Stochastic thermal modal characteristics of a plate with free boundary conditions induced by a random heating position based on a thermally coupled model

Temperature has significant effects on thermal modal characteristics of a structure; especially, its distribution uncertainty makes thermal modal characteristics to be more complicated. Such un-certainty also makes definitely predicted results greatly deviate from thermal modal experimental results at high temperature, and even their change trends with temperature would be different. In this work, stochastic thermal modal characteristics of a plate with free boundary conditions induced by a random heating position are studied based on a thermally coupled model. Tem-perature field distributions of the plate under two-parameter Gaussian heating sources are first obtained. A thermally coupled dynamic model of the plate is then established based on a ther-mally coupled constitutive relation theory, and its modal parameters are obtained by a differ-ential quadrature method. A statistical analysis method with a small sample based on an improved Bootstrap method and folded normal distribution is proposed to study stochastic thermal modal characteristics of the plate induced by a random heating position, which includes probability density functions of natural frequencies and their confidence intervals. Relevant research will be of great significance to reliability evaluation of thermodynamic experimental results, and error analysis between experimental and theoretical results.