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首页> 外文会议>The 2001 ASME International Mechanical Engineering Congress and Exposition, 2001, Nov 11-16, 2001, New York, New York >EXACT SOLUTIONS FOR THE FREE VIBRATIONS AND BUCKLING OF RECTANGULAR PLATES WITH LINEARLY VARYING IN-PLANE LOADING
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EXACT SOLUTIONS FOR THE FREE VIBRATIONS AND BUCKLING OF RECTANGULAR PLATES WITH LINEARLY VARYING IN-PLANE LOADING

机译：平面内线性变化的矩形板自由振动和屈曲的精确解

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摘要

An exact solution procedure is formulated for the free vibration and buckling analysis of rectangular plates having two opposite edges simply supported when these edges are subjected to linearly varying normal stresses. The other two edges may be clamped, simply supported or free, or they may be elastically supported. The transverse displacement (w) is assumed as sinusoidal in the direction of loading (x), and a power series is assumed in the lateral (y) direction (i.e., the method of Frobenius). Applying the boundary conditions yields the eigenvalue problem of finding the roots of a fourth order characteristic determinant Care must be exercised to obtain adequate convergence for accurate vibration frequencies and buckling loads, as is demonstrated by two convergence tables. Some interesting and useful results for vibration frequencies and budding loads, and their mode shapes, are presented for a variety of edge conditions and in-plane loadings, especially pure in-plane moments.
机译：为矩形板的自由振动和屈曲分析制定了精确的求解程序，该矩形板具有两个相对的边缘，当这些边缘承受线性变化的法向应力时，这些边缘被简单支撑。其他两个边缘可以夹紧，简单支撑或自由支撑，也可以弹性支撑。假定横向位移（w）在载荷方向（x）上为正弦曲线，并且假定幂级数在横向（y）方向上（即Frobenius方法）。应用边界条件会产生寻找四阶特征行列式的根的特征值问题，必须谨慎行事，以针对准确的振动频率和屈曲载荷获得足够的收敛，如两个收敛表所示。针对各种边缘条件和平面载荷，尤其是纯平面矩，给出了一些有趣的，有用的振动频率和萌芽载荷及其模态形状的结果。

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