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Nonlinear Vibrations
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Nonlinear Vibrations

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Acoustics and Vibrations".

Deadline for manuscript submissions: closed (15 April 2022) | Viewed by 9136

Special Issue Editor

Dr. Kaifa Wang

E-Mail Website
Guest Editor
School of Science, Harbin Institute of Technology, Shenzhen 518055, China
Interests: micro and nano-mechanics; smart materials and structural mechanics; nonlinear mechanics

Special Issue Information

Dear Colleagues,

Structural vibrations could play an important role in the performance of many engineering systems, with typical amplitudes ranging from meters to a few nanometers. Experimental observation indicates that the structural vibrations behave linearly at very small amplitudes, but nonlinearities occur with increasing amplitudes. Due to the large displacements and motions, structural nonlinearity becomes important when more accurate measurement and control are needed. Identifying, modelling and controlling nonlinear vibrations are becoming increasingly important in a range of engineering applications such as mechanical, structural, civil, aeronautical, ocean, electrical, and control systems. Papers (including analytical, computational, and experimental methods) are invited to make contributions to enrich the knowledge of structural nonlinear vibration.

Dr. Kaifa Wang
Guest Editor

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Keywords

  • nonlinear vibration
  • vibration control
  • geometric nonlinearity
  • bifurcations
  • chaos

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Published Papers (4 papers)

