A tutorial review on time-frequency analysis of non-stationary vibration signals with nonlinear dynamics applications

Time-frequency analysis (TFA) for mechanical vibrations in non-stationary operations is the main subject of this article, concisely written to be an introducing tutorial comparing different time-frequency techniques for non-stationary signals. The theory was carefully exposed and complemented with sample applications on mechanical vibrations and nonlinear dynamics. A particular phenomenon that is also observed in non-stationary systems is the Sommerfeld effect, which occurs due to the interaction between a non-ideal energy source and a mechanical system. An application through TFA for the characterization of the Sommerfeld effect is presented. The techniques presented in this article are applied in synthetic and experimental signals of mechanical systems, but the techniques presented can also be used in the most diverse applications and also in the numerical solution of differential equation

Remarks on the sommerfeld effect characterization in the wavelet domain

In many applications in engineering, a mechanical system operates in the nonstationary regime, either partially of fully, creating the possibility to generate nonlinearities in them. Great efforts have been made to better understand and characterize these phenomena. One of several methods that are being used for the processing of signals of a nonstationary nature, as well as for the characterization of nonlinearities in mechanical systems, is the wavelet transform. A particular phenomenon that is seen in systems operating in the nonstationary regime is the Sommerfeld effect, which occurs due to the nonlinear interaction between a nonideal energy source and a mechanical system. This phenomenon can lead to high amplitudes of vibration for the system that in turn can cause damage in it. Therefore, this work presents an application of the continuous wavelet transform and the wavelet packet transform for the characterization of the Sommerfeld effect in mechanical systems where only the time response is at hand. Experimental procedures were performed where a nonideal energy source (an unbalanced DC motor) was used to excite (a) a portal frame and (b) a three-story shear-building. The results showed the effectiveness and the potential of the methods proposed25198108CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQNão te

Instrumentation Of a Nonlinear Pendulum Using Arduino

Abstract. In this paper the Arduino microcontroller together with the gyroscopic sensor for measuring vibrations in mechanical systems are used. The objective is to present the Arduino platform as an alternative for low cost signal acquisition, easy use and good precision for educational purpose. In this application the system presents a nonlinear behavior for certain initial conditions. The characterization of the system’s nonlinearities are done by the comparison between the signal measured and a numerical solution of the classic equation of motion of the pendulum. It is also presented a scenario where the pendulum is excited by an magnetic interaction. The results showed in conformity with the literature. Keywords: Arduino microcontroller, sensor, vibrations, nonlinear, educatio

Голос Верхней Туры. 2014. № 02

The objective of this study was to evaluate the effect of heterosis on the lactation curve components of Girolando cattle obtained by fitting different mathematical models. Data consisted of 258,891 test day milk yield records of the first lactation from 37,965 cows of Minas Gerais State (Brazil) between 1998 and 2014. Those cows were from the Holstein breed (H), Gyr breed (G) and six genetic cross-breedings of Holstein Gyr, (1/4H, 3/4G (1/4H); 3/8H, 5/8G (3/8H); 1/2H, 1/ 2G (1/2H), 5/8H, 3/8G (5/8H); 3/4H, 1/4G (3/4H); 7/8H, 1/8G (7/8H)), which is officially named as Girolando breed in Brazil. The Wood’s linear model (WDlin), Wood’s non-linear model (WDnlin), Wilmink’s model (WL) and Ali and Schaeffer’s model (ASH) were used for estimating the peak milk yield (PY), time to peak yield (PT), 305-day milk yield (TMY) and four different persistency measures (P, P2:1, P3:1 and P3:2). Regardless of the fitted model, the highest estimates of PY and TMY were for the H group. The heterosis effect was significant (p < .001) for TMY and all components of the lactation curve, except for P2:1. Girolando cattle presented a heterosis effect of 12.30% and 13.03% for PY and TMY, respectively. The magnitude of heterosis effect was larger for PT (24.18%), whereas the different persistency measures presented the smallest magnitude of heterosis values. The producers may use the different genetic groups to benefit from the heterosis mainly for the time to peak, peak yield and 305-day milk yield