Enhanced Multistage Homotopy Perturbation Method: Approximate Solutions of Nonlinear Dynamic Systems

Olvera, D.; Elı́as-Zúñiga, Alex

doi:10.1155/2014/486509

Cited by 3 publications

(3 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this work, we introduce some modifications to the MHPM and focus on the derivation of approximate solutions of DDEs equations with variable coefficient terms. This new approach is based on the enhanced multistage homotopy perturbation method (EMHPM) introduced in [17] to obtain the solution of nonlinear ordinary differential equations.…”

Section: The Emhpm Methodology To Solve Ddesmentioning

confidence: 99%

Approximate Solutions of Delay Differential Equations with Constant and Variable Coefficients by the Enhanced Multistage Homotopy Perturbation Method

Olvera¹,

Elı́as-Zúñiga

Lacalle³

et al. 2015

Abstract and Applied Analysis

View full text Add to dashboard Cite

We expand the application of the enhanced multistage homotopy perturbation method (EMHPM) to solve delay differential equations (DDEs) with constant and variable coefficients. This EMHPM is based on a sequence of subintervals that provide approximate solutions that require less CPU time than those computed from the dde23 MATLAB numerical integration algorithm solutions. To address the accuracy of our proposed approach, we examine the solutions of several DDEs having constant and variable coefficients, finding predictions with a good match relative to the corresponding numerical integration solutions.

show abstract

Section: The Emhpm Methodology To Solve Ddesmentioning

confidence: 99%

Approximate Solutions of Delay Differential Equations with Constant and Variable Coefficients by the Enhanced Multistage Homotopy Perturbation Method

Olvera¹,

Elı́as-Zúñiga

Lacalle³

et al. 2015

Abstract and Applied Analysis

View full text Add to dashboard Cite

show abstract

“…In the development of a 3-D stability model for the machining of thin walls and thin floors, Campa et al [300,301] also considered the flexibility of both the machine and the workpiece in three Cartesian directions. Olvera and Elías-Zúñiga introduced an enhanced multistage homotopy perturbation method (EMHPM) to solve differential equations with strong nonlinearities [302]. This method has been utilized to calculate the stability lobes for a multivariable milling tool with variable pitch, variable helix and variable rake angle [286,287,303].…”

Section: Stability Diagram and Chatter Predictionmentioning

confidence: 99%

Chatter detection in milling processes—a review on signal processing and condition classification

Navarro-Devia

Chen

Dao

et al. 2023

Int J Adv Manuf Technol

View full text Add to dashboard Cite

Among the diverse challenges in machining processes, chatter has a significant detrimental effect on surface quality and tool life, and it is a major limitation factor in achieving higher material removal rate. Early detection of chatter occurrence is considered a key element in the milling process automation. Online detection of chatter onset has been continually investigated over several decades, along with the development of new signal processing and machining condition classification approaches. This paper presents a review of the literature on chatter detection in milling, providing a comprehensive analysis of the reported methods for sensing and testing parameter design, signal processing and various features proposed as chatter indicators. It discusses data-driven approaches, including the use of different techniques in the time–frequency domain, feature extraction, and machining condition classification. The review outlines the potential of using multiple sensors and information fusion with machine learning. To conclude, research trends, challenges and future perspectives are presented, with the recommendation to study the tool wear effects, and chatter detection at dissimilar milling conditions, while utilization of considerable large datasets—Big Data—under the Industry 4.0 framework and the development of machining Digital Twin capable of real-time chatter detection are considered as key enabling technologies for intelligent manufacturing.

show abstract

“…In [42], the optimal homotopy perturbation method (OHPM) was applied to find the solutions for a nonconservative dynamical system of a rotating electrical machine. Very recently in [43], Olvera and Elías-Zúñiga have introduced the enhanced multistage homotopy perturbation method (EMHPM) approach to solve nonlinear dynamical systems.…”

Section: Introductionmentioning

confidence: 99%

The Multistage Homotopy Perturbation Method for Solving Chaotic and Hyperchaotic Lü System

Chowdhury

Razali

Asrar

et al. 2015

Abstract and Applied Analysis

View full text Add to dashboard Cite

The multistage homotopy-perturbation method (MHPM) is applied to the nonlinear chaotic and hyperchaotic Lü systems. MHPM is a technique adapted from the standard homotopy-perturbation method (HPM) where the HPM is treated as an algorithm in a sequence of time intervals. To ensure the precision of the technique applied in this work, the results are compared with a fourthorder Runge-Kutta method and the standard HPM. The results show that the MHPM is an efficient and powerful technique in solving both chaotic and hyperchaotic systems.

show abstract

Enhanced Multistage Homotopy Perturbation Method: Approximate Solutions of Nonlinear Dynamic Systems

Cited by 3 publications

References 28 publications

Approximate Solutions of Delay Differential Equations with Constant and Variable Coefficients by the Enhanced Multistage Homotopy Perturbation Method

Approximate Solutions of Delay Differential Equations with Constant and Variable Coefficients by the Enhanced Multistage Homotopy Perturbation Method

Chatter detection in milling processes—a review on signal processing and condition classification

The Multistage Homotopy Perturbation Method for Solving Chaotic and Hyperchaotic Lü System

Contact Info

Product

Resources

About