Construction of three-dimensional orthogonal surface basis functions and well-conditioned boundary traction vector estimation Original Research Article

A well-conditioned technique for the solution of the inverse problem of boundary traction estimation, in the frequency domain, from measured vibration responses on a solid structure is proposed. The technique is based on recent results regarding lack of mode orthogonality on sub-domains of the structure. This is one of the reasons that modal-based solutions to the inverse problems may be numerically ill-conditioned. Herein construction of orthogonal three-dimensional basis functions, over a sub-domain of the structure, and a well-posed model for inverse boundary traction estimation are proposed. The technique is validated on a three-dimensional example using direct FE-calculated responses as simulation of measured responses with very good results.