An exact solution of a partial differential equation including elastic compliance constant s'/sub 56/, with respect to stress function /spl psi/ has been found for torsional modes of vibration of an arbitrary (singly, doubly, triply) rotated beam with a pair of parallel free edges. The solution is obtained by relaxing the condition that the edge planes are perpendicular to the main faces of the beam. That is, the edges are off perpendicular by the angle /spl Theta/=arctan(-s'/sub 56//8'/sub 55/). The exact solution can reduce the difference of the calculated and measured values for a thickness-to-width ratio which gives the first-order temperature coefficient /spl alpha/=0. Also, a comparatively large inclination of the edge cuts is required to reduce the unwanted complicated mode shapes to simple ones.
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机译：对于任意旋转的（单，双，三重）旋转梁的扭转振动模式，已经找到了关于应力函数/ spl psi /的包括弹性柔度常数s'/ sub 56 /在内的偏微分方程的精确解。一对平行的自由边。该解决方案是通过放宽边缘平面垂直于光束主面的条件而获得的。也就是说，边缘偏离垂直角度为/ spl Theta / = arctan（-s'/ sub 56 // 8'/ sub 55 /）。对于给出一阶温度系数/ spl alpha / = 0的厚度/宽度比，精确的解决方案可以减少计算值和测量值之间的差异。另外，需要将边缘切口的倾斜度较大，以将不想要的复杂模式形状减小为简单形状。
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