Method of electromechanical analogies in calculations of natural frequencies of multi-mass mechanical and biological systems

With the growth of industry, transportation and machinery the issue of studying and damping vibrations and acoustic oscillations has become critical. Up to 4,000 earthquakes occur on Earth each year. Structures such as skyscrapers and bridges must be designed to withstand ground vibrations without damage. Machinery and tools operate with components that torsion and vibrate in the form of structural nodes. These nodes are connected by specific links to form complex multi-mass mechanical systems. Preventing vibration damage to multi-mass structures remains a pressing problem today. Therefore, the development of methods to calculate the amplitude, frequency and phase of the generated vibrations is a relevant task. Currently known methods of dynamic calculations are the use of analytical techniques for determining the intrinsic frequency of transverse and longitudinal oscillations of shells, rods and rotating machine parts (L.D. Landau, E.M. Lifshitz, V.I. Mossakovskiy, K.V. Frolov). Each task solved with these methods must strictly define the initial and boundary conditions of the oscillatory process. The application of these computational methods to multi-mass systems is very labor-intensive because, in addition to the calculation of amplitude, frequency, and phase, it is necessary to take into account the mode of oscillation. The study of free oscillations in multi-mass systems requires the formation of a system of linear differential equations and the use of cyclic frequency equations for multi-mass systems. Currently, simpler engineering methods such as electromechanical analogies were widely adopted in engineering practice. This period also saw the beginning of research into the resonant frequencies of living organisms to ensure the safety of vehicles subjected to vibration loads. This research was particularly important to the aerospace industry. When launching rockets carrying astronauts, spacecraft experience tremendous vibration shocks. In order to avoid harmful resonance effects, the natural frequencies of the astronaut's body and its organs must be determined. We have used a method based on electromechanical analogies to calculate the resonance frequencies. This method is based on the model of the astronaut's body as a vibrating system proposed by Prof. I. K. Kosko. The computational scheme of this model was developed for the first time. The astronaut's body was modeled as a lumped mass system connected by elastic links, the stiffness of which was determined according to the series and parallel rules. The study used data on the elastic modulus and mass of each part of the astronaut's body. The intrinsic frequency of the astronaut's body was calculated to be 1.702 Hz. The results highlight the importance of taking these data into account when designing the damping system for the astronaut's seat in order to prevent the vibration frequency of the rocket from coinciding with the resonance frequency of the astronaut's body. This approach allows the identification of frequencies that must be avoided to minimize the risk of damage caused by vibration loads. This work demonstrates the application of electromechanical analogies as a simplified engineering method for determining the natural frequencies of complex multi-mass systems such as the human body.