Displacement and Strain Statistics of Thermally Buckled Plates

Abstract

Previously, we used the single-mode Fokker-Planck distribution to predict displacement histograms of the numerical simulations and strain histograms of the plate experiments. Such an elemental distribution has proven effective in capturing the overall behavior of numerical displacement histograms. This is because the Fokker-Planck distribution is realizable. On the other hand, there are two possible equilibrium strain distributions derived from the Fokker-Planck distribution, one of which drops out when the forcing power input is small. By restricting the other strain distribution to a small forcing range, we have exhibited the skewing of experimental strain histograms toward the negative strain. We show here that the actual strain histograms of numerical simulation are neither one of the equilibrium strain distributions, but can be modeled by a linear combination of them. Hence, the unequal strain peaks may not be entirely due to a temperature gradient across the plate thickness, as previously proposed.