Abstract
In this article, we obtain the viscous damping coefficient β theoretically and experimentally in the spring–mass–viscodamper system. The calculation is performed to obtain the quasi-period τ. The influence of the viscosity of the fluid and the damping coefficient is analyzed using three fluids, water, edible oil, and gasoline engine oil SAE 10W-40. These processes exhibit temporal fractality and non-local behaviors. Our general non-local damping model incorporates fractional derivatives of Caputo type in the range [Formula: see text], and the viscous damping coefficients are determined in terms of the inverse Mittag-Leffler function. The classical models are recovered when the order of the fractional derivatives is equal to 1.
Highlights
IntroductionThe representation of physical models based on non-integer order derivative has attracted a considerable interest due to the fact that these models can describe memory and the hereditary properties of various materials and processes.[1,2,3,4,5,6] For example, fractional derivatives have been used successfully to model viscoelastic behavior of materials,[7] frequencydependent damping behavior,[8,9,10,11,12,13,14] viscoelastic singlemass systems,[15] and viscoelasticity and anomalous diffusion.[16,17,18,19] they are used in modeling of chemical processes, control theory, electromagnetism, thermodynamics, and many other problems in physics, engineering, and the various works cited therein.[20,21,22,23]
While our experience in the laboratory with the mass–spring–viscodamper system, we studied only system that crossed 30 times; see Table 1; this is because the quasi-period used came from the average of the measurements we made during the experiment
While our experience in the laboratory with the spring–mass–viscodamper system, we studied only system that crossed 15 times; see Table 4; this is because the quasi-period average employee came from measurements that we made during the experiment
Summary
The representation of physical models based on non-integer order derivative has attracted a considerable interest due to the fact that these models can describe memory and the hereditary properties of various materials and processes.[1,2,3,4,5,6] For example, fractional derivatives have been used successfully to model viscoelastic behavior of materials,[7] frequencydependent damping behavior,[8,9,10,11,12,13,14] viscoelastic singlemass systems,[15] and viscoelasticity and anomalous diffusion.[16,17,18,19] they are used in modeling of chemical processes, control theory, electromagnetism, thermodynamics, and many other problems in physics, engineering, and the various works cited therein.[20,21,22,23]. As before, that the y(t) function is the exponential curve that defines the solution of equation (17); we have y(t) = y0 Á EgfÀ(b=2m)tp1Àgtgg; from the experiment, we know that y(0) = 0:05 and t5 was the last time for which the mass passes through its equilibrium point before moving out indistinguishable; with these considerations, it can be assumed that. Times measured for which the mass crosses its equilibrium point are obtained; see Figure 8
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