Abstract
Temperature has significant effects on the modal parameters of a structure. In general, as the temperature increases, the natural frequencies of a structure decrease with the softening of mechanical properties of the material at high temperature. However, it can be found from some thermal modal experiments that the natural frequencies of a structure do not monotonically decrease with temperature, which is regarded as the nonmonotonical behavior (NMB) of thermal modal characteristics of the structure. The mechanism of this experimental phenomenon is unclear. The first purpose of this work is to further confirm that the NMB of the thermal modal characteristics of a titanium plate with free boundary conditions occurs, and it is not affected by uncertain factors in the temperature field. The second purpose of this work is to use a thermally coupled dynamic shell model of the titanium plate with geometrical imperfection to explain the NMB of the titanium plate with free boundary conditions. By considering the significant effect of the geometrical imperfection of the plate on its thermal modal characteristics, the third purpose of this work is to propose a new method for thermal modal design by precreating the geometrical imperfection of the plate. Some interesting results of the thermal modal design of the titanium plate are presented.