Finite Cross-Section Method (FCSM) for Mode Shape Recognition of Highly Coupled Beam-Type Structures

The mode shapes of beam-type structures, such as aircraft wings and wind turbine blades, involve a high degree of coupling between bending and torsional deformation. In the case of wind turbine blades, different types of deformation are typically easily recognized by visual observation. However, this visual approach is sometimes challenging for high-order mode shapes, which involve coupling of both bending and torsional deformations. This work proposes a novel mode shape recognition algorithm, called Finite Cross-Section Method (FCSM), for application to highly coupled beam-type structures not only to identify the deformation components of the complex beam mode shapes, but more importantly, to quantify their respective relative contribution. In the application case study for the FCSM method, the entire structure is discretized into multiple cross-sections. The flap-wise, edge-wise, and torsional deformation components of the entire structure are determined at the cross-section level. The deformation components of the entire structure and their respective contribution is obtained from assembling all cross-sections. To validate the mode shape recognition performance, FCSM is applied to and demonstrated on four test cases: (1) numerical mode shapes of a simple cantilever beam, (2) numerical mode shapes from a straight wind turbine blade, (3) numerical mode shapes of a swept wind turbine blade, and (4) experimental mode shapes from a high spatial resolution 3D SLDV modal test. Both numerical and experimental studies demonstrate that FCSM can successfully recognize the quantitative contribution of flap-wise, edge-wise, and torsional deformation.