Observations of how boundary conditions affect estimates of Poisson's ratio from simulated mode shapes

Abstract

This research extends a method for direct estimation of Poisson's ratio from mode shapes of plates with hinged-hinged boundary conditions to include combinations of clamped and free boundary conditions. Using finite element simulations, we observe the effects of boundary conditions on the estimate of Poisson's ratio using the combination of Time-Average Scanning Digital Holography and Cornu's method. First, we introduce the abstraction of the span-to-width ratio to an effective antinode region. This abstraction enables us to extend the direct estimation technique to plates with various boundary conditions. Second, for long and thin enough plates, the effects of boundary conditions become negligible and Cornu's method is sufficient for direct estimation of the true value of Poisson's ratio from an out-of-plane bending mode shape. We note that for many situations, the necessary plate dimensions could be a limitation. Therefore, as a third concept, we discuss the behavior of the direct estimate of Poisson's ratio with respect to each type of boundary condition. Ultimately, this research initiates a path forward for a common processing technique for making a direct estimate of Poisson's ratio across different types of opposing boundary conditions for thin plates.