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Potential energy of a string
Hi,
I have to use Hamilton pricinple to evaluate the diff. equation of motion of a string. As shown in the figure below, the string is hanged from one end and is free at the other. The flexural stiffness of the string is negligible.
I have a problem with the potential energy of the string! required in the Hamilton principle. Since the flexural stiffness of the string is assumed to be negligible, is there any other term for potential energy?
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Re: Potential energy of a string
Yes, weight of the string.
Arash
Might seem so obvious, but I
Might seem so obvious, but I don't understand when the motion of the string is in y direction, how its weight(in x direction) does work! and affects the potential energy!? :(
strain energy
Dear Laleh: you still need the strain energy due to the extension of the string.
You are right, but as said
You are right, but as said earlier, the flexural stiffness of the string is assumed to be negligible!
discrete problem
Dear Laleh:
You can have stretching stiffness even when there is no flexural stiffness. The stretching stiffness comes from the extension of the string whereas the flexural one comes from its bending. For illustration purposes, let us think on a discrete version of your problem. Imagine a set of points with mass m=rho*L connected by springs with stiffness K=E*A/L, where rho is the linear mass density of the string, A its cross sectional area, E the Young's modulus of the material and L the spacing between the points. Such system does not have flexural stiffness but still has a component due to its extension. I hope this clarifies my previous statement.
Regards,
Julian
Thanks a lot. I got it :)
Thanks a lot. I got it :)
You're welcome!
You're welcome!
Julian