Free Vibration Of a Two_DOF System

6.1 Objective

To find the natural frequencies of a two degrees-of-freedom (DOF) system, and the phase differences between the masses in the system in different modes of vibration. In the present case, free transverse vibrations of a simply supported beam carrying two discs is considered.


6.2  Basic definitions

Free vibration takes place when a system oscillates under the action of forces inherent in the system itself due to initial disturbance, and when the externally applied forces are absent. The system under free vibration will vibrate at one or more of its natural frequencies, in which the lowest natural frequency is called the Fundamental Natural Frequency. Depending upon the initial disturbance on the system, it may vibrate at one or more of its natural frequencies.

In reality, a signal can be a combination of different frequencies. This includes the required frequency range and some unwanted frequency which comes inadvertently such as from noise, the line frequency, etc. To remove these unwanted signals and to get only the relevant signal, filters (analog or digital) are used. This process is called filtering. There are different types of filters.


6.2.3 Types of filters:

1.  Low-pass filter - It allows low frequencies to pass and attenuates higher frequencies.

2.  High-pass filter - It allows higher frequencies to pass and attenuates lower frequencies.

3.  Band-pass filter - It allows frequencies those are within the frequency band.

4.  Band-stop filter - It attenuates the frequencies those are within the frequency band.


6.2.4 Cut off frequency: The filter will attenuate the frequencies those are beyond this cut off frequency.