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Research

27 pages, 1259 KiB  
Article
Dynamic Analysis of a Wiper Blade in Consideration of Attack Angle and Clarification of the Jumping Phenomenon
by Zihan Zhao, Hiroshi Yabuno and Katsuya Kamiyama
Appl. Sci. 2022, 12(9), 4112; https://doi.org/10.3390/app12094112 - 19 Apr 2022
Cited by 2 | Viewed by 3437
Abstract
Automobile windshields are typically curved, creating an oblique angle of attack between the wiper blade and the windshield. This attack angle means that the wiper may jump off the windshield while wiping, causing a chattering noise and preventing the rainwater from being fully [...] Read more.
Automobile windshields are typically curved, creating an oblique angle of attack between the wiper blade and the windshield. This attack angle means that the wiper may jump off the windshield while wiping, causing a chattering noise and preventing the rainwater from being fully wiped off the windshield. Thus, it is important to examine the dynamics of the wiper blade under friction. In this study, the relationship between the attack angle and the jumping phenomenon is clarified through dynamic analysis. We introduce an analytical two-link model corresponding to an actual wiper blade that considers the exchange of dynamic and static friction between the windshield and the blade. The dynamic friction is assumed to be negatively correlated with the relative velocity, and the static friction is described by a set-valued function. As the motion transitions from the stick state to the slip state, the equation to be solved changes. Hence, the initial condition after a transition must agree with the final condition before the transition. Because the governing equations are nonlinear and the solution is highly dependent on the initial condition, the transition time and corresponding state variables are vital. The slack variable method is used to obtain the exact transition time and initial conditions. The sign of the normal force acting on the blade from the windshield determines the occurrence of the jump phenomenon. A larger attack angle makes the jump phenomenon more likely. However, the jump phenomenon does not occur when the motion of the blade reverses. Experimental observations support the theoretical description of the wiper blade. Full article
(This article belongs to the Special Issue Nonlinear Vibrations)
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33 pages, 12037 KiB  
Article
ALIPPF-Controller to Stabilize the Unstable Motion and Eliminate the Non-Linear Oscillations of the Rotor Electro-Magnetic Suspension System
by Nasser A. Saeed, Jan Awrejcewicz, Abd Allah A. Mousa and Mohamed S. Mohamed
Appl. Sci. 2022, 12(8), 3902; https://doi.org/10.3390/app12083902 - 12 Apr 2022
Cited by 3 | Viewed by 1663
Abstract
Within this work, an advanced control algorithm was proposed to eliminate the non-linear vibrations of the rotor electro-magnetic suspension system. The suggested control algorithm is known as the Adaptive Linear Integral Positive Position Feedback controller (ALIPPF-controller). The ALIPPF-controller is a combination of first-order [...] Read more.
Within this work, an advanced control algorithm was proposed to eliminate the non-linear vibrations of the rotor electro-magnetic suspension system. The suggested control algorithm is known as the Adaptive Linear Integral Positive Position Feedback controller (ALIPPF-controller). The ALIPPF-controller is a combination of first-order and second-order filters that are coupled linearly to the targeted non-linear system in order to absorb the excessive vibratory energy. According to the introduced control strategy, the dynamical model of the controlled rotor system was established as six non-linear differential equations that are coupled linearly. The obtained dynamical model was investigated analytically applying the asymptotic analysis, where the slow-flow equations were extracted. Based on the derived slow-flow equations, the bifurcation behaviors of the controlled system were explored by plotting the different bifurcation diagrams. In addition, the performance of the ALIPPF-controller in eliminating the rotor lateral vibrations was compared with the conventional Positive Position Feedback (PPF) controller. The acquired results illustrated that the ALIPPF-controller is the best control technique that can eliminate the considered system’s lateral vibrations regardless of the angular speed and eccentricity of the rotating shaft. Finally, to demonstrate the accuracy of the obtained analytical results, numerical validation was performed for all obtained bifurcation diagrams that were in excellent agreement with the analytical solutions. Full article
(This article belongs to the Special Issue Nonlinear Vibrations)
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35 pages, 10387 KiB  
Article
The Stability Analysis of a Vibrating Auto-Parametric Dynamical System Near Resonance
by Tarek S. Amer, Roman Starosta, Ashraf Almahalawy and Abdelkarim S. Elameer
Appl. Sci. 2022, 12(3), 1737; https://doi.org/10.3390/app12031737 - 8 Feb 2022
Cited by 20 | Viewed by 1871
Abstract
This paper examines a new vibrating dynamical motion of a novel auto-parametric system with three degrees of freedom. It consists of a damped Duffing oscillator as a primary system attached to a damped spring pendulum as a secondary system. Lagrange’s equations are utilized [...] Read more.
This paper examines a new vibrating dynamical motion of a novel auto-parametric system with three degrees of freedom. It consists of a damped Duffing oscillator as a primary system attached to a damped spring pendulum as a secondary system. Lagrange’s equations are utilized to acquire the equations of motion according to the number of the system’s generalized coordinates. The perturbation technique of multiple scales is applied to provide the solutions to these equations up to a higher order of approximations, with the aim of obtaining more accurate novel results. The categorizations of resonance cases are presented, in which the case of primary external resonance is examined to demonstrate the conditions of solvability of the steady-state solutions and the equations of modulation. The time histories of the achieved solutions, the resonance curves in terms of the modified amplitudes and phases, and the regions of stability are outlined for various parameters of the considered system. The non-linear stability, in view of both the attained stable fixed points and the criterion of Routh–Hurwitz, is investigated. The results of this paper will be of interest for specialized research that deals with the vibration of swaying buildings and the reduction in the vibration of rotor dynamics, as well as studies in the fields of mechanics and space engineering. Full article
(This article belongs to the Special Issue Nonlinear Vibrations)
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27 pages, 6755 KiB  
Article
Nonlinear Analyses of Porous Functionally Graded Sandwich Piezoelectric Nano-Energy Harvesters under Compressive Axial Loading
by Shan Zeng, Zhangtao Peng, Kaifa Wang, Baolin Wang, Jinwu Wu and Tianxi Luo
Appl. Sci. 2021, 11(24), 11787; https://doi.org/10.3390/app112411787 - 11 Dec 2021
Cited by 6 | Viewed by 1570
Abstract
In this study, a sandwich piezoelectric nano-energy harvester model under compressive axial loading with a core layer fabricated of functionally graded (FG) porous material is presented based on the nonlocal strain gradient theory (NSGT). The von Karman type geometric nonlinearity and the axial [...] Read more.
In this study, a sandwich piezoelectric nano-energy harvester model under compressive axial loading with a core layer fabricated of functionally graded (FG) porous material is presented based on the nonlocal strain gradient theory (NSGT). The von Karman type geometric nonlinearity and the axial loading were considered. The electromechanical governing equations were obtained using Hamilton’s principle. The nonlinear vibration frequencies, root mean square (RMS) voltage output and static buckling were obtained using the Galerkin method. The effects of different types of porous distribution, porosity coefficients, length scale parameters, nonlocal parameters, flexoelectricity, excitation frequencies, lumped mass and axial loads on the natural frequency and voltage output of nanobeams were investigated. Results show that the porous distributions, porosity coefficient of porous materials, the excitation frequencies and the axial load have a large effect on the natural frequency and voltage output of the sandwiched piezoelectric nanobeams. When the NSGT is considered, the critical buckling load depends on the values of the nonlocal parameters and strain gradient constants. In addition, the electromechanical conversion efficiency of the post-buckling process is significantly higher than that of the pre-buckling process. The flexoelectric effect can significantly increase the RMS voltage output of the energy harvester. Full article
(This article belongs to the Special Issue Nonlinear Vibrations)
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