tliyou / recplatevibration

Calculate the vibration modes of a rectangular plate with free-free boundary conditions by the Ritz method.

RecPlateVibration

Calculate the vibration modes of a rectangular plate with free-free boundary conditions by the Ritz method. The vibration shape functions and natural frequencies are given in the MATLAB program.

Application condition:

1. Boundary conditions are not symmetric about the diagonal, including square plates and rectangular plates;
2. Boundary conditions are symmetric about the diagonal, while length-width ratio has great difference.

Not suitable for use:

1. Square plates with boundary conditions symmetric about the diagonal;
2. Rectangular plates with length-width ratio near 1(0.8 < a/b < 1.25).

Reference：

• Young D. Vibration of rectangular plates by the Ritz method[J]. Journal of Applied Mechanics-Transactions of the ASME, 1950, 17(4): 448-453.

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矩形平板振动

采用里茨法（双向梁函数组合级数逼近，单项组合法）计算自由-自由边界条件下矩形平板的振动模态，包括振型函数及固有频率。

适用情况：

1. 边界条件不以对角线为对称的板（包括方板、矩形板）；
2. 边界条件以对角线为对称的矩形板（两临边边长相差较大）。

不适用情况：

1. 边界条件以对角线为对称的方板；
2. 接近方形板的矩形板（0.8 < 长宽比 < 1.25）。

参考文献：

• 曹志远. 板壳振动理论[M]. **铁道出版社, 1989.