Vibration on the Results of the Asymptotic Perturbation Method for Multiple Degrees of Freedom Nonlinear Mechanics Systems with Quadratic Terms

2011 ◽  
Vol 47 (01) ◽  
pp. 62
Author(s):  
Li YANG
Keyword(s):  
Perturbation Method ◽  
Degrees Of Freedom ◽  
Nonlinear Mechanics ◽  
Multiple Degrees Of Freedom ◽  
Asymptotic Perturbation Method ◽  
Asymptotic Perturbation

Periodic and Chaotic Motions of a Simply Supported FGM Plate with Two Degrees-of-Freedom

2008 ◽  
Vol 47-50 ◽  
pp. 1137-1140
Author(s):  
Yu Xin Hao ◽  
Wei Zhang ◽  
Jie Yang ◽  
Li Hua Chen
Keyword(s):  
Perturbation Method ◽  
Degrees Of Freedom ◽  
Functionally Graded ◽  
Bottom Surface ◽  
Graded Materials ◽  
Chaotic Motions ◽  
Simply Supported ◽  
Asymptotic Perturbation Method ◽  
Asymptotic Perturbation ◽  
Two Degree Of Freedom

In this paper, we use the asymptotic perturbation method to investigate the nonlinear oscillation and chaotic dynamic behavior of a simply supported rectangular plate made of functionally graded materials (FGMs). We assume that the plate is made from a mixture of ceramics and metals with continuously varying compositional profile such that the top surface of the plate is ceramic rich, whereas the bottom surface is metal rich. The equations motion of the FGM plate with two-degree-of-freedom under combined parametrical and external excitations are obtained by using Galerkin’s method. Based on the averaged equation obtained by the asymptotic perturbation method, the phase portrait and waveform are used to analyze the periodic and chaotic motions. It is found that the FGM plate exhibits chaotic motions under certain circumstances.

scholarly journals Nonlinear Vibrations of a Rotor-Active Magnetic Bearing System with 16-Pole Legs and Two Degrees of Freedom

2020 ◽  
Vol 2020 ◽  
pp. 1-29 ◽  
Author(s):  
W. Zhang ◽  
R. Q. Wu ◽  
B. Siriguleng
Keyword(s):  
Perturbation Method ◽  
Electromagnetic Force ◽  
Nonlinear Vibrations ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Time Varying ◽  
Asymptotic Perturbation Method ◽  
Amb System ◽  
Asymptotic Perturbation ◽  
Quadratic And Cubic Nonlinearities

The asymptotic perturbation method is used to analyze the nonlinear vibrations and chaotic dynamics of a rotor-active magnetic bearing (AMB) system with 16-pole legs and the time-varying stiffness. Based on the expressions of the electromagnetic force resultants, the influences of some parameters, such as the cross-sectional area Aα of one electromagnet and the number N of windings in each electromagnet coil, on the electromagnetic force resultants are considered for the rotor-AMB system with 16-pole legs. Based on the Newton law, the governing equation of motion for the rotor-AMB system with 16-pole legs is obtained and expressed as a two-degree-of-freedom system with the parametric excitation and the quadratic and cubic nonlinearities. According to the asymptotic perturbation method, the four-dimensional averaged equation of the rotor-AMB system is derived under the case of 1 : 1 internal resonance and 1 : 2 subharmonic resonances. Then, the frequency-response curves are employed to study the steady-state solutions of the modal amplitudes. From the analysis of the frequency responses, both the hardening-type nonlinearity and the softening-type nonlinearity are observed in the rotor-AMB system. Based on the numerical solutions of the averaged equation, the changed procedure of the nonlinear dynamic behaviors of the rotor-AMB system with the control parameter is described by the bifurcation diagram. From the numerical simulations, the periodic, quasiperiodic, and chaotic motions are observed in the rotor-active magnetic bearing (AMB) system with 16-pole legs, the time-varying stiffness, and the quadratic and cubic nonlinearities.

Analysis of Nonlinear Dynamics of a Rotor-Active Magnetic Bearing System With 16-Pole Legs

2017 ◽  
Author(s):  
Ruiqin Wu ◽  
Wei Zhang ◽  
Ming Hui Yao
Keyword(s):  
Nonlinear Dynamics ◽  
Perturbation Method ◽  
Primary Resonance ◽  
Magnetic Bearing ◽  
Active Magnetic Bearing ◽  
Chaotic Motions ◽  
Dimensionless Equation ◽  
Asymptotic Perturbation Method ◽  
Amb System ◽  
Asymptotic Perturbation

