Dynamic Behavior of Nonlinear Cable System. I

Equations of motion for a plane, nonlinear prestressed truss are expressed in terms of six generalized coordinates. Three coordinates define a dominant centrally symmetric vibration mode. The dominant coordinate of that mode, $q_1\text{,}$ is a centrally symmetric rotation of the compressive struts about the supports. The equation for coordinate $q_1$ is of the cubic hardening type. For two common types of applied loads, the centrally symmetric mode is excited only through the $q_1$ coordinate. $q_1$ is excited in an additive way by antisymmetric forces and in a parametric way by symmetric forces. For a broad range of excitation frequencies, two coordinates of the centrally symmetric mode respond statically, and the mode can be defined by only the $q_1$ coordinate. With such a simplification, the equation for the $q_1$ coordinate excited by antisymmetric forces is of the Duffing type, while the equation for the $q_1$ coordinate excited by symmetric forces is of the nonlinear Mathieu type.