Damping of Oscillations

Damping of Oscillations


a decrease in intensity of oscillations with time caused by energy losses in the oscilla-tory system. The simplest case of energy loss for an oscillation is the conversion of energy into heat as a result of friction in mechanical systems and of resistance in electrical systems. In electrical systems, damping of oscillations may also be due to the radiation of electromagnetic energy.

The law of damping of oscillations is determined by the nature of the energy loss and other properties of the system. The case that has been studied most thoroughly is the damping of oscillations caused by reduction in energy that is proportional to the square of the motion velocity in a mechanical system or, correspondingly, to the square of the current value in an electrical system; it is valid for linear systems. The law is then exponential—that is, the peak-to-peak values of the oscillations decrease according to the law of a geometric progression (see Figure 1).

Figure 1. Decay of oscillations: (A0) initial amplitude, (T) period

The energy losses in a system that cause damping of oscillations disturb their periodicity, so that the damped oscillations are not a periodic process and, strictly speaking, the concepts of period and frequency are not applicable to them. However, when damping is small, the conditions of the system repeat approximately, so that it is possible arbitrarily to use the concept of a period as the time interval between two successive passages of an oscillating physical quantity (current, voltage, peak-to-peak vibrations of a pendulum, and so on) in the same direction through the maximum value. An evaluation of the relative decrease in the amplitude of the oscillations during a period gives the logarithmic decrement. The damping rate is related to the quality of the oscillatory system.

References in periodicals archive ?
The use of the damping tool system during turning operations and the internal boring of highly precise items allows to guarantee a more efficient dynamic damping of oscillations during the process of machining the work pieces than it was possible before, as the absorption coefficient is raised and oscillations are dampened due to large dissipative forces of the resistance of the material of the tool holder that has a texture with different metal deformation -conditioned orientations.
These oscillations can be modelled by an RLC circuit, where the values of resistance (R), inductance (L), and capacitance (C) determine the frequency and damping of oscillations [19].
The slightly enlarged value of R2 (the resistance of central airways and the device) caused damping of oscillations to a greater extent, as can be seen in Fig.
Damping of oscillations of the deformed solid, Naukova Dumka, Kiev, 1985.
They will contribute to an increase of damping of oscillations of this subsystem, which gives us a possibility to increase the cut-off frequency [[omega].
The diameter of the fibre should be optimal: too thin or too thick fibres do not provide sufficient sensitivity, as thinner fibres are not stiff enough to transfer the vibration energy to the QTF, while in case of thicker fibres there is a high damping of oscillations due to the fluid resistance.