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

Abstract

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 deformations. 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 complex coupling of both bending and torsional deformations. This work proposes a novel mode shape recognition algorithm, called the finite cross-section method (FCSM), for application to highly coupled beam-type structures not only to identify the deformation components of complex beam mode shapes but also more importantly to quantify their respective relative contribution. In the application case study for the FCSM, 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 are 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 scanning laser Doppler vibrometer (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.