Abstract
Mechanical vibration is a vast field composed of thousands of studies and experiments regarding individual systems and structures’ vibrations and oscillations. The problems of vibro-safety are connected with the consideration of the human reaction to various mechanical inputs. Traditionally this problem is solved as a mechanical system with concentrated (not distributed) parameters. The goal of this study is to set up a mechanical system closely following the actual conditions of the human arm undergoing mechanical vibrations. The results will show how to generalize the analysis of the effect of vibration frequencies, and harmonic wave propagation along the human arm. In order to understand the effect on the system, a mathematical model of two viscoelastic rods connected by a hinge was derived. Using this model, it was possible to derive the propagation of both the longitudinal and bending vibrations of the arm, and find the resonance frequencies of the system from the elbow to the shoulder.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Viktorova, I., Holden, L., Stocks, S.B.: Analysis of Resonance Frequencies for the Problem of Induced Vibrations along the Human Arm. In: Rychtář, J., Chhetri, M., Gupta, S., Shivaji, R. (eds.) Collaborative Mathematics and Statistics Research. Springer Proceedings in Mathematics & Statistics, vol. 109, pp. 67–73. Springer, Cham (2015)
Christensen, R.M.: Theory of Viscoelasticity: An Introduction. 2nd edn. Academic Press, New York: (1982)
Coleman, B.D., Gurtin, M.H., Herrera, R.I., Truesdell, C.: Wave Propagation in Dissipative Materials. Springer, Berlin Heidelberg (1965)
Misyurin, SYu., Kreinin, G.V.: Power optimization criteria of a mechanical unit of an automated actuator. Dokl. Phys. 60(1), 15–18 (2015)
Misyurin, SYu., Ivlev, V.I., Bozrov, V.M., Nelyubin, A.P.: Parameterization of an air motor based on multiobjective optimization and decision support. J. Mach. Manuf. Reliab. 42(5), 353–358 (2013)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Viktorova, I., Alekseeva, S. (2020). Mathematical Methods for the Analysis of Vibrations Along the Human Arm. In: Misyurin, S., Arakelian, V., Avetisyan, A. (eds) Advanced Technologies in Robotics and Intelligent Systems. Mechanisms and Machine Science, vol 80. Springer, Cham. https://doi.org/10.1007/978-3-030-33491-8_43
Download citation
DOI: https://doi.org/10.1007/978-3-030-33491-8_43
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-33490-1
Online ISBN: 978-3-030-33491-8
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)