Aperiodic

In physics and technology, the term aperiodic denotes - at least in international standards for electrical engineering - "a non-oscillating transition from one stationary state to another". This transition is a balancing process that subsides over time.

In the specialist literature, the term “aperiodic” is used inconsistently. Then he has the meaning

• either "not periodic"
• or “without oscillating parts”.

Different waveforms:
Only the one with is periodic . With the given definition, only those with are aperiodic . ${\displaystyle \zeta =0}$
${\displaystyle \zeta \geq 1}$

To use the term in mathematics, see aperiodicity .

Operations

An aperiodic process is a special course in a system that is principally capable of oscillation. Mathematically, it is treated as one of the solutions to the oscillation equation , a linear ordinary differential equation .

The term vibration is used very broadly in standardization (see DIN 1311), the term period rather narrow.

Periodic process

A periodic process fulfills the condition

${\displaystyle y(t)=y(t+T)}$     for any time and for the period . ${\displaystyle t}$ ${\displaystyle T={\text{konst}}>0}$

The best known example of this is the harmonic oscillation according to the equation

${\displaystyle y(t)=A\cos(\omega t)}$.

Creeping process

The course of a very strongly damped oscillatory system is called aperiodic oscillation (creeping movement) towards a rest position. For this is considered a possible solution to the oscillation equation

${\displaystyle y(t)=A_{1}\mathrm {e} ^{\lambda _{1}t}+A_{2}\mathrm {e} ^{\lambda _{2}t}}$     for and . ${\displaystyle t\geq 0}$ ${\displaystyle \lambda _{1},\,\lambda _{2}<0}$

This course fulfills both of the above-mentioned possible meanings of an aperiodic course; it is “not periodic” and “without oscillating components”.

The oscillation differential equation also provides the solution of the aperiodic limit case , which behaves like the creep case, but is mathematically on the limit of the oscillation case.

Oscillating, but not periodic process

This weakly damped, non-periodic oscillation contains an oscillating component

This temporary oscillation pulse of a PAL television signal contains an oscillating component

Furthermore, there are non-periodic oscillations with a course that oscillates over a rest position. This includes the decaying oscillation of a weakly damped oscillatory system. For this is considered a possible solution to the oscillation equation

${\displaystyle y(t)=A\mathrm {e} ^{-\delta t}\cos(\omega t)}$     for and . ${\displaystyle t\geq 0}$ ${\displaystyle \delta >0}$

The sine wave pulse ( burst signal ; in audio engineering: tone pulse) is one of the non-periodic vibrations. It is short-lived.

Both examples fulfill the meaning of an aperiodic course in the sense of “not periodic”, but they do not fulfill the meaning of an aperiodic course in the sense of “without oscillating components”. So they do not meet the standardized definition.

Further use

The use of the term “aperiodic” in physics and technology beyond electrical engineering is demonstrated by a few examples.

• In (physics, general oscillation theory) a movement of a body becomes aperiodic when it gradually returns to its rest position without swinging beyond it.
• In (fluid mechanics), when the pressure pipeline of a hydropower plant is slowly closed, an alternating but decaying pressure oscillation or an aperiodically decaying pressure oscillation can occur.
• In (measurement technology), a measuring device is aperiodically damped if its moving part is in equilibrium position without vibrations - in contrast to a measuring device with vibration damping, which is in equilibrium position after a few vibrations.
• In (control engineering), a distinction is made depending on the degree of damping or the following cases: ${\displaystyle D}$ ${\displaystyle \zeta }$

• ${\displaystyle D>1}$ aperiodic creeping,
• ${\displaystyle D=1}$ aperiodic borderline case,
• ${\displaystyle 0<D<1}$ decaying swing,
• ${\displaystyle D=0}$ Continuous oscillation,
• ${\displaystyle D<0}$ evanescent swing.

Web links

Wiktionary: aperiodic  - explanations of meanings, word origins, synonyms, translations

Individual evidence

1. ↑ IEC 60050, see DKE German Commission for Electrical, Electronic and Information Technologies in DIN and VDE: Internationales Electrotechnical Dictionary - IEV . IEV numbers 101-14-05 and 103-05-10.
2. ^ Tilo Peifer, Paul Profos (Ed.): Handbook of industrial measurement technology. Oldenbourg, 6th edition, 1994, p. 53
3. ↑ DIN 5483-1: Time-dependent quantities; Name of the time dependency . 1983, No. 2
4. ↑ DIN 1311-1: Vibrations and systems capable of vibrating; Part 1: Basic concepts, classification . 2000, chap. 5.1.1
5. ↑ DIN 1311-2: Vibrations and systems capable of vibrating; Part 2: Linear, time-invariant vibratory systems with one degree of freedom . 2002, chap. 6.2.3
6. ↑ Chr. Gerthsen, HO Kneser: Physics: A textbook for use in addition to lectures . Springer, 11th ed., 1971, p. 87
7. ↑ E. Truckenbrodt: Fluid Mechanics: Volume 2: Elementary Flow Processes… . Springer, 1980, p. 61
8. ↑ Eberhard Seiler (ed.): Basic concepts of measurement and calibration . Vieweg, 1983, p. 47
9. ↑ Wolfgang Schneider: Practical control engineering: A text and exercise book for non-electrical engineers . Springer, 1994, p. 224