A study has been carried out of the free vibrations of a solid-wing structure with a diamond-shaped profile. Vibration frequencies and modes are obtained at different levels of the temperature, which is distributed in a way that is typical for such wings at high speed. It is found that the lowest Vibration modes are of local character for wings with elevated temperature. Large displacements in the local modes include membrane stresses, so flutter in such modes must be of limited amplitude. In addition, a very small imperfection in the midplane of the plate is sufficient to make the lowest frequencies relatively insensitive to thermal buckling. Thermal buckling of the leading edge, then, is not likely to change the aeroelastic properties of the wing severely.

Vibration analysis of heated plates

SUMMARY The thermal buckling of solid wings with all edges free is analyzed by the Rayleigh-Ritz method. First wings of large aspect ratios are treated and the end effect is neglected. A double series of orthogonal polynomials is assumed for the de­ flection function, and by the use of successively increasing num­ bers of terms the predominance of the simple torsional distortion is established for a number of typical temperature distributions for wings of constant thickness and of parabolic cross section. The effect of variation of aspect ratio in this analysis is also ex­ amined. The validity of the conclusion about the predominance of the simple torsional distortion is then verified by a buckling analysis for a wing of constant thickness and small aspect ratio, using an approximate solution of the thermal-stress problem of a finite rectangular plate. Having been established as a good approximation, the tor­ sional analysis is now modified to include wings of small aspect ratio also. It is shown that the effects of chordwise normal stresses and shear stresses cancel out, and that the critical tem­ perature of a finite wing can be obtained from that of an infinite wing by multiplication by an "end effect factor." This factor is calculated for various temperature distributions for wings of constant thickness, parabolic cross section and double wedge shape, and shown to be approximately the same for different typical temperature distributions and nearly unaffected by the shape of the cross section. The end effect is found to be signifi­ cant (more than 10 per cent for aspect ratios below 6), but can be included with very little additional work.

Josef Singer

Papers

Thermal Buckling of Solid Wings of Arbitrary Aspect Ratio