We model small deviations from linear mechanical behaviour of a loaded vertically suspended helical spring. A Taylor expansion of the elasticity equations governing the axial extension of the spring is used to determine the relative magnitudes of linear and (quadratic and cubic) nonlinear terms in the force–extension relationship. This relationship is the basis for the derivation of a model for...

In this paper we discuss numerical strategies to find periodic orbits of nonlinear dynamic system. These orbits shall be open-loop stable and robust with respect to bounded disturbances. For this aim, we review and extend existing techniques from the field of reachability analysis and ellipsoidal calculus to compute robust positive invariant tubes for nonlinear dynamic systems. We suggest a con...

Abstract This paper aims to study the dynamics of single-degree-of-freedom magnetic spring-based oscillator system. The proposed system contains a nonmagnetic shaft, floating permanent magnet (PM), and two fixed magnets (PMs). All PMs are placed in such way that they can repel each other. At first, system's properties restoring force studied. Experimental numerical analyses have been carried ou...

In this study, numerical analysis of a composite spring with nonlinear elastic force-displacement relationship was performed. Due to the lightness and durability materials, their use in automotive industry is increasing production methods allow for high performance design. The behavior pair leaf springs working tandem cross-section profiles be obtained by using involute curve spur gear pairs un...

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The larger a size of a storage ring becomes, the bigger value the chromaticity reaches, which should be corrected by strong sextupole magnets. Hence, for the purpose of precisely controlling the chromaticity, it is necessary to know the nonlinear behavior. In this paper we derive the perturbative expression for the higher order terms of nonlinear chromaticity in terms of the nonlinear dispersio...

This paper advocates disturbance observer based control (DOBC) for uncertain nonlinear systems. Within this framework, a nonlinear controller is designed based on the nominal model in the absence of disturbance and uncertainty where the main design specifications are to stabilize the system and achieve good tracking performance. Then a nonlinear disturbance observer is designed to not only esti...