UDC 621.542 THE MATHEMATICAL IMPLICATIONS OF HAND-ARM VIBRATION SYNDROME © I.V. Viktorova, PhD, Clemson University, USA S.I. Alekseeva, DSc, Blagonravov Mechanical Engineering Research Institute of RAS, Moscow, Russia M. Fleck, Student, Clemson University, USA M. Kose, Student, Clemson University, USA Abstract. <...> Mechanical vibration is a vast field composed of thousands of studies and experiments regarding individual systems and structures' vibrations and oscillations. <...> 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. <...> The harmful effect of these frequencies is discussed with regards to Hand-Arm Vibration Syndrome, a disease stemming from repeated contact with vibrating objects. <...> A sample set of construction tools is analyzed and compared with the modeled resonance frequencies of the arm. <...> Considering the resonance frequencies of the arm is significant for tools manufacturers. <...> Any individual machine or mechanism, human tissue or bone can emit vibrations at a specific frequency, and if it is at or near the natural frequency of the material in the human arm or hand, can cause devastating damage and more quickly lead to the development of Hand-Arm Vibration Syndrome. <...> Therefore it is important to know accurately the resonance frequencies in the arm and compare them to the individual frequencies emitted by construction technology. <...> Due to the lack of data on the human arm from a living subject, models of the arm are a practical solution to the resonance problem. <...> RESONANCE Resonance is the phenomenon at which an externally forced frequency coincides with the natural frequency, defined by a ratio close to one between the two frequencies. <...> When damping is present, pseudo resonance will occur with the maximum amplitude of the vibrating object. <...> In general, amplitude is not linearly dependent on frequency. <...> An important case of resonance, including the hand-arm system, relates amplitude A to the square of the frequency ω [1]. <...> The 92 Engineering and Automation Problems, № 3 – 2016 case of resonance in the hand-arm system will be examined later. <...> The vast complexity of the body makes it incredibly difficult to predict, record, or analyze information about bones or organs <...>