A Numerical Study of the Dynamics of a Rotating Curved Spring Using a Single Coil as a Finite Element

A method is developed for numerical calculation of the motion of a curved coiled spring excited by the rotation of one of the grips. For the simulation purposes, the spring is replaced by a discrete set of coils, each of which is considered as a finite element. To construct a geometrically non-linear finite element, that is a coil that takes account of large displacements and rotations, small displacements are counted from an intermediate «shadow» position, in which the element is not deformed. To exclude special points, full rotations are represented as a combination of a tensor and a vector, where the tensor of the large rotation is constant at the integration step, while the variable small part of the rotation is described by the Eluer vector. The method of obtaining the tangent of the rigidity matrix, the generalized mass matrix and the hydroscopic matrix of the finite element (coil) are presented. Non-linear equations are obtained describing the motion of the spring model constructed of such finite elements and numerically integrated by the Newmark method. The calculations results are confirmed by the data obtained through full-scale experiments with a rotating curved spring.

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