Spatial discretization of axially moving media vibration problems

Spatial discretization of axially moving media eigenvalue problems is exami ned from the perspectives of moving versus stationary system basis function , conifiguration space versus state space form discretization, and subcriti cal versus supercritical speed convergence. The moving string eigenfunction s, which have previously been shown to give excellent discretization conver gence under certain conditions, become linearly dependent and cause numeric al problems as the number of terms increases. This problem does nor occur i n a discretization of the state space form of the eigenvalue problem, altho ugh convergence is slower, not monotonic, and not necessarily from above. U se of the moving string basis at supercritical speeds yields strikingly poo r results with either the configuration or state space discretizations. The stationary system eigenfunctions provide reliable eigenvalue predictions a cross the range of problems examined Because they have known exact solution s, the moving string on elastic foundation and the traveling, tensioned bea m are used as illustrative examples. Many of the findings, however, apply t o more complex moving media problems, including nontrivial equilibria of no nlinear models. [S0739-3717(00)02103-6].