Modal coupling in thermally stressed plates

Abstract

An approximate, but general, solution for the frequencies, thus the effective stiffnesses, in the first and second modes of initially deformed, thermally stressed plates of any planform shape and with any boundary condition is found in terms of quantities that may be obtained from the application of linear theory. It is shown that all plates exhibit the same characteristic changes in frequency, thus stiffness, independent of planform shape, boundary conditions and temperature distribution except as these factors affect the thermal buckling eigenvalues (AT critical) and the natural, uniform temperature frequencies. Coupling between the modes is shown to depend upon the ratio of the thermal buckling eigenvalues and the uniform temperature frequency ratio. Analytical data are presented to show that the second mode stiffness for a plate for certain values of the parameters does not always increase in the postbuckled region as implied in the literature. Experimental data, obtained from cantilever plates of different planforms, are presented to show that mode coupling is readily detected and cannot be neglected if a correct prediction of the effective stiffness of a plate is desired. The analysis may readily be extended to any desired number of modes. Only a qualitative comparison is made between theory and experiment in this paper. A carefully controlled test program will be required to produce data for a quantitative comparison.