Attached is the vibration equation of a plate.
φ(y) is the mode shape and η(t) is the dynamic response.
I want to perform delta variation (δ) on this equation in order to use Hamilton's principle.
But when I calculate the kinetic energy and potential energy of the system, both φ(y) and η(t) emerge. My question is which one of these should be considered for delta variation and why?
This comes under "Proper Orthogonal Projection" method. Both sets of functions should be varied, after introducing a time-averaged norm.
Hi...
Actually Hamilton principle is based on the fact that the Time is freezed.
So the delta operator acts on modes shape only.
@Ali, I don't think that time is freezed in Hamilton's principle. Look at the Wikipedia article, for example: http://en.wikipedia.org/wiki/Hamilton%27s_principle .
@Nicolas, I guess delta is an operand which acts on system motion trajectory.
It assumes that system is freezed conceptually, and based on this assumption, the motion occurs in a way that minimum energy is consumed. I mean that by using this principle, the best trajectory of the system is determined considering all constraints are preserved.
This comes under "Proper Orthogonal Projection" method. Both sets of functions should be varied, after introducing a time-averaged norm.
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