Deformation of Operating Deflection Shapes by sparse structural modification

To deform ODSs (Operating Deflection Shapes) with small structural modifications is useful for reducing vibrations at the designated frequency. In this study, we developed a method for achieving structural modifications to deform ODSs with as few structural modifications as possible by utilizing sparse modeling techniques. This method is designed to devise doubly sparse structural modifications, in which the initial mass and stiffness matrices are maintained in their sparsity while only some of the elements with values in the matrices are changed, when a finite element model of the target structure exists. The first sparsity was achieved using the Constrained Eigenstructure Assignment Method (CEAM). Furthermore, to ensure the second sparsity, we used the Least Absolute Shrinkage and Selection Operator (LASSO) to search for the weighting coefficients in CEAM. LASSO makes it possible to appropriately minimize the squared error of the ODSs with as few weighting coefficients, that is regularization, as possible. By combining CEAM and LASSO, we were able to obtain a heuristic solution search method that can achieve the desired operating mode by changing only the inertia and stiffness of some of the elements of the design.