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Potential energy of a string

Submitted by L2020 on
vibration
string
potential energy

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? 

 

Julian J. Rimoli

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

Sun, 02/21/2010 - 18:57 Permalink