# damping

When damping is defined as the phenomenon that during a vibratable system, in principle, the amplitude of oscillation decreases with time or can no vibration occur depending on circumstances. After energy has been supplied once, the oscillation is based on the interrelation of two forms of energy; z. B. with a mechanical shaft , kinetic energy and potential energy are mutually exchanged. If energy is branched off into a third form of energy - often as heat - this is the cause of the damping.

The term damping is also applied to a weakening phenomenon that is related to oscillation, radiation or wave-like processes, although these are stationary . These processes can take place without a time limit if the energy given off as heat is continuously replaced by other types of energy.

## Time-dependent processes

### Basis, parameter

The attenuation may be undesirable, e.g. B. in a clockwork that is supposed to oscillate indefinitely. But it may also be desirable, for. B. in an electromechanical measuring mechanism that should come to rest quickly after a change in the measured variable .

In the case of a damped, oscillatory system, a distinction is made between an oscillation case , a creep case and the aperiodic borderline case in between , but which also exhibits creeping behavior. An oscillation is only possible at all if the damping is sufficiently weak. For the mathematical representation, reference is made to the main articles.

In the differential equation of oscillation, damping can be seen in the fact that a term appears with the first derivative of the dependent variable . In the case of mechanical processes, this derivation stands for the speed, the term for the influence of friction .

Weakly damped oscillation with an exponentially decreasing limit

With weak damping, the natural angular frequency of the oscillation is lower than its value with undamped oscillation. The amplitude decays in an exponential relationship with time, so that the oscillation through ${\ displaystyle \ omega _ {d}}$${\ displaystyle \ omega _ {0}}$

${\ displaystyle y = {\ hat {y}} \ \ mathrm {e} ^ {- \ delta t} \ sin \ omega _ {d} t}$

is writable. Here is called the decay coefficient with . ${\ displaystyle \ delta}$ ${\ displaystyle \ delta> 0}$

An oscillating system with a low degree of damping or high quality can be operated undamped as an oscillator by a constant supply of energy (e.g. under mechanical or electrical voltage) . When excited with an alternating quantity, resonance is possible. By inhibition or by dependent on the deflection (non-linear) damping necessary to prevent the system that builds up until the destruction ( resonance catastrophe ).

### Examples of attenuation

#### mechanics

• A vibrating string emits energy through the body of a musical instrument, preferably through the propagation of sound .
• Vibrations in the chassis of vehicles are weakened by shock absorbers ; these become hot when driving fast on bumpy roads. The damping comes about through friction brakes, for example through flow resistance due to viscosity when oil is pushed through narrow nozzles. For further possibilities see also under vibration damper .

#### Electrical engineering

Setting in the aperiodic limit case
Damped oscillating setting
A system that can oscillate comes into its rest position the fastest in the aperiodic borderline case. The most favorable damping to get safely into a rest position, however, is a lower damping, so that an overshoot occurs, whereby the oscillation quickly drops to a narrow range. This settling is particularly useful when static friction is to be expected. For commercially available electromechanical measuring devices, an overshoot of up to 20% of the scale length is permitted with a display change of von of the scale length.

## Stationary processes

### Basis, parameters

Here, too, there is the undesirable and the desired damping. The latter requires an attenuator .

One specifies for components, transmission paths and systems

• the damping factor ${\ displaystyle D = {\ frac {X} {Y}} = {\ frac {1} {V}}}$
where = input variable, = output variable, = transfer or gain factor .${\ displaystyle X}$${\ displaystyle Y}$${\ displaystyle V}$
• the logarithmic attenuation ,${\ displaystyle a = \ ln | D | {\ text {Np}} = 20 \; \ lg | D | {\ text {dB}}}$
when the input and output variables are of the same type on which the power depends on the square.

Of the (possibly complex) quantities and , the one whose magnitude is greater than one is used; thus the amount always has a positive logarithm. ${\ displaystyle D}$${\ displaystyle V}$

### Examples of attenuation

#### Electrical engineering

• Electromagnetic waves that penetrate matter are subject to dielectric absorption when permanent electrical dipoles in the dielectric are aligned by polarization . This absorption leads to a conversion of energy from the alternating field into heat - both intentionally for dielectric heating and unintentionally on the transmission paths of communications technology. The possible range is limited by the attenuation without amplification.
• Wanted attenuators are also referred to as attenuators. In addition to components that should be frequency-independent over as broad a range as possible, specific frequency-dependent elements such as high-pass or low-pass are used.
• The shielding is a technical measure to protect against electrical, magnetic and electromagnetic fields . Their effectiveness is quantified by the shielding attenuation .

For the attenuation of electromagnetic radiation when passing through the earth's atmosphere, see Atmospheric window .

#### optics

The decadic or natural logarithm is also common for designation in optics,

#### Acoustics

Different types of sound absorption can occur during sound propagation :

#### mechanics

In machine and vehicle construction and in structural dynamics , increased internal damping of the materials used ("material damping ") is often desirable in order to reduce vibrations .

## literature

• Dieter Meschede: Gerthsen Physics. 23rd edition, Springer-Verlag, Berlin / Heidelberg / New York 2006, ISBN 978-3-540-25421-8
• Jürgen Detlefsen, Uwe Siart: Basics of high frequency technology. 2nd edition, Oldenbourg Verlag, Munich / Vienna 2006, ISBN 3-486-57866-9
• Herbert Zwaraber: Practical setup and testing of antenna systems. 9th edition, Dr. Alfred Hüthig Verlag, Heidelberg 1989, ISBN 3-7785-1807-0
• Gregor Häberle, Heinz Häberle, Thomas Kleiber: Expertise in radio, television and radio electronics. 3. Edition. Verlag Europa-Lehrmittel, Haan-Gruiten 1996, ISBN 3-8085-3263-7