Damage identification method for cantilever beams based on the curvature of free end inclination influence line
A technology of damage identification and influence lines, applied in elastic testing, testing of machine/structural components, instruments, etc.
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Embodiment 1
[0087] Embodiment one: see Figure 7 , the span of the cantilever beam with equal cross-section is 100cm, and a unit is divided by 5cm, a total of 20 units and 21 measuring points (the numbers in the upper circle in the figure are the unit numbers, and the lower numbers are the measuring point numbers). The cross-sectional size of the plate is b×h=4.5cm×1.5cm, and the elastic modulus of the material is 2.7×10 3 MPa, Poisson's ratio is 0.37, density is 1200kg / m 3 .
[0088] The damage in the actual engineering structure, such as the generation of cracks, material corrosion or the reduction of elastic modulus, generally only causes a large change in the structural stiffness, but has little impact on the quality of the structure. Therefore, in the finite element calculation, it is assumed that the damage of the structural element only causes the decrease of the stiffness of the element, and does not cause the change of the mass of the element. Damage to elements is simulated b...
Embodiment 2
[0097] Embodiment two: see Figure 12 , the span of the variable-section cantilever beam is 100cm, and the division of units and nodes is the same as in Embodiment 1. The free end of the plate section size is b×h=4.5cm×1.5cm, and the fixed support end is b×h=22.5cm×3.0cm, The modulus of elasticity of the material is 2.7×10 3 MPa, Poisson's ratio is 0.37, density is 1200kg / m 3 .
[0098] The damage condition is the same as that in Embodiment 1.
[0099] The specific implementation steps are as follows:
[0100] Step 1: Apply a moving load of 1kN to obtain the influence line of the measured inclination angle of the free end measuring point 21 after the cantilever beam is damaged, respectively as follows Figure 13 .
[0101] Step 2: Calculate the curvature of the influence line of the dip angle after the damage of the beam structure, such as Figure 14 , the results show that there is an obvious peak at the unit 10, and it can be preliminarily judged that the unit 10 is da...
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