Dynamical analysis of a vertical excited pendulum using He’s perturbation method

Galal, A. A.; Amer, T. S.; Amer, W. S.; Elkafly, H.F.

doi:10.1177/14613484231176247

Journal of Low Frequency Noise, Vibration and Active Control

2023

DOI: 10.1177/14613484231176247

|View full text |Cite

Dynamical analysis of a vertical excited pendulum using He’s perturbation method

A. A. Galal

T. S. Amer

W. S. Amer

et al.

Abstract: The current paper investigates the nonlinear dynamics of an excited pendulum by a crank-shaft-slider mechanism (CSSM), in which it is restricted to move vertically. He’s method of homotopy is employed to obtain the analytical solution of the governing differential equation. The numerical solution of this equation is obtained using the fourth-order Runge-Kutta method (RKM). The comparison between both solutions demonstrates a high level of consistency, which confirms the precision of the gained analytic solutio… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2023

2024

Publication Types

Select...

Article5

Relationship

Self Cite1

Independent4

Authors

Journals

Cited by 5 publications

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Effects of pendulum orientation and excitation type on the energy harvesting performance of a pendulum based wave energy converter

Reid,

Sorokin,

2024

Nonlinear Dyn

View full text Add to dashboard Cite

With global electricity requirements due to increase in the coming years and growing pressure to reduce dependence on fossil fuels, universal demand for renewable energy is projected to grow. Marine energy, including wave energy, is an active research area, with potential to meet future energy demands, due to its high energy density. With a view to using a pendulum system in a floating object to extract energy from ocean waves, this paper analyses the effects of pendulum orientation and excitation type on the system’s dynamics. Three excitation scenarios, surge, heave and dynamic tilt of the floating object, with various pendulum orientations, were analysed and simulated. Both linearised and nonlinear systems were investigated with the former providing insight into the nonlinear system’s behaviour. Effects of pendulum orientation on power output potential differs significantly with excitation type and pendulum properties. While expected peak power output is observed at the resonant frequency and twice the resonant frequency under direct and parametric excitations respectively for both systems, the linearised system also exhibits regions of instability. These instability regions under parametric excitations were investigated with consideration for energy harvesting applications. Theoretical and experimental findings revealed that dynamic tilt excitations can be utilised for broadband energy harvesting at the expense of the peak power output. While peak average power output for these excitations for the considered system parameters is relatively low, 1 W versus 12.5 W for heave excitation, the bandwidth is very broad and starts from 0 rad/s frequency if tilt excitation amplitude is above 1.1 rad.

show abstract

Effects of pendulum orientation and excitation type on the energy harvesting performance of a pendulum based wave energy converter

Reid,

Sorokin,

2024

Nonlinear Dyn

View full text Add to dashboard Cite

show abstract

On the Stability of a 3DOF Vibrating System Close to Resonances

Amer,

El-Sabaa,

Moatimid

et al. 2024

J. Vib. Eng. Technol.

View full text Add to dashboard Cite

Purpose In the current work, the motion of a three degrees-of-freedom (DOF) dynamical system as a vibrating model is examined. The proposed system is of high importance in vibration engineering applications, such as the analysis of the control of flexible arm robotics, flexible arm vibrational motion as a dynamic system, pump compressors, transportation devices, rotor dynamics, shipboard cranes, and human or walking analysis robotics. Methods Lagrange's equations (LE) are used to derive the equations of motion of the controlling system. The analytic solutions (AS) are obtained utilizing the multiple-scales method (MSM) up to the third order. Results The framework for removing secular terms provides the requirements for the solvability of this problem. Various resonance scenarios are categorized and the modulation equations (ME) are constructed. To graphically demonstrate the beneficial impacts of the distinct parameters of the problem, the time histories (TH) of the approximate solutions as well as the resonance curves (RC) are depicted. The Runge-Kutta algorithm (RKA) is employed to obtain the numerical solutions (NS) of the regulating system. Conclusion A comparison of the AS and NS reveals the accuracy of the perturbation approach. The stability/instability zones are studied using Routh-Hurwitz criteria (RHC), and then they are examined using a steady-state situation. Basically, the used perturbation method is considered a traditional method that is applied to solve a new dynamical system. Then, the achieved results are considered new because they weren’t obtained previously, which indicates the novelty of this work.

show abstract

Studying highly nonlinear oscillators using the non-perturbative methodology

Moatimid,

Amer,

Galal

2023

Sci Rep

View full text Add to dashboard Cite

Due to the growing concentration in the field of the nonlinear oscillators (NOSs), the present study aims to use the general He's frequency formula (HFF) to examine the analytical representations for particular kinds of strong NOSs. Three real-world examples are demonstrated by a variety of engineering and scientific disciplines. The new approach is evidently simple and requires less computation than the other perturbation techniques used in this field. The new methodology that is termed as the non-perturbative methodology (NPM) refers to this innovatory strategy, which merely transforms the nonlinear ordinary differential equation (ODE) into a linear one. The method yields a new frequency that is equivalent to the linear ODE as well as a new damping term that may be produced. A thorough explanation of the NPM is offered for the reader's convenience. A numerical comparison utilizing the Mathematical Software (MS) is used to verify the theoretical results. The precise numeric and theoretical solutions exhibited excellent consistency. As is commonly recognized, when the restoration forces are in effect, all traditional perturbation procedures employ Taylor expansion to expand these forces and then reduce the complexity of the specified problem. This susceptibility no longer exists in the presence of the non-perturbative solution (NPS). Additionally, with the NPM, which was not achievable with older conventional approaches, one can scrutinize examining the problem's stability. The NPS is therefore a more reliable source when examining approximations of solutions for severe NOSs. In fact, the above two reasons create the novelty of the present approach. The NPS is also readily transferable for additional nonlinear issues, making it a useful tool in the fields of applied science and engineering, especially in the topic of the dynamical systems.

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

hi@scite.ai

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Dynamical analysis of a vertical excited pendulum using He’s perturbation method

Cited by 5 publications

References 35 publications

Effects of pendulum orientation and excitation type on the energy harvesting performance of a pendulum based wave energy converter

Effects of pendulum orientation and excitation type on the energy harvesting performance of a pendulum based wave energy converter

On the Stability of a 3DOF Vibrating System Close to Resonances

Studying highly nonlinear oscillators using the non-perturbative methodology

Contact Info

Product

Resources

About