speed can be obtained, and it is found that the wave speed monotonically increases with the increase of the cross-sectional bending stiffness.

3. The method of claim 2, wherein, The cross-sectional stiffness includes the cross-sectional size and the elastic modulus of the cross-sectional material, and can effectively comprehensively reflect the comprehensive performance of the cross-sectional stiffness of the tested beam section.

4. The method of claim 1, wherein, The actual bending wave speed in the beam is identified by piezoelectric sensing technology and wavelet transform algorithm, the piezoelectric sensor is connected to a high-frequency signal acquisition instrument to obtain the time history signal of the wave response in the beam, and the actual propagation speed c of the bending propagation wave is identified by wavelet transform a .

5. The method of claim 4, wherein, The actual bending stiffness of the beam member is evaluated by comparing and analyzing the measured bending propagating wave propagation speed and the theoretical wave speed: c a ≥c t then the actual flexural stiffness of the beam is superior to the design stiffness, c a is the actual propagation speed of the flexural propagating wave, c t is the theoretical wave speed of the propagating wave; c a <c t If the actual bending stiffness of the beam is less than the design bending stiffness, then the actual bending stiffness of the beam is less than the design bending stiffness. and real-time monitoring of c a The change of the cross-section bending stiffness evolution process is obtained, and the change of the cross-section stiffness is monitored through the change of the wave velocity.

6. The method of claim 1, wherein, The piezoelectric sensor is arranged in the form of being embedded in the beam or being pasted on the surface of the steel beam, and only needs to be connected to a collection instrument during monitoring, and if a sensor is damaged due to aging, it can be directly replaced without affecting the test results and without the need for recalibration.

7. A system for implementing the method of flexural stiffness monitoring of a beam based on the bending wave transfer function according to any one of claims 1 to 6, characterized in that, The device comprises a vibration excitation device, a piezoelectric sensor and a high-frequency signal collection instrument, the piezoelectric sensor is connected to the high-frequency signal collection instrument to collect elastic wave signals in the beam, the vibration excitation device is used to transversely impact the beam body to excite bending waves.

8. The system of claim 7, wherein, The piezoelectric sensor is embedded in the beam at a fixed interval along the length direction of the beam.

Images