Sensitivity of fundamental mode shape and static deflection for damage identification in cantilever beams

Fundamental mode shape and static deflection are typical features frequently used for identification of damage in beams. Regarding these features, an interesting question, still pending, is which one is most sensitive for use in damage identification. The present study addresses the key sensitivity of these features for damage identification in cantilever beams, wherein these features are extremely similar in configurations. The intrinsic relation between the fundamental mode shape and static deflection is discussed, and in particular, an explicit generic sensitivity rule describing the sensitivity of these features to damage in cantilever beams is proposed. The efficiency of this rule in identifying damage is investigated using Euler–Bernoulli cantilever beams with a crack. The validity of the approach is supported by three-dimensional elastic finite element simulation, incorporating the potential scatter in actual measurements. The results show that the generic sensitivity rule essentially provides a theoretical basis for optimal use of these features for damage identification in cantilever beams.