Thermal impact produced onto a thermoelastic plate that demonstrates special boundary conditions

The problem of forced vibrations of plates exposed to the thermal impact is interesting both as a theoretical implication and an issue of practical importance. A thermal impact causes formation of a non-steady temperature field. Thereafter, some materials turn fragile and cannot withstand the exposure to the impact of a thermal field. The authors propose a solution to the problem of influence of a thermal impact onto an isotropic plate that demonstrates special boundary conditions, if its two opposite edges are simply supported, and the surface temperature is equal to zero, while the two other edges might have an arbitrary type of fixation and an arbitrary thermal mode. In the first part of the paper, the authors provide their derivation of the elastic plate vibration equation, if the plate is exposed to the thermal impact under the pre-set boundary conditions. In the second part of the paper, the authors provide their solution to the aforementioned problem based on a strictly mathematical approach. Their solution is presented as an integral function of the plate deflection. The solution in question may be reduced to algebraic frequency equations by using the method of expansion of trigonometric functions. Thus, it is possible to identify natural frequencies of the plate vibration caused by the thermal impact