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Title: Vibrational amplitude frequency characteristics analysis of a controlled nonlinear meso-scale beam
Authors: Ying, ZG
Ni, YQ 
Issue Date: Aug-2021
Source: Actuators, Aug. 2021, v. 10, no. 8, 180
Abstract: Vibration response and amplitude frequency characteristics of a controlled nonlinear meso-scale beam under periodic loading are studied. A method including a general analytical expression for harmonic balance solution to periodic vibration and an updated cycle iteration algorithm for amplitude frequency relation of periodic response is developed. A vibration equation with the general expression of nonlinear terms for periodic response is derived and a general analytical expression for harmonic balance solution is obtained. An updated cycle iteration procedure is proposed to obtain amplitude frequency relation. Periodic vibration response with various frequencies can be calculated uniformly using the method. The method can take into account the effect of higher harmonic components on vibration response, and it is applicable to various periodic vibration anal-yses including principal resonance, super-harmonic resonance, and multiple stationary responses. Numerical results demonstrate that the developed method has good convergence and accuracy. The response amplitude should be determined by the periodic solution with multiple harmonic terms instead of only the first harmonic term. The damping effect on response illustrates that vibration responses of the nonlinear meso beam can be reduced by feedback control with certain damping gain. The amplitude frequency characteristics including anti-resonance and resonant response var-iation have potential application to the vibration control design of nonlinear meso-scale structure systems.
Keywords: Amplitude frequency characteristics
Damping effect
Harmonic balance solution
Meso-scale beam
Nonlinear vibration
Updated cycle iteration algorithm
Vibration control
Publisher: Molecular Diversity Preservation International (MDPI)
Journal: Actuators 
ISSN: 2076-0825
DOI: 10.3390/act10080180
Rights: © 2021 by the authors.Licensee MDPI, Basel, Switzerland.This article is an open access articledistributed under the terms andconditions of the Creative CommonsAttribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
The following publication Ying, Z.-G.; Ni, Y.-Q.Vibrational Amplitude FrequencyCharacteristics Analysis of aControlled Nonlinear Meso-ScaleBeam. Actuators 2021, 10, 180 is available at https://doi.org/10.3390/act10080180
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