Vibration and local instability of thermally stressed plates

The vibration and buckling of a double wedge square cantilever plate has been investigated. It is shown that the free vibration modes, which occur at ΔT_ref = 0, transition into the buckled modes which occur at ΔT_ref = ΔT_refcr for the respective mode. ΔT_refcr for a particular mode is defined as the magnitude of thermal load at which the frequency of the particular mode vanishes. The analysis, in which no assumption whatsoever is made about the shape of the vibration modes, about the vibration frequencies, about the shape of the buckled modes, or about the magnitude of the critical loads, yields the same number of buckling eigenvalues and buckling modes as there are vibration eigenvalues and vibration modes. Gradual application of the load in the analysis permits the change in each vibration frequency of interest and its associated mode to be followed up to the load at which the frequency of the mode becomes zero. This constitutes the limit of linear theory. Only linear theory is used in this paper; thus, no post buckled behavior is considered. As the load is increased, the thin edges of the plate begin to duform during vibration. This local deformation, which begins in the vibration mode, is shown to transition into the phenomena of local edge buckling at ΔT_refcr for the mode.