In this paper, we use the asymptotic perturbation method to analyze the nonlinear dynamics of a rotor-active magnetic bearing (AMB) system with 16-pole legs. The motion governing equation is derived by using classical Newton law. The resulting dimensionless equation of motion for the system is expressed as a two-degree-of-freedom system including the parametric excitation, quadratic and cubic nonlinearities. The asymptotic perturbation method is used to obtain the averaged equation when the primary resonance and 1/2 sub-harmonic resonance are taken into consideration. From the averaged equations obtained, numerical simulations are presented to investigate the modulation of vibration amplitudes of the rotor-AMB system. Based on a specific set of parameters, it is found that there exist the periodic, quasi-periodic and chaotic motions in the modulated amplitude of the rotor in the system.

scholarly journals Nonlinear and Stability Analysis of a Ship with General Roll-Damping Using an Asymptotic Perturbation Method

2021 ◽  
Vol 26 (2) ◽  
pp. 33
Author(s):  
Muhammad Usman ◽  
Shaaban Abdallah ◽  
Mudassar Imran
Keyword(s):  
Stability Analysis ◽  
Perturbation Method ◽  
Primary Resonance ◽  
Bifurcation Curve ◽  
Stability Theorems ◽  
Asymptotic Perturbation Method ◽  
Restoring Forces ◽  
The Stability ◽  
External Forces ◽  
Asymptotic Perturbation

In this work, the response of a ship rolling in regular beam waves is studied. The model is one degree of freedom model for nonlinear ship dynamics. The model consists of the terms containing inertia, damping, restoring forces, and external forces. The asymptotic perturbation method is used to study the primary resonance phenomena. The effects of various parameters are studied on the stability of steady states. It is shown that the variation of bifurcation parameters affects the bending of the bifurcation curve. The slope stability theorems are also presented.

scholarly journals Design, Fabrication, and Testing of a Novel 3D 3-Fingered Electrothermal Microgripper with Multiple Degrees of Freedom

Micromachines ◽  
2021 ◽  
Vol 12 (4) ◽  
pp. 444
Author(s):  
Guoning Si ◽  
Liangying Sun ◽  
Zhuo Zhang ◽  
Xuping Zhang
Keyword(s):  
Degrees Of Freedom ◽  
Dynamic Properties ◽  
Three Dimensional ◽  
Polyimide Film ◽  
Zebrafish Embryos ◽  
Multiple Degrees Of Freedom ◽  
Electrothermal Actuator ◽  
3D Space ◽  
Pick And Place

This paper presents the design, fabrication, and testing of a novel three-dimensional (3D) three-fingered electrothermal microgripper with multiple degrees of freedom (multi DOFs). Each finger of the microgripper is composed of a V-shaped electrothermal actuator providing one DOF, and a 3D U-shaped electrothermal actuator offering two DOFs in the plane perpendicular to the movement of the V-shaped actuator. As a result, each finger possesses 3D mobilities with three DOFs. Each beam of the actuators is heated externally with the polyimide film. The durability of the polyimide film is tested under different voltages. The static and dynamic properties of the finger are also tested. Experiments show that not only can the microgripper pick and place microobjects, such as micro balls and even highly deformable zebrafish embryos, but can also rotate them in 3D space.

scholarly journals The emerging technology of biohybrid micro-robots: a review

2021 ◽  
Author(s):  
Zening Lin ◽  
Tao Jiang ◽  
Jianzhong Shang
Keyword(s):  
Self Assembly ◽  
Degrees Of Freedom ◽  
High Energy ◽  
Living Cells ◽  
Multiple Degrees Of Freedom ◽  
The Past ◽  
Great Prevalence ◽  
Performance Decline ◽  
High Energy Efficiency ◽  
Living Tissues

Abstract In the past few decades, robotics research has witnessed an increasingly high interest in miniaturized, intelligent, and integrated robots. The imperative component of a robot is the actuator that determines its performance. Although traditional rigid drives such as motors and gas engines have shown great prevalence in most macroscale circumstances, the reduction of these drives to the millimeter or even lower scale results in a significant increase in manufacturing difficulty accompanied by a remarkable performance decline. Biohybrid robots driven by living cells can be a potential solution to overcome these drawbacks by benefiting from the intrinsic microscale self-assembly of living tissues and high energy efficiency, which, among other unprecedented properties, also feature flexibility, self-repair, and even multiple degrees of freedom. This paper systematically reviews the development of biohybrid robots. First, the development of biological flexible drivers is introduced while emphasizing on their advantages over traditional drivers. Second, up-to-date works regarding biohybrid robots are reviewed in detail from three aspects: biological driving sources, actuator materials, and structures with associated control methodologies. Finally, the potential future applications and major challenges of biohybrid robots are explored. Graphic abstract

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