The accuracy of modal superposition methods for determining displacement or strain field of structures largely depends on the selection of modes relevant to its deformation. Analytical methods for modal selection have been developed to minimise errors in reconstructing deformation through a linear combination of modal shapes. This study constitutes an initial step towards the development of structural health-monitoring algorithms for large engineering machines, where continuous monitoring of strain and stress, assuming a linear elastic field, is critical. The focus is on selecting modes that significantly contribute to the reconstruction of static deformation of structures. A detailed analytical approach, derived from established structural dynamics principles, leads to the formulation of modal selection criteria. These criteria are based on two fundamental quantities from dynamic and elastic theory: the modal participation factor and internal strain potential energy. Three criteria are introduced: the directional participation factor criterion (DPFC), the global participation factor criterion (GPFC), and the internal strain potential energy criterion (ISPEC). While DPFC and GPFC rely on displacements, ISPEC uses strains. The methods are validated through a case study involving a rectangular plate subjected to various loads, demonstrating their applicability to complex deformation scenarios, which require the combination of multiple modes to fully describe the static deformation. The proposed criteria are formulated for linear elastic systems and are therefore applicable, in principle, to plate-like components, machine casings, thin structural panels, and certain civil and aerospace panels, under the assumptions of small strains, linear constitutive behaviour, and validity of modal superposition. The approach also represents a first step towards the integration of modal selection with machine learning for structural health-monitoring applications and presents a computational cost significantly lower than that of full finite element analyses.
Liuzzo et al. (Fri,) studied this question.