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发表于 2010-11-10 16:26:32
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来自 上海
25# lovelyzibing的解答有道理。最近我看了Peter Avitabile的《Modal Space --- in our own little world》中说到有关模态振型出现的顺序问题。文中原话如下: The simple fact is that the frequency and mode shape sequence is due to the mass and stiffness distribution of the structural configuration and not due to anything else. In order to illustrate the mode sequence arrangement possibilities, three different plate configurations with different length to width aspect ratios were generated and finite element solutions were obtained for each. These are shown in the figure with the arrangement from lowest to highest mode from top to bottom. The modes are further indicated with a B for bending along the longer length of the plate, B2 for bending along the shorter length of the plate, and T for torsion about the symmetry axis. For the three different plates analyzed, there is no specific ordering of the mode shape sequence. Each of the plates has a different combination as seen in the figure. And as long as we are on the subject of mode shapes, the question to ask is if the bending along the longer length of the plate (B) will always occur at a lower frequency than the bending along the shorter length of the plate (B2)? Now before you too quickly just answer that question, stop and think about it for a minute…….. Is this a trick question? What do I need to think about before I answer that question? What are the material properties? And are they the same along the long and short length? If the material is homogeneous, then the bending mode along the long length (B) will occur before the bending mode along the short length (B2). But what if the material is a reinforced carbon fiber composite where the stiffening fibers run along the longer length of the plate? Then there is a possibility that the plate will be much stiffer along that length. Then it is also possible that the frequency of the bending along the shorter length (B2) may occur before the frequency along the longer length (B). (Oh my, Toto – I am not sure we are in Kansas anymore!). Obviously, the bottom line here is that you really need to think about this possibility. It is a very possible reality! I have tried to answer your question about mode order for a plate. Obvoiusly, this holds true for any structural configuration that has characteristic bending and torsion modes – not just a plate configuration.
基本事实就是频率和各阶模态振型出现的次序只受结构质量和刚度分布的影响,不受其他因素影响。
为了说明各阶模态可能出现的次序,用有限元方法生成三个不同构造的平板结构,长宽比不同,求解每一个结构。下图中给出了三个不同结构的前五阶模态,从顶部到底部模态次序依次为从最低阶到最高阶(仅考虑前五阶)。其中字母B表示沿长边方向的弯曲模态,B2表示沿短边方向的弯曲模态,T表示沿对称轴的扭转模态。分析这三个不同构造的平板,可以看出平板没有特定的模态振型出现次序。从图中可以看出,每个结构的模态出现次序都不相同。
只要我们关心各阶模态振型出现的先后次序,那么有人就会问,是否沿平板长边方向的弯曲模态(B)总是比沿短边方向的弯曲模态(B2)先出现?在快速回答这个问题之前,停下来作进一步的思考……
这是一个欺诈性的问题?在回答这个问题之前,我需要思考什么?材料属性是什么?沿长边和短边的属性相同吗?如果材料是各向同性材料,那么沿长边方向的弯曲模态(B)将会先于沿短边方向的弯曲模态(B2)出现。但如果材料是加强的碳纤维复合材料,加强的碳纤维沿平板长边方向分布,那么情况又怎样呢?那么这时可能的情况是沿长边方向平板的刚度更大。因此,此时也有可能是沿短边方向的弯曲频率(B2)先于沿长边方向的弯曲频率 (B) 出现。显然,原则就是你确实需要思考这种可能性,现实中完全是可能的!
我已经设法回答了平板的各阶模态可能出现的次序这个问题。显然,任何构造的结构都有自身特有的弯曲和扭转模态,不仅仅是平板结构,其各阶模态出现的次序也不是特定,取决于质量和刚度的分布。
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