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Stability Of Networks Under Tension And Pressure, Anthony Roy Day, H. Yan, M. F. Thorpe
Stability Of Networks Under Tension And Pressure, Anthony Roy Day, H. Yan, M. F. Thorpe
Anthony Roy Day
The number of zero-frequency modes of an elastic network is an important quantity in determining the stability of the network. We present a constraint-counting method for finding this number in general central-force networks that are under an external tension. The technique involves isolating the backbone and then counting constraints in the same way as for free standing networks. A detailed example of this counting is given for a random two-dimensional network subject to an external tension. The results are shown to agree with the number of zero-frequency modes as determined by a direct matrix diagonalization.