Exploring the Limits of a Deflection-Based Method for the Estimation of Dynamic Stress in Beams

Abstract

Estimation of the dynamic stress in structures, such as beams and plates, has previously been made using the relationship between stress and velocity spatial maxima based on farfield assumptions. This paper presents a method for the estimation of dynamic stress in a beam using Euler-Bernoulli beam theory, where deflection data from a grid of measurement points on the surface of the beam is used to estimate the dynamic bending stress in the structure. The limitations of the method are investigated via response data provided by a numerical model of a free-free beam. A non-dimensional wavenumber analysis is used to determine the number of points required for an accurate estimate of stress. Beams with a range of material and geometric parameters are modelled in order to explore the limits of the estimation method, and parameters representative of several real-world materials are used to assess the suitability of the method for practical applications.