The paper is devoted to a simply supported rectangular plate subjected to two types of compressive edge loads. The first load is applied uniformly along a part of two opposite edges, the second one has a non-uniform distribution (defined by a half wave of the sin^k function). The critical load value of the plate is located between the values for uniformly distributed and concentrated load. Critical value of thickness of the plate is determined. The problem is solved by the orthogonalization method, and the results are compared with those of numerical analysis done by means of the finite element method.

For thin-walled structures invariably exposed to thermal and noise environment, their dynamic response is an extreme concern in the design of the component of advanced hypersonic aircraft. To address the problem, three theoretical models are established with three typical graded thermal distributions considered. By introducing the thermal moment, membrane forces and acoustic loadings into the vibration equation of plate, the governing equation is derived and it is solved combined with boundary conditions of the plate, the modal function and velocity compatibility equations at the fluid-structure coupling surface. The accuracy of the theoretical predictions is checked against finite element results with good agreement achieved. The results show that not the physical parameters with variation of temperature but the thermal moments and membrane forces, cause the buckling phenomenon. It is noted that buckling phenomenon occurs not only in uniform temperature field but also in graded temperature distribution filed. The mechanism analysis about modal snap-through and losing phenomenon indicates that thermoacoustic loadings will affect the stiffness matrix and mass matrix of structure. With the increase of temperature, the lower modes of the plate are lost, the higher modes appear in advance, and the losing phenomenon occurs in accordance with the order.