The Vibration of a Tight Cable Containing a Turnbuckle

摘要

The partial differential equations for the vibration of a cable containing a turnbuckle are solved by the method of the Laplace transformation and also by separation of variables. Since the turnbuckle renders the boundary conditions inhomogeneous, the eigenfunctions are not orthogonal in the classical sense, and a special scalar product is defined to make them orthogonal. The solution by separation of variables is simpler in form than the Laplace transform result for this particular problem and is shown by the use of identities in the eigenfunctions to yield the identical expansions as the Laplace transform method. The results simplify considerably when the turnbuckle is located in the center of the cable or at one end. The properties of these special cases are discussed. (Author)