Solution of mass-spring-damper fractional systems using Caputo derivative and orthogonal collocation

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.

Citation

Lima, J.V.C.F., Lobato, F.S. and Steffen Jr, V. (2022), "Solution of mass-spring-damper fractional systems using Caputo derivative and orthogonal collocation", Engineering Computations, Vol. 39 No. 4, pp. 1432-1450. https://doi.org/10.1108/EC-04-2021-0199