DYNAMIC TRACTION VECTOR FIELD ESTIMATION IN A STRUCTURE USING HYBRID STRAIN ANALYSIS

Abstract

The three-dimensional dynamic traction vector of a vibrating structure is obtained with the aid of the so-called hybrid strain analysis. Hybrid strain analysis is a method where vibration response measured at a limited number of points and numerically approximated continuous Hilbert space basis functions combined with spatial differentiation yields the frequency-dependent strain tensor field in a vibrating structure.Here, an extension and special application of hybrid strain analysis is proposed. In a special case with a built-up structure with unknown dynamic properties in the interfaces between the parts, the frequency- and spatial-dependent stress tensors, and thus also the traction vector, are obtained for the structural parts using the proposed technique.The method is validated using numerical simulation of measured vibration responses, with very good agreement between the calculated and the true traction vector. The calculated traction vector is shown to converge towards the true traction vector in an arbitrary small area on the boundary of the structure.The method is demonstrated for isotropic elastic material properties. This is, however, no limitation for the method; it can be also applied to a structure with anelastic material properties.