Boundary traction vector estimation in a vibrating structure using series expansion of the stress tensor

Abstract

Well-conditioned estimation of the inverse problem of calculating the dynamic boundary traction vector, acting on a vibrating structure is addressed. In this paper a well-conditioned, fully three-dimensional method in the frequency domain is proposed. The method is based on linear three-dimensional continuum mechanics and Hilbert space Fourier series. Moreover, the three-dimensional displacement vector and the second order stress tensor are expanded in spatial Fourier series. The proposed method is demonstrated on an analytical one-dimensional example consisting of a beam, and validated on a three-dimensional example. The validation gives very good results, especially in the L2-norm over the surface of interest.