A Damage Identification Method for Simply Supported Beams Based on the Curvature of Uniform Load Surface in Damage State
A technology of damage identification and surface curvature, applied in the direction of instrumentation, design optimization/simulation, calculation, etc., to achieve good results
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[0082] The technical solution of the present invention will be described in further detail below in conjunction with the accompanying drawings and specific embodiments.
[0083] 1 Damage identification method
[0084] 1.1 Curvature of uniform load surface in damage state
[0085] The flexibility matrix F of the structure can be obtained from the mode shape normalized by mass as follows:
[0086]
[0087] Where: Φ=[φ 1 ,φ 2 ,…,φ m ] is the mode matrix, m is the mode order, φ i =[φ i1 φ i2 … φ in ] T is the i-th mode shape vector, n is the number of extracted mode shape nodes, is a diagonal matrix, ω i is the natural frequency of the i-th mode.
[0088] The flexibility matrix of the damaged state structure is:
[0089]
[0090] The displacement of the structure under load can be calculated by the flexibility matrix:
[0091] w=F·P (3)
[0092] In the formula: w is the displacement, P is the load column vector.
[0093] When P is taken as the unit of unifo...
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