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Modes of vibration of inextensible cables suspended from two points

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  • The equations of motion of a suspended, inextensible cable in the absence of damping are studied. A method is developed and illustrated for determining the frequencies and mode shapes for small oscillations about the equilibrium configuration. With the introduction of a new variable, the fourth order equation governing tangential displacement takes a form with polynomial coefficients. This form, previously undiscovered, permits application of the method of Frobenius for solution. The system consisting of this differential equation and the boundary conditions determined by attachment points, contains a set of eigenvalues which correspond to possible frequencies of oscillation. A criterion for selection of the eigenvalues is developed from the boundary conditions. A digital computer was used to perform the calculation of the fundamental frequency of several different cable configurations. The results agree favorably with previously published values.
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