Solution of mass-spring-damper fractional systems using Caputo derivative and orthogonal collocation. Issue 4 (2nd November 2021)

• Record Type: Journal Article
• Authors: Lima, Juliana V.C.F.; Lobato, Fran Sérgio; Steffen Jr, Valder
• Is Part Of: Engineering computations. Volume 39:Issue 4(2022)
• Page Start: 1432
• Page End: 1450
• Publication Date: 2021-11-02
• Subjects: Mass-spring-damper systems -- Fractional differential equation -- Orthogonal collocation; Computer-aided engineering -- Periodicals; Computer graphics -- Periodicals; 620.00285
• DOI: 10.1108/EC-04-2021-0199
• Languages: English
• ISSNs: 0264-4401

Abstract

Abstract : Purpose: In this contribution, the solution of Mass-Spring-Damper Systems in the fractional context by using Caputo derivative and Orthogonal Collocation Method is investigated. For this purpose, different case studies considering constant and periodic sources are evaluated. The dimensional consistency of the model is guaranteed by introducing an auxiliary parameter. The obtained results are compared with those found by using both the analytical solution and the predictor-corrector method of Adams–Bashforth–Moulton type. The influence of the fractional order on the mechanical system is evaluated. Design/methodology/approach: In the present contribution, an extension of the Orthogonal Collocation Method to solve fractional differential equations is proposed. Findings: In general, the proposed methodology was able to solve a classical mechanical engineering problem with different characteristics. Originality/value: The development of a new numerical method to solve fractional differential equations is the major contribution.