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首页> 外文期刊>Applied Mechanics and Engineering >FREE TRANSVERSE VIBRATIONS OF MONOCLINIC RECTANGULAR PLATES WITH CONTINUOUSLY VARYING THICKNESS AND DENSITY
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FREE TRANSVERSE VIBRATIONS OF MONOCLINIC RECTANGULAR PLATES WITH CONTINUOUSLY VARYING THICKNESS AND DENSITY

机译：厚度和密度连续变化的单斜矩形板的自由横向振动

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摘要

Free transverse vibrations of a rectangular plate composed of a monoclinic elastic material are discussed. The plate is considered to be exponentially varying in density and thickness along one direction of the plate. Hamilton's principle is used to derive the equation of motion and its solution is obtained using Chebyshev collocation technique. Frequency equations are derived for three boundary value problems when two edges of the plate are simply supported and the other two have different possibilities, namely (ⅰ) C - S - C - S (ⅱ) C - S - S - S (ⅲ) C-S-F-S, where C, S and F denote the clamped, simply supported and free edge respectively. Effects of thickness and density variation on modes of vibrations have been analyzed. Numerical computations have been performed for a specific model of monoclinic plates and the results obtained are compared with those for orthotropic plates already given in Lal (2003).
机译：讨论了由单斜弹性材料组成的矩形板的自由横向振动。认为板沿板的一个方向在密度和厚度上呈指数变化。使用汉密尔顿原理导出运动方程，并使用切比雪夫搭配技术获得其解。当简单地支撑板的两个边缘并且另外两个边缘具有不同的可能性时，针对三个边值问题导出频率方程，即（ⅰ）C-S-C-S（ⅱ）C-S-S-S（ⅲ） CSFS，其中C，S和F分别表示夹紧的，简单支撑的和自由边缘。分析了厚度和密度变化对振动模式的影响。已经对单斜板的特定模型进行了数值计算，并将获得的结果与Lal（2003）中已经给出的正交各向异性板的结果进行了比较。

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