Damage identification method for beam structures based on mode weighted modal flexibility

Abstract

The invention discloses an identification method for beam structure damage of vibration mode weighing modal flexibility. The method comprises the following steps: obtaining frequency and the vibration mode of the beam structure before and after the damage through a modal test; calculating vibration mode curvature sign function weighing damage index based on the frequency and the vibration mode before and after the damage to locate the damaged structure, calculating a beam structure node damage degree according to a relative change of the vibration mode curvature sign function weighing damage index before and after the damage, and then calculating a unit damage degree. The identification method for the beam structure damage of the vibration mode weighing modal flexibility can effectively determine a damage location of a single-damage and multi-damage working condition for the beam structure, the calculation method of the damage degree of the corresponding index under a statically determinate structure and a statically indeterminate structure can be used to identify the damage degree accurately, the shortcomings that the existing modal flexibility curvature index cannot be used to identify the damage degree are overcome, and the method can be applied to the nondestructive testing and damage degree assessment of the beam structure.

Description

technical field

[0001] The invention belongs to the field of structural health monitoring, and in particular relates to a beam structure damage identification method based on vibration mode weighted modal flexibility. Background technique

[0002] Bridge structures are widely used in highways, high-speed railways and other civil engineering fields that play an important role in national economic development. They are the lifeline projects of traffic throat and national economic development, and their health status is increasingly concerned by the public. At present, many countries have installed health monitoring systems on newly-built important bridge structures, such as the Tsing Ma Bridge in Hong Kong, the Sutong Bridge, the Runyang Yangtze River Highway Bridge, and the Akashi Kaikyo Bridge in Japan. How to analyze a large amount of collected data and judge the state of the structure is a research hotspot at home and abroad.

[0003] Structural damage identification is a...

Examples

Embodiment 1

[0128] Embodiment one: see image 3 , is a simply supported beam with a span of 10m and is equally divided into 20 units (the numbers in the upper circle in the figure are the unit numbers, and the lower numbers are the node numbers). The cross-sectional size is b×h=300mm×500mm, and the elastic modulus of the material is E=3.25×10 4 MPa, the density is 2500kg / m 3 . The damage of the unit is simulated by the reduction of the elastic modulus, and the damage conditions of the beam structure are shown in Table 1:

[0129] Table 1 Damage conditions of simply supported beams

[0130]

[0131] The specific implementation steps are as follows:

[0132] Step 1: Obtain the first three vertical frequencies and mode shapes of the simply supported beam before and after damage through finite element model simulation analysis.

[0133] Step 2: Calculate the weighted damage index of the mode shape curvature sign function according to the frequency and mode shape before and after the d...

Embodiment 2

[0135] Embodiment two: see Figure 8 , is a three-span continuous beam finite element model, its span layout is 10m+15m+10m, 1.0m is divided into one unit, a total of 35 units, 36 nodes, (the number in the upper circle in the figure is the unit number, The numbers in the lower row are node numbers). The cross-sectional size is b×h=300mm×500mm, and the elastic modulus of the material is E=3.25×10 4 MPa, the density is 2500kg / m 3 . The damage of the unit is simulated by the reduction of the elastic modulus, and the damage conditions of the beam structure are shown in Table 2:

[0136] Table 2 Damage conditions of three-span continuous beams

[0137]

[0138] The specific implementation steps are as follows:

[0139] Step 1: Obtain the first three vertical frequencies and mode shapes of the three-span continuous beam before and after damage through finite element model simulation analysis.

[0140] Step 2: Calculate the weighted damage index of the mode shape curvature s...

technical field

[0001] The invention belongs to the field of structural health monitoring, and in particular relates to a beam structure damage identification method based on vibration mode weighted modal flexibility. Background technique

[0002] Bridge structures are widely used in highways, high-speed railways and other civil engineering fields that play an important role in national economic development. They are the lifeline projects of traffic throat and national economic development, and their health status is increasingly concerned by the public. At present, many countries have installed health monitoring systems on newly-built important bridge structures, such as the Tsing Ma Bridge in Hong Kong, the Sutong Bridge, the Runyang Yangtze River Highway Bridge, and the Akashi Kaikyo Bridge in Japan. How to analyze a large amount of collected data and judge the state of the structure is a research hotspot at home and abroad.

[0003] Structural damage identification is a...

Examples

Embodiment 1

[0128] Embodiment one: see image 3 , is a simply supported beam with a span of 10m and is equally divided into 20 units (the numbers in the upper circle in the figure are the unit numbers, and the lower numbers are the node numbers). The cross-sectional size is b×h=300mm×500mm, and the elastic modulus of the material is E=3.25×10 4 MPa, the density is 2500kg / m 3 . The damage of the unit is simulated by the reduction of the elastic modulus, and the damage conditions of the beam structure are shown in Table 1:

[0129] Table 1 Damage conditions of simply supported beams

[0130]

[0131] The specific implementation steps are as follows:

[0132] Step 1: Obtain the first three vertical frequencies and mode shapes of the simply supported beam before and after damage through finite element model simulation analysis.

[0133] Step 2: Calculate the weighted damage index of the mode shape curvature sign function according to the frequency and mode shape before and after the d...

Embodiment 2

[0135] Embodiment two: see Figure 8 , is a three-span continuous beam finite element model, its span layout is 10m+15m+10m, 1.0m is divided into one unit, a total of 35 units, 36 nodes, (the number in the upper circle in the figure is the unit number, The numbers in the lower row are node numbers). The cross-sectional size is b×h=300mm×500mm, and the elastic modulus of the material is E=3.25×10 4 MPa, the density is 2500kg / m 3 . The damage of the unit is simulated by the reduction of the elastic modulus, and the damage conditions of the beam structure are shown in Table 2:

[0136] Table 2 Damage conditions of three-span continuous beams

[0137]

[0138] The specific implementation steps are as follows:

[0139] Step 1: Obtain the first three vertical frequencies and mode shapes of the three-span continuous beam before and after damage through finite element model simulation analysis.

[0140] Step 2: Calculate the weighted damage index of the mode shape curvature s...

Images