Page 30 - Shock and Vibration