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Several comments:
If accepted, I could add most of these addendums. Hyprwfrcp ( talk 04:48, 21 May 2015 (UTC)
Someone please add which motions of the system above the two normal modes represent! -- 128.252.125.40 19:41, 27 September 2007 (UTC)
pick your favorite:
(never made a mechanical diagram before.) - Omegatron 14:17, Jul 21, 2004 (UTC)
All are nicely down. I vote for the third. MathKnight 16:25, 21 Jul 2004 (UTC)
Isn't it a way you can crop the 3rd one? MathKnight 18:07, 21 Jul 2004 (UTC)
I consider myself reasonably informed, but I'm completely daunted by the maths on this page. Isn't there another way to explain what this means? Electricdruid 00:36, 29 January 2006 (UTC)
The article is nice but it seems to imply a lots of things and not really state much... On a slightly different note, perhaps it should be mentioned at the very beginning that normal modes generally refer to systems of coupled oscillators? And that its not simply a matter of frequency but also the relative phase differences?
For example three springs connected in such a way that masses are on the points of a triangle. One possible mode would be the 'breather mode' where all the springs compress and extend in phase. Another would that one spring contracts while the other two extends. Or maybe the coupled pendulum case may be more easily related as swings (but personally I find it less intuitive in terms of eigenvectors - its so easy to choose another basis set, I'm more aware of the eigenvectors more oscillators are involved! ) And that these modes form a complete set of `different types of oscillations' - the eigenvectors, from which all possible forms of oscillations may be constructed. 141.2.215.190 19:12, 4 January 2007 (UTC)
Dynamic modes are important to any system governed by linear homogenous differential equations, this includes aircraft stability modes, shimmy, flutter, hunting, etc. I have used this article as a cross reference from Gyro monorail but it is not sufficiently general. The alternative reference to Eigenvalues is really too arcane, even for the above average reader who could cope with the maths in the monorail article.
May I suggest introducing the subject with reference to the classical eigenvalue problems. The first is the ancient problem of how slender a column can be made before it will buckle. This dates back to the ancient Greeks, who considered slender columns to be aesthetically more pleasing than the squat pillars characteristic of Egyptian architecture. The solution is the Euler buckling theory, which is a simple eigenvalue problem. There is an infinite number of failure loads, each corresponding to a different deformation shape. Each deformation shape is a mode. The fact that we are only usually concerned with the lowest buckling load is irrelevant - we can always imagine a situation where a large load is suddenly applied - invoking a higher order mode.
Staying with the ancient Greeks, the first recorded eigenvalue problem is the prediction of the pitch of a taut string when it is plucked. Pythagoras used the ratios of string lengths to relate number to harmony. Here again, the string has an infinite number of modes which may be excited by plucking or bowing. Both the strut and stretched string may be illustrated with diagrams of sinusoidal deformations. After all a mode is essentially a shape which characterises the displacement of the system from its undisturbed state, and a frequency of the associated motion (or, in the strut case an associated buckling load).
These descriptions could be backed up by mathematics, but this should not be necessary. After all, most school kids are aware that a six inch ruler is harder to buckle than a 12inch ruler. Most people have noticed that blowing harder into a recorder causes the pitch to suddenly double. I suggest that appeal to everday experience, rather than to apparently obscure and esoteric applications is more likely to convey the idea to a wide audience. Gordon Vigurs 11:25, 7 March 2007 (UTC)
Well I merged it.
