Structural Differences in the Analysis of Mechanical and Electrical Systems

Parfentiev Nikolay Andreevich

doi:10.11648/j.ajesa.20180601.12

Abstract

Mechanical systems, the description of which differs from the electrical circuits of similar structure, are studied. As an example, the scheme of a spring pendulum with a zero periodic displacement of the point of application of the forcing harmonic force is considered. In contrast to the unique representation of electrical circuits mechanical system with a serial connection of mechanical elements can be modeled by different electrical circuits. In this case, the family of frequency characteristics of such a system contains a singular point, which is at a frequency <img width="20" height="20" src="http://article.sciencepublishinggroup.com/journal/236/2361007_20180425/image001.png" /> less than the resonance frequency. The force modulus at this point does not depend on the value of the viscous resistance.

Highlights

In the sections of mechanics and electrical engineering the General scheme for the analysis of a spring pendulum and an oscillating circuit is usually applied
In some textbooks the parallel and serial connection of springs is considered by analogy with connection of capacitors and resistors
It can be used to describe all variants of the scheme of the spring pendulum, and the section of forced oscillations of the mechanical resonator can be described in the manner of describing the alternating current in electrical engineering

Summary

Introduction

In the sections of mechanics and electrical engineering the General scheme for the analysis of a spring pendulum and an oscillating circuit is usually applied. It can be used to describe all variants of the scheme of the spring pendulum, and the section of forced oscillations of the mechanical resonator can be described in the manner of describing the alternating current in electrical engineering. A possible reason for limiting the use of the method of electromechanical analogies is the desire to first determine the mechanical displacement (the most obvious) while, with a single approach, the speed is a direct analogue of the alternating current in electrical engineering. An attempt is made to present the mechanics section in a uniform manner, producing in some cases paradoxical and unusual results

An Example of a Mechanical System That Does Not Have a Direct Electric Analog

Analysis of the System with a Source of Linearly Increasing Velocity

Conclusion