Non-linear and linear, static and dynamic analyses of helical springs

Constitutive modeling of crimped collagen fibrils in soft tissues

“…Inspired by the work of Jiang et al (1989), who introduced two auxiliary strain variables for their solution of the helical spring boundary problem, two auxiliary stretches are introduced herê…”

Dynamic Stiffness Formulation, Free Vibration and Wave Motion of Helical Springs

“…Jiang et al [5,6] obtained non-linear equations of motion and from them linearized equations for the vibration of a spring. They studied the coupling between axial and torsional motion in more detail than Wittrick, deriving the complex form of the oscillations of the spring in the time domain due to the interaction and superposition of the component waves.…”

Nonlinear planar model for helical structures

“…Depending on which problem is addressed, analytical or finite element models have been proposed. Love's theory [1] set the base for curved wire based models, developed in later years by Hruska [2], Utting and Jones [3], Jiang [4], Sathikh [5] and Costello [6], just to name a few. Similarly applicable to thin structures, the general theory of rods by Green and Laws [7] has been the base for the work of Ramsey [8] on helical wires.…”