A well-conditioned technique for solving the inverse problem of boundary traction estimation for a constrained vibrating structure

 Estimation of the frequency and spatial dependent boundary traction vector from measured vibration responses in a vibrating structure is addressed. This problem, also referred to as the inverse problem, may in some circumstances be ill-conditioned. Here a technique to overcome the ill-conditioning is proposed. A subset of a set of available eigenmodes is chosen such that the problem becomes well-conditioned enough. It is shown that the ill-conditioning originates from the fact that not all eigenmodes are orthogonal over the surface where the traction vector is sought. Consequently, by choosing a set of eigenmodes orthogonal over the surface of interest, the problem becomes well-conditioned. The calculated traction vector is shown to converge to the true one in the sense of a L₂-norm on the boundary of the body. The proposed technique is verified, using numerical simulation of measured responses, with good agreement. Received: 10 January 2002 / Accepted: 24 October 2002 This work was performed under contract from the Swedish Defence Material Administration (FMV). The funding provided is gratefully acknowledged. The author would like to thank all staff at the Structural Dynamics research group, Department of Structures and Materials, Aeronautics Division, Swedish Defence Research Agency.