Dynamic analysis of prestressed cables with uncertain pretension

This paper deals with finite element dynamic analysis of prestressed cables with uncertain pretension subjected to deterministic excitations. The theoretical model addressed for cable modeling is a two-dimensional finite-strain beam theory, which allows us to eliminate any restriction on the magnitude of displacements and rotations. The dynamic problem is formulated by referring the motion to the inertial frame, which leads to a simple uncoupled quadratic form for the kinetic energy. The effect of the externally applied stochastic pretension is approximately described by means of an uncertain 'axial' component of stress resultant, which is assumed constant along the cable in its dead load configuration. The so-called improved perturbation approach is employed to solve this stochastic problem, obtaining two coupled systems of nonlinear deterministic ordinary differential equations, governing the mean value and deviation of response. An efficient and accurate iterative procedure is proposed to obtain the solution of these equations. In order to investigate the influence of random pretension on structural response, few numerical applications are presented and results are discussed.