Improved Homotopy Perturbation Solution for Nonlinear Transverse Vibration of Orthotropic Membrane

Zhang, Yafei.; Song, Weiju; Yin, Huimin; Ma, Jingsheng

doi:10.1007/s42417-021-00424-5

Cited by 8 publications

(2 citation statements)

References 16 publications

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“…There are many analytical methods for finding approximate solutions and discussing the characteristics of nonlinear systems. Some of these methods are the homotopy analysis method, 1,2 the homotopy perturbation method, [3][4][5][6][7] Newton-Raphson method, [8][9][10][11] He's frequency formula method, 12 Taylor series method, 13,14 and bisection method. 15 Riahi and Qattan studied the nonlinear, non-convex optimization problem under system dynamic constraints and applied their analysis to parameter identification of systems governed by general nonlinear differential equations.…”

Section: Introductionmentioning

confidence: 99%

The analysis for the dynamic pull-in of a micro-electromechanical system

Feng

Niu

2022

Journal of Low Frequency Noise, Vibration and Active Control

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Section: Introductionmentioning

confidence: 99%

The analysis for the dynamic pull-in of a micro-electromechanical system

Feng

Niu

2022

Journal of Low Frequency Noise, Vibration and Active Control

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“…It has been demonstrated that it can be used to analyze highly nonlinear vibrational issues and create a multiplicity of real-world engineering challenges. The fundamental equations of exceedingly nonlinear excitations of orthotropic structural components are deduced using the Von Karman huge defection hypothesis and the Galerkin method to achieve a precise and effective alternative approach to the nonlinear vibrational problem of the membrane 21 . Using HPM, an analytical solution to the problem of free vibration of rectangular plates with convoluted border circumstances in a plane was suggested 22 .…”

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confidence: 99%

Dynamical analysis of a damped harmonic forced duffing oscillator with time delay

Moatimid

Amer

2023

Sci Rep

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This paper is concerned with a time-delayed controller of a damped nonlinear excited Duffing oscillator (DO). Since time-delayed techniques have recently been the focus of numerous studies, the topic of this investigation is quite contemporary. Therefore, time delays of position and velocity are utilized to reduce the nonlinear oscillation of the model under consideration. A much supplementary precise approximate solution is achieved using an advanced Homotopy perturbation method (HPM). The temporal variation of this solution is graphed for different amounts of the employed factors. The organization of the model is verified through a comparison between the plots of the estimated solution and the numerical one which is obtained utilizing the fourth order Runge–Kutta technique (RK4). The outcomes show that the improved HPM is appropriate for a variety of damped nonlinear oscillators since it minimizes the error of the solution while increasing the validation variety. Furthermore, it presents a potential model that deals with a diversity of nonlinear problems. The multiple scales homotopy technique is used to achieve an estimated formula for the suggested time-delayed structure. The controlling nonlinear algebraic equation for the amplitude oscillation at the steady state is gained. The effectiveness of the proposed controller, the time delays impact, controller gains, and feedback gains have been investigated. The realized outcomes show that the controller performance is influenced by the total of the product of the control and feedback gains, in addition to the time delays in the control loop. The analytical and numerical calculations reveal that for certain amounts of the control and feedback signal improvement, the suggested controller could completely reduce the system vibrations. The obtained outcomes are considered novel, in which the used methods are applied on the DO with time-delay. The increase of the time delay parameter leads to a stable case for the DO, which is in harmony with the influence of this parameter. This drawn curves show that the system reaches a stable fixed point which assert the presented discussion.

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Analytical and numerical study of a vibrating magnetic inverted pendulum

2023

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The current study investigates the stability structure of the base periodic motion of an inverted pendulum (IP). A uniform magnetic field affects the motion in the direction of the plane configuration. Furthermore, a non-conservative force as one that dampens air is considered. Its underlying equation of motion is derived from traditional analytical mechanics. The mathematical analysis is made simpler by substituting the Taylor theory in order to expand the restoring forces. The modified Homotopy perturbation method (HPM) is employed to achieve a roughly adequate regular result. To support the prior result, a numerical method based on the fourth-order Runge-Kutta method (RK4) is employed. The graphs for both the analytic and numerical solutions are highly consistent with one another, which indicates that the perturbation strategy is accurate. The solution time history curve exhibits a decaying performance and indicates that it is steady and without chaos. The resonance and non-resonance cases are found through the stability study by using the time scale method. In all perturbation approaches, the methodology of multiple time scales is actually regarded as a further standard approach. The time history is used to create a collection of graphs. Some graphical representations are used to illustrate how the typical physical values affect the behavior of the discovered solution. It has been discovered that the statically unstable IP can have its instability reduced by raising the spring torsional constant stiffness as well as the damped coefficient. Moreover, the magnetic field has a significant role in the stability configuration, which explains that at higher values of this field, the decaying waves take much more time than the smaller values of this field. Accordingly, it can be employed in various engineering devices that need a certain period of time to be more stable.

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Improved Homotopy Perturbation Solution for Nonlinear Transverse Vibration of Orthotropic Membrane

Cited by 8 publications

References 16 publications

The analysis for the dynamic pull-in of a micro-electromechanical system

The analysis for the dynamic pull-in of a micro-electromechanical system

Dynamical analysis of a damped harmonic forced duffing oscillator with time delay

Analytical and numerical study of a vibrating magnetic inverted pendulum

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