Geodesic
Model study of the influence of multi-joint muscles on the frequency characteristics of the human body
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 16 (2020) no. 3, pp. 267-276

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It is noted that the Kelvin—Voigt model is unsuitable for describing some polymers and biological tissues. In these cases, a three-component combination of elements, which consists of a spring and damper, connected in parallel and a spring sequentially attached to them, is used. The force characteristic of such a combination includes not only the strain, strain rate, and force, but also the rate of force change. Examples of such systems are the blood vessel wall and the intervertebral disc, which have been given special attention. Since the motion of such systems is described by an ordinary third-order differential equation, they are classified as systems with a non-integer number of degrees of freedom. For a single-mass oscillating system with one and a half degrees of freedom, a transfer function was constructed using the Laplace transform. In addition, the amplitude-frequency response (AFR) was also constructed. Analysis of this characteristic showed that increasing the damping coefficient from zero to infinity first leads to a decrease in its maximum to a certain non-zero value, and then to an increase and reaching infinity with an infinite value of the damping coefficient. The same feature is demonstrated on a two-mass system of chain structure, each link of which has one and a half degrees of freedom. A sequential combination of seven such links was used to model the lumbar spine in the structure of a General body model of a sitting person subject to vertical vibration. Multi-link elastic-viscous joints were used to model the multi-articular muscles of the lumbar spine. Additional experimental studies are needed to determine the numerical values of the parameters of the proposed model.
Keywords: mechanical system, amplitude-frequency response, non-integer number of degrees of freedom, resonant frequency. 
@article{VSPUI_2020_16_3_a4,
     author = {V. P. Tregubov and N. K. Egorova},
     title = {Model study of the influence of multi-joint muscles on the frequency characteristics of the human body},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {267--276},
     publisher = {mathdoc},
     volume = {16},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2020_16_3_a4/}
}
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V. P. Tregubov; N. K. Egorova. Model study of the influence of multi-joint muscles on the frequency characteristics of the human body. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 16 (2020) no. 3, pp. 267-276. http://geodesic.mathdoc.fr/item/VSPUI_2020_16_3_a4/