Structural Intensity Assessment on Shells via the Projection of Experimental Data on a Finite-Element Mesh

摘要

The computation of the structural intensity on the basis of measured displacement fields is an approach that permits the visualization of energy paths taking place on thin structures. The development of such an analysis is made feasible when the sample is assumed to behave in accordance with the Kirchhoff-Love postulates. This permits the generalized forces within the structure to be estimated through the differentiation of displacement data, which in turn are the inputs to assess the vibrational energy flow. Such an analysis is widely documented in cases, which the sample is either a plate or a shell-like structure with simple geometrical configurations. However, it is from the author's knowledge that such an analysis has not yet been performed on arbitrary geometries, such as doubly curved shells. This work proposes a method that allows the structural intensity of an arbitrary geometry to be computed on the basis of measured displacement fields and spatial coordinates from a sample's outer-surface. After measuring these fields via a Digital Image Correlation set-up, it is assumed that the geometrical data can be represented as an assembly of flat plates. The elements of this assembly overlap with the sample's spatial coordinates and are treated as the constituents of a finite element mesh. Afterwards, the experimental displacement fields are projected on the nodes of that mesh via a global least-squares minimization approach, which in turn enables the nodal deformations to be differentiated with proper finite element shape functions. By assuming that the elements of the mesh behave in accordance with the Kirchhoff-plate theory, it is feasible to estimate the generalized forces on the sample's mid-surface and to assess the structural intensity vector field. By treating the geometrical spatial coordinates as a finite element mesh and the displacement data as projected degrees of freedom, the presented method has shown itself to be a reliable tool to extract the vibrational energy taking place on arbitrary shells.