This paper discusses the non-linear dynamical response of a shape-memory non-ideal oscillator. The non-ideal excitation originates from a DC electric motor with limited power supply driving an unbalanced rotating mass. The restoring force provided by the shape-memory device is described by a thermomechanical model capable of accounting for the hysteretic behavior via the evolution of a suitable internal variable. The non-linear dynamic response of the system is investigated with the voltage as control parameter. Numerical simulations show the occurrence of regular and quasi-periodic motions, which are investigated via bifurcation diagrams and phase plane portraits. The 0-1 test is used for quantitative characterization of chaotic responses. The computation of basins of attraction points out the strong dependence of the response on small changes of initial conditions, along with meaningful modifications of competing basins with variations of the control parameter. Finally, variations of the mechanical and thermal parameters of the pseudoelastic oscillator are considered, with the aim to evaluating the effects produced by the non-ideal excitation source on the non-linear dynamics of the shape memory devic

The nonlinear dynamics of a shape memory oscillator (SMO) subjected to an ideal or nonideal excitation is studied. The restoring force of the oscillator is provided by a shape memory device (SMD), described by a thermomechanical model capable of reproducing the hysteretic behavior via the evolution of a suitable internal variable. Due to nonlinearities in the model, the SMO can exhibit periodic or non-periodic behaviors. The effects of the external sources on the response of SMO are studied through the scalogram analysis of continuous wavelet transform by using a new measure, called the Scale index (Benitez R, Bolos VJ and Ramirez ME. A wavelet-based tool for studying non-periodicity. Comput Math Appl 2010; 60: 634–641). Numerical results show that the Scale index can successfully detect the behavior of the system when the signal is periodic or nonperiodic, and distinguish between them in a way consistent with the indications provided by the alternative 0-1 test.

SDRE applied to position and vibration control of a robot manipulator with a flexible link

The present paper proposes a new procedure to determine the optimal parameters of a dynamic vibration absorber (DVA), considering both damped and undamped primary system. The DVA design is formulated as an optimization problem in which the objective function is constructed based on Den Hartog's equal-peak method. The DVA parameters are selected to minimize the response of the primary system when it is subjected to harmonic force or base motion. Firstly, we propose a numerical strategy based on Frequency Response Curve (FRC) in which the parameters of the absorber are updated by minimizing the objective function. The results are presented for a set of reference parameters, which demonstrate the feasibility of the proposed method for determining the optimal parameters of the absorber for both excitations. Taking into account the system response with respect to reference parameters, the bilinear interpolation technique was employed in order to obtain explicit formulas of the damping and frequency ratios of the DVA.