Types of mechanical power for harmonic vibrations


DOI: 10.34759/trd-2022-122-03

Аuthors

Popov I. P.

Kurgan State University, 63/4, Sovetskaya str., Kurgan, 640020, Russia

e-mail: ip.popow@yandex.ru

Abstract

The purpose of the study consists in detailing the types of mechanical power while harmonic oscillations. Due to the irreversibility of thermal energy, its derivative takes only positive values. With this, derivatives can be taken of both potential and kinetic energy. Harmonic oscillations herewith at which the derivatives (instantaneous powers) are necessarily sign-changing functions, which fundamentally distinguishes them from thermal power, deliver the most interesting case. The inductance coil magnetic field energy is the kinetic energy analog in electrical engineering, the capacitor electric field is the potential energy analog, and thermal energy dissipated by the resistor is the mechanical energy analog. The article shows that at mechanical vibrations not only sign-positive thermal power develops but the sign-variable reactive powers as well, which characterize the potential and kinetic energies reversibility. The active power is understood as the average value of instantaneous power over half a period, and reactive power is its amplitude value. The total mechanical power, on the one hand, is being described by the Pythagorean formula, and on the other hand, it is equal to the product of the rms values of the harmonic quantities. A feature of the complex representation consists in the fact that while the total power calculating, one of the multiplied vectors should be conjugate. The concept of mechanical reactive, active and apparent powers is a generalization of the corresponding concepts from electrical engineering, which is a manifestation of electro-mechanical dualism.

Keywords:

mechanical power, kinetic energy, potential energy, complex representation, vector representation

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