Graduate Thesis Or Dissertation
 

Vibrations of suspended cables

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  • The equations of motion of an elastic cable suspended in a viscous medium from two arbitrary points are derived. These are then linearized for the undamped, inextensible case, and it is found that the equations describing the in-plane motion of the cable are then independent of the equation describing the out-of-plane motion of the cable. The linearized differential equations of motion of the cable contain coefficients which are irrational functions of the independent variable. A change of independent variable is made that transforms the equations of motion to a form with polynomial coefficients. Solution of these equations, using the method of Frobenius, yields both the in-plane and out-of-plane natural frequency ratios of the cable. The first six natural frequency ratios for both in-plane and out-of-plane motion are presented for a variety of cable geometries. Using the equations developed for the normal mode motion, a technique is presented for determination of the displacements and tensions throughout a cable when one end is subjected to a prescribed tangential displacement of known frequency. Maximum cable tensions are presented as a function of the forcing frequency for a variety of cable geometries.
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