Intrinsic Finite Element Modeling of Nonlinear Dynamic Response in Helical Springs

Abstract

This paper presents an efficient intrinsic finite element approach for modeling and analyzing the forced dynamic response of helical springs. The finite element treatment employs intrinsic curvature (and strain) interpolation and vice rotation (and displacement) interpolation and, thus, can accurately and efficiently represent initially curved and twisted beams with a sparse number of elements. The governing equations of motion contain nonlinearities necessary for large curvatures. In addition, a constitutive model is developed, which captures coupling due to nonzero initial curvature and strain. The method is employed to efficiently study dynamically-loaded helical springs. Convergence studies demonstrate that a sparse number of elements accurately capture spring dynamic response, with more elements required to resolve higher frequency content, as expected. Presented results also document rich, amplitude-dependent frequency response. In particular, moderate loading amplitudes lead to the presence of secondary resonances (not captured by linearized models), while large loading amplitudes lead to complex dynamics and transverse buckling.