Abstract
This article studies the entropy generation of a mass-spring-damper mechanical system, under the conformable fractional operator definition. We perform several simulations by varying the fractional order γ and the damping ratio ζ , including the usual dynamic response when γ = 1.0 and the typical damping cases. We analyze the entropy production for this system and its strong dependency on both γ and ζ parameters. Therefore, we determine their optimal values to obtain the highest efficiency of the MSD response, as well as other impressive features.
Highlights
Mass-spring-damper (MSD) systems are vastly known as strong conceptual strategies for modeling purposes in diverse areas of knowledge
This work studied the natural response of the simple MSD system presented in Figure 1, using the conformable fractional derivative model developed in Equation (13), and its entropy generation rate obtained in Equation (16)
Responses with lower fractional orders have a greater magnitude of velocity, which is directly related to the kinetic energy
Summary
Mass-spring-damper (MSD) systems are vastly known as strong conceptual strategies for modeling purposes in diverse areas of knowledge. The concept of an MSD system has been implemented on a vast number of practical fields, such as in the reduction of vibrations [1,2], in control systems analysis [3,4], and in power generation [5,6] Those systems have been independently studied under different lenses, such as fractional calculus and entropy production. Berman et al solved a damped mechanical harmonic oscillator system with asymptotic behavior by employing the Caputo fractional derivative definition and Laplace transform [30]. Their solution showed an evident difference with respect to that for the standard oscillator. Results are discussed, and the most relevant conclusions are stated
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