Remarks on the Sommerfeld effect characterization in the wavelet domain

Abstract

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 proposed.

A Short Note on Synchrosqueezed Transforms for Resonant Capture, Sommerfeld Effect and Nonlinear Jump Characterization in Mechanical Systems

“…In the signal processing, the Morlet wavelet filter was used for the CWT ans SWT, while for the STFT one Hamming window with 128 points length for analysis. A detailed description of the mechanical system and DC motor proprieties can be found in [5].…”

“…The use of CWT presents a good resolution in the time-frequency plane, but the CWT may obfuscate other components when there is a high concentration of energy at some frequency. The success of this analysis depends on the choice of the wavelet filter, as shown in [5,14]. The results obtained through the use of SWT proved to be more suitable for analysis, presenting excellent time-frequency resolution and small energy dispersion.…”

“…One may find in the literature many works concerning systems with non-ideal energy sources [2][3][4]. In this paper, the responses of a portal frame excited by an unbalanced DC motor are measured and analyzed in the time and frequency domain [5]. Time-frequency analysis methods have been successfully used to characterize nonlinearities in the mechanical system [5][6][7].…”

Numerical and experimental investigation of the dynamic behavior of a cantilever beam driven by two non-ideal sources

“…The Sommerfeld effect is a serious problem faced by designers, and it can lead to catastrophic failures due to the high stresses generated by the amplitude increase, which may take values that, due to the modeling procedure followed, may not have been predicted. Some papers that address the Sommerfeld effect in various systems are given by references [7,[14][15][16][17]. Hu et al [18] present a case study on a wind turbine system.…”

“…As for the CWT, it allows good resolution in time-frequency spectrum, but higher energy frequencies can blur other frequency components. Also, the analysis based on the CWT is sensitive to the wavelet filter used, as shown by Varanis et al [14] and Varanis and Pederiva [29].…”