Damping ratio
The degree of damping, damping factor or even teaching cal damping ratio, is a measure of the damping of a vibrating system. To him can be read as the system behaves after excitation. As a symbol for the degree of damping is a large common. It is a dimensionless quantity.
- 3.1 Logarithmic decrement
- 3.2 of damping in the acoustic
- 3.3 of damping in electrical engineering
Background
The differential equation for a linear damped oscillator can be brought regardless of the physical background of the vibration system in the following form:
Where:
- : Damping ratio
- : Natural angular frequency of the undamped system
Mechanical Systems
For a spring / mass oscillator, the Lehr's damping calculated as:
Where:
Based on the use of the English language can be the damping ratio as the ratio of damping constant to the critical damping constant understand. that is
In this case, the critical damping constant, the attenuation that is needed to achieve the aperiodic limiting case.
Electrical Systems
For electrical resonant circuits applies:
Here are
The degree of damping is also referred to as damping in this context and is expressed in the auxiliary unit decibels ( dB).
Stability analysis
The degree of damping can be used to characterize the vibration behavior. For this, we consider the solution of the characteristic polynomial of the differential equation:
Now it is different depending on the size of the damping ratio:
- : Unstable - Aufschwingendes system
- : Undamped unstable - continuous oscillation with constant amplitude
- : Damped oscillation (case of weak damping)
- : Aperiodic limit - just no overshoot ( case of critical damping )
- : Aperiodic solution - not vibrating ( asymptotic approximation to the center of oscillation for, Kriechfall )
Other attenuation measurements
Logarithmic decrement
The damping ratio is dimensionless. He describes the vibration behavior of an entire physical system. It is directly related to the logarithmic decrement of the equation:
This size is also found as a logarithmic damping ratio in dB.
Of damping in the acoustic
The damping ratio with the formula sign is when a plane wave, the logarithmic ratio of the amplitudes of a field variable (eg sound pressure ) behind the other two in the direction of sound propagation points; (DIN 1320).
Of damping in electrical engineering
In the electrical behavior of the damping of resonant circuits is given by the quality factor. Between quality factor and damping ratio, the relationship applies: