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首页> 外文会议>AMD-vol.256; American Society of Mechanical Engineers(ASME) International Mechanical Engineering Congress and Exposition; 20051105-11; Orlando,FL(US) >NONLINEAR VIBRATIONS OF RECTANGULAR PLATES WITH DIFFERENT BOUNDARY CONDITIONS: THEORY AND EXPERIMENTS
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NONLINEAR VIBRATIONS OF RECTANGULAR PLATES WITH DIFFERENT BOUNDARY CONDITIONS: THEORY AND EXPERIMENTS

机译：具有不同边界条件的矩形板的非线性振动：理论与实验

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摘要

Large-amplitude vibrations of rectangular plates subjected to harmonic excitation are investigated. The von Karman nonlinear strain-displacement relationships are used to describe the geometric nonlinearity. A specific boundary condition, with restrained normal displacement at the plate edges and fully free in-plane displacements, not previously considered, has been introduced as a consequence that it is very close to the experimental boundary condition. Results for this boundary condition are compared to nonlinear results previously obtained for: (ⅰ) simply supported plates with immovable edges; (ⅱ) simply supported plates with movable edges, and (ⅲ) fully clamped plates. The nonlinear equations of motion are studied by using a code based on arclength continuation method. A thin rectangular stainless-steel plate has been inserted in a metal frame; this constraint is approximated with good accuracy by the newly introduced boundary condition. The plate inserted into the frame has been measured with a 3D laser system in order to reconstruct the actual geometry and identify geometric imperfections (out-of-planarity). The plate has been experimentally tested in laboratory for both the first and second vibration modes for several excitation magnitudes in order to characterize the nonlinearity of the plate with imperfections. Numerical results are able to follow experimental results with good accuracy for both vibration modes and for different excitation levels once the geometric imperfection is introduced in the model. Effects of geometric imperfections on the trend of nonlinearity and on natural frequencies are shown; convergence of the solution with the number of generalized coordinates is numerically verified.
机译：研究了矩形板在谐波激励下的大振幅振动。 von Karman非线性应变-位移关系用于描述几何非线性。由于它非常接近实验边界条件，因此引入了一种特定的边界条件，其在板边缘处的法向位移受到限制，并且以前没有考虑过完全自由的平面内位移。将该边界条件的结果与先前获得的非线性结果进行比较：（compared）具有固定边缘的简单支撑板； （ⅱ）具有活动边缘的简单支撑板，以及（ⅲ）完全夹紧的板。使用基于弧长连续法的代码研究了非线性运动方程。一块薄的矩形不锈钢板已插入金属框架中。通过新引入的边界条件可以很好地近似此约束。为了重建实际的几何形状并识别几何缺陷（平面外），已使用3D激光系统对插入框架中的板进行了测量。为了表征具有缺陷的板的非线性，已经在实验室中对板的第一和第二振动模式进行了多种激励幅度的实验测试。一旦在模型中引入了几何缺陷，则对于振动模式和不同激励水平，数值结果都能够以良好的精度跟随实验结果。显示了几何缺陷对非线性趋势和固有频率的影响。通过数值验证了该解与广义坐标数的收敛性。

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