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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

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2024

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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.

2

Decentralized static output feedback controller design for linear interconnected systems

Fadhilah Helisyah Nur, Adzkiya Dieky, Arif Didik Khusnul, Zhai Guisheng, Mardlijah

International Journal of Applied Mathematics and Computer Science

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2023

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Vol. 33, no. 1

83--96

EN

Many interconnected systems in the real world, such as power systems and chemical processes, are often composed of subsystems. A decentralized controller is suitable for an interconnected system because of its more practical and accessible implementation. We use the homotopy method to compute a decentralized controller. Since the centralized controller constitutes the starting point for the method, its existence becomes very important. This paper introduces a non-singular matrix and a design parameter to generate a centralized controller. If the initial centralized controller fails, we can change the value of the design parameter to generate a new centralized controller. A sufficient condition for a decentralized controller is given as a bilinear matrix inequality with three matrix variables: a controller gain matrix and a pair of other matrix variables. Finally, we present numerical examples to validate the proposed decentralized controller design method.

3

Oblique stagnation flow of a thermodynamically-valid Walters' B liquid: a series solution

Mortazavi N., Sadeghy K., Alikbar V., Alizadeh-Pahlavan A.

International Journal of Applied Mechanics and Engineering

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2009

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Vol. 14, no 3

829-852

EN

A thermodynamically-valid exact solution was found for laminar, two-dimensional, oblique stagnation point flow of a Walters' B fluid above a stretching sheet. To circumvent the problem with the extra boundary condition, and also to be able to obtain results at large elasticity numbers, use will be made of the homotopy analysis method in order to find an analytical solution. The analytical solution so obtained shows that the behavior of fluids with a negative elasticity number is completely different from those with a positive elasticity number. For example, while for the wall shear stress is increased by an increase in the elasticity number, for it is predicted to decrease when the elasticity number is increased. A comparison of the results obtained using the homotopy analysis method with those obtained using the perturbation method (Mahapatra et al., 2007) suggests that the perturbation method may not be so reliable when addressing viscoelastic fluids.

4

A stable homotopy approach to horizontal linear complementarity problems

Ralph D.

Control and Cybernetics

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2002

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Vol. 31, no 3

575-599

EN

We are interested in the solution of Horizontal Linear Complementarity Problems, HLCPs, that is complementarity problems with more variables than equations. Globally metrically regular HLCPs have nonempty solution sets that are stable with respect to "right-hand-side perturbations" of the data, hence are numerically attractive. The main purpose of the paper is to show how the stability on conditioning properties of globally metrically regular HLCPs are preserved by a homotopy framework for solving the HLCP that finds a "stable" direcaion at each iteration as a local minimizer of a strongly convex quadratic program with linear complementarity constraints, QPCC. Apart from intrinsic interest in numerical solution of HLCPs, this investigation has application in solving horizontal nonlinear complementarity problems and more broadly in the area of mathematical programs with complementarity constraints, MPCCs.