The contents of the Mode Shape page were merged into Normal mode. For the contribution history and old versions of the redirected page, please see its history; for the discussion at that location, see its talk page. |
Kallog ( talk) 03:57, 20 March 2010 (UTC)
hope you're all happy with my clarification on why the determinant must be zero. Reading the article, I found it was easy to mistakenly think that the matrix would have to be invertible, as the singular link in fact links to the article about non-singular matrices.-- Ask a Physicist ( talk) 17:01, 3 December 2011 (UTC)
This
level-5 vital article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||||||||||
|
Several comments:
If accepted, I could add most of these addendums. Hyprwfrcp ( talk 04:48, 21 May 2015 (UTC)
Someone please add which motions of the system above the two normal modes represent! -- 128.252.125.40 19:41, 27 September 2007 (UTC)
pick your favorite:
(never made a mechanical diagram before.) - Omegatron 14:17, Jul 21, 2004 (UTC)
All are nicely down. I vote for the third. MathKnight 16:25, 21 Jul 2004 (UTC)
Isn't it a way you can crop the 3rd one? MathKnight 18:07, 21 Jul 2004 (UTC)
I consider myself reasonably informed, but I'm completely daunted by the maths on this page. Isn't there another way to explain what this means? Electricdruid 00:36, 29 January 2006 (UTC)
The article is nice but it seems to imply a lots of things and not really state much... On a slightly different note, perhaps it should be mentioned at the very beginning that normal modes generally refer to systems of coupled oscillators? And that its not simply a matter of frequency but also the relative phase differences?
For example three springs connected in such a way that masses are on the points of a triangle. One possible mode would be the 'breather mode' where all the springs compress and extend in phase. Another would that one spring contracts while the other two extends. Or maybe the coupled pendulum case may be more easily related as swings (but personally I find it less intuitive in terms of eigenvectors - its so easy to choose another basis set, I'm more aware of the eigenvectors more oscillators are involved! ) And that these modes form a complete set of `different types of oscillations' - the eigenvectors, from which all possible forms of oscillations may be constructed. 141.2.215.190 19:12, 4 January 2007 (UTC)
Dynamic modes are important to any system governed by linear homogenous differential equations, this includes aircraft stability modes, shimmy, flutter, hunting, etc. I have used this article as a cross reference from Gyro monorail but it is not sufficiently general. The alternative reference to Eigenvalues is really too arcane, even for the above average reader who could cope with the maths in the monorail article.
May I suggest introducing the subject with reference to the classical eigenvalue problems. The first is the ancient problem of how slender a column can be made before it will buckle. This dates back to the ancient Greeks, who considered slender columns to be aesthetically more pleasing than the squat pillars characteristic of Egyptian architecture. The solution is the Euler buckling theory, which is a simple eigenvalue problem. There is an infinite number of failure loads, each corresponding to a different deformation shape. Each deformation shape is a mode. The fact that we are only usually concerned with the lowest buckling load is irrelevant - we can always imagine a situation where a large load is suddenly applied - invoking a higher order mode.
Staying with the ancient Greeks, the first recorded eigenvalue problem is the prediction of the pitch of a taut string when it is plucked. Pythagoras used the ratios of string lengths to relate number to harmony. Here again, the string has an infinite number of modes which may be excited by plucking or bowing. Both the strut and stretched string may be illustrated with diagrams of sinusoidal deformations. After all a mode is essentially a shape which characterises the displacement of the system from its undisturbed state, and a frequency of the associated motion (or, in the strut case an associated buckling load).
These descriptions could be backed up by mathematics, but this should not be necessary. After all, most school kids are aware that a six inch ruler is harder to buckle than a 12inch ruler. Most people have noticed that blowing harder into a recorder causes the pitch to suddenly double. I suggest that appeal to everday experience, rather than to apparently obscure and esoteric applications is more likely to convey the idea to a wide audience. Gordon Vigurs 11:25, 7 March 2007 (UTC)
Well I merged it.
The contents of the Mode Shape page were merged into Normal mode. For the contribution history and old versions of the redirected page, please see its history; for the discussion at that location, see its talk page. |
Kallog ( talk) 03:57, 20 March 2010 (UTC)
hope you're all happy with my clarification on why the determinant must be zero. Reading the article, I found it was easy to mistakenly think that the matrix would have to be invertible, as the singular link in fact links to the article about non-singular matrices.-- Ask a Physicist ( talk) 17:01, 3 December 2011 (UTC)