A unified expression for estimating Poisson’s ratio from a hinged–hinged beam with a use for abnormality detection

Abstract

Cycle fatigue weakens a structure. Poisson’s ratio is a sensitive indicator of cycle fatigue. The amount of fatigue is proportional to the severity of an abnormality, such as a crack, delamination or other imperfection. Our prior work confirms that direct estimates of Poisson’s ratio by Cornu’s method must be identical for all antinodes of a mode shape of a homogeneous, thin, hinged–hinged beam. Therefore, if a direct estimate at any antinode was found to be significantly different from the other estimates at the other antinodes, then that would simultaneously indicate fatigue and identify the location of the abnormality. We use simulations of Besselograms and apply Cornu’s method to directly estimate Poisson’s ratio at all antinodes of a beam. We transform finite element simulations of the out-of-plane bending displacements of mode shapes by simulating time-average scanning digital holography. We show that amount of disagreement between the direct estimation Poisson’s ratio and the true value of Poisson’s ratio depends on the ratio of the distance between nodes of a mode shape divided by the width of the beam. We call this distance between the nodes of a mode shape the ‘Span’. We then define a unified expression for predicting the simulated direct estimate given the true value of Poisson’s ratio and the Span-to-Width ratio. Next, we invert the unified expression, which enables us to use the Span-to-Width ratio and simulated direct estimates of Poisson’s ratio as the independent variables to compute the adjusted value of Poisson’s ratio. We find that our inverse expression makes it possible to obtain an estimate of Poisson’s ratio that is within ±2% of the true value for thin hinged–hinged beams and plates that have a Span-to-Width ratio greater than 1. We also find that if the material is known to have a Poisson’s ratio greater than zero, which can be assessed by our previous statement, then we can extend our confidence to Span-to-Width ratios greater than 0.1. That was the lower limit of our testing. Finally, we show how to use direct estimates of Poisson’s ratio to statistically detect and localize an abnormality along a hinged–hinged plate or beam. We believe that our combination of Cornu’s method and time-averaging could eventually offer the ability to directly estimate Poisson’s ratio from hinged–hinged beams and plates as well as to unambiguously monitor cycle fatigue for changes in effective material properties, predict time-to-failure, and do so without contact.