Free Vibration of Thermally Pre/post-buckled Circular Thin Plates Embedded with Shape Memory Alloy Fibers

Axisymmetric deformations of a uniformly heated pre-buckled and post-buckled thin circular plate reinforced with shape memory alloy (SMA) fibers placed in the radial direction only are studied. Effects of von Kármán’s nonlinearities are incorporated in the problem formulation. The matrix is assumed to be linear thermoelastic and the thermo-mechanical response of the SMA is modeled by one-dimensional constitutive relation. By assuming that plate’s deflections can be additively decomposed into three parts, namely radial displacements of a pre-buckled plate, radial and lateral displacements during post-buckling deformations, and infinitesimal radial and lateral displacements during vibration of a post-buckled plate, boundary-value problems for determining these displacements for plate edges either simply supported or clamped have been formulated. The coupled nonlinear differential equations have been numerically solved by the shooting method that has been verified by good agreement between the presently computed results with those available in the literature. The dependence of the first three frequencies upon the temperature rise, for both pre-buckled and postbuckled plates, has been delineated. Characteristic curves relating the frequency with the temperature rise for different values of the volume fraction and the pre-strain in the SMA fibers are exhibited. It is found that reinforcement of an aluminum plate with SMA fibers changes plate’s natural frequencies and enhances its resistance to buckling due to temperature rise.