Wyniki wyszukiwania - BazTech

1

The variational iteration method for a pendulum with a combined translational and rotational system

Amir Muhammad, Ashraf Asifa, Haider Jamil Abbas

Acta Mechanica et Automatica

|

2024

|

Vol. 18, no. 1

48--54

EN

The dynamic analysis of complex mechanical systems often requires the application of advanced mathematical techniques. In this study, we present a variation iteration-based solution for a pendulum system coupled with a rolling wheel, forming a combined translational and rotational system. Furthermore, the Lagrange multiplier is calculated using the Elzaki transform. The system under investigation consists of a pendulum attached to a wheel that rolls without slipping on a horizontal surface. The coupled motion of the pendulum and the rolling wheel creates a complex system with both translational and rotational degrees of freedom. To solve the governing equations of motion, we employ the variation iteration method, a powerful numerical technique that combines the advantages of both variational principles and iteration schemes. The Lagrange multiplier plays a crucial role in incorporating the constraints of the system into the equations of motion. In this study, we determine the Lagrange multiplier using the Elzaki transform, which provides an effective means to calculate Lagrange multipliers for constrained mechanical systems. The proposed solution technique is applied to analyse the dynamics of a pendulum with a rolling wheel system. The effects of various system parameters, such as the pendulum length, wheel radius and initial conditions, are investigated to understand their influence on the system dynamics. The results demonstrate the effectiveness of the variation iteration method combined with the Elzaki transform in capturing the complex behaviour of a combined translational and rotational system. The proposed approach serves as a valuable tool for analysing and understanding the dynamics of similar mechanical systems encountered in various engineering applications.

2

The homotopy perturbation method for electrically actuated microbeams in mems systems subjected to van der waals force and multiwalled carbon nanotubes

Amir Muhammad, Haider Jamil Abbas, Ashraf Asifa

Acta Mechanica et Automatica

|

2024

|

Vol. 18, no. 1

123--128

EN

This paper presents a summary of a study that uses the Aboodh transformation and homotopy perturbation approach to analyze the behavior of electrically actuated microbeams in microelectromechanical systems that incorporate multiwalled carbon nanotubes and are subjected to the van der Waals force. All of the equations were transformed into linear form using the HPM approach. Electrically oper-ated microbeams, a popular structure in MEMS, are the subject of this work. Because of their interaction with a nearby surface, these mi-crobeams are sensitive to a variety of forces, such as the van der Waals force and body forces. MWCNTs are also incorporated into the MEMSs in this study because of their special mechanical, thermal, and electrical characteristics. The suggested method uses the HPM to model how electrically activated microbeams behave when MWCNTs and the van der Waals force are present. The nonlinear equations controlling the dynamics of the system can be roughly solved thanks to the HPM. The HPM offers a precise and effective way to analyze the microbeam's reaction to these outside stimuli by converting the nonlinear equations into linear forms. The study's findings shed im-portant light on how electrically activated microbeams behave in MEMSs. A more thorough examination of the system's performance is made possible with the addition of MWCNTs and the van der Waals force. With its ability to approximate solutions and characterize system behavior, the HPM is a potent instrument that improves comprehension of the physics at play and facilitates the design and optimization of MEMS devices. The aforementioned method's accuracy is verified by comparing it with published data that directly aligns with Anjum et al.'s findings. We have faith in this method's accuracy and its current application.

3

Solutions of the nonlinear evolution problems and their applications

Amir Muhammad, Haider Jamil Abbas, Rahman Jamshaid Ul, Ashraf Asifa

Acta Mechanica et Automatica

|

2023

|

Vol. 17, no. 3

357--363

EN

In this article, a well-known technique, the variational iterative method with the Laplace transform, is used to solve nonlinear evolution problems of a simple pendulum and mass spring oscillator, which represents the duffing equation. In the variational iteration method (VIM), finding the Lagrange multiplier is an important step, and the variational theory is often used for this purpose. This paper shows how the Laplace transform can be used to find the multiplier in a simpler way. This method gives an easy approach for scientists and engineers who deal with a wide range of nonlinear problems. Duffing equation is solved by different analytic methods, but we tackle this for the first time to solve the duffing equation and the nonlinear oscillator by using the Laplace-based VIM. In the majority of cases, Laplace variational iteration method (LVIM) just needs one iteration to attain high accuracy of the answer for linearization anddiscretization, or intensive computational work is needed. The convergence criteria of this method are efficient as compared with the VIM. Comparing the analytical VIM by Laplace transform with MATLAB’s built-in command Simulink that confirms the method’s suitability for solving nonlinear evolution problems will be helpful. In future, we will be able to find the solution of highly nonlinear oscillators.