Numerical and experimental investigation of the dynamic behavior of a cantilever beam driven by two non-ideal sources
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(2020) 42:516
TECHNICAL PAPER
Numerical and experimental investigation of the dynamic behavior of a cantilever beam driven by two non‑ideal sources Marcus Varanis1 · Arthur Mereles2 · Anderson L. Silva3 · Maurizio Radloff Barghouthi3 · José Manoel Balthazar4 · Eduardo M. O. Lopes3 · Carlos Alberto Bavastri3 Received: 19 December 2019 / Accepted: 25 August 2020 © The Brazilian Society of Mechanical Sciences and Engineering 2020
Abstract Non-ideal energy sources are present in several engineering applications where the power source interacts with the dynamics of the structure to which it is coupled. The systems driven by this kind of source present a rich dynamic behavior and some phenomena that can only be observed under non-ideal consideration. The modeling of such systems becomes much more complex due to the interaction between the system and the energy source, requiring an additional equation. The present work proposes a continuous vibration model of a cantilever beam with two unbalanced DC motors. The motors are considered non-ideal energy sources. The advantage of the continuous approach is that the position of the motors can be easily varied. In addition, time–frequency methods are performed in order to characterize and identify the occurrence of the Sommerfeld effect on the non-stationary operation. In order to validate the model, experimental measurements were performed and, subsequently, compared with the numerical results. Keywords Continuous system · Nonlinear dynamics · Sommerfeld effect · Wavelet synchrosqueezed transform
1 Introduction The present work investigates a non-ideal continuous model, which was first presented by the authors in [1]. The current work has focused on experimental validation of the non-ideal continuous model. Non-ideal systems have been largely studied in the literature [2, 3] and are still challenging researches in the field of engineering due to their intrinsic complexity. In such systems, the dynamics of the structures influence the power source, which can be a motor. This interaction can cause the motor to stall and not give the specified speed at a certain power input, since, unlike ideal energy sources, the Technical Editor: Thiago Ritto. * Marcus Varanis [email protected] 1
Faculty of Engineering, Federal University of Grande Dourados (UFGD), Dourados, MS, Brazil
2
Faculty of Mechanical Engineering, University of Campinas (UNICAMP), Campinas, SP, Brazil
3
Department of Mechanical Engineering (UFPR), Federal University of Paraná, Curitiba, PR, Brazil
4
Federal University of Technology - Paraná (UTFPR), Ponta Grossa, PR, Brazil
power supply is limited. Different phenomena arise when there is a strong interaction between the system and the energy source, such as the resonance capture phenomena, also known in the literature as the Sommerfeld effect [4]. Though already observed in experiments, this phenomenon cannot be seen in models that consider the power source to be ideal. Some other phenomena that arise in non-ideal systems with nonlinearities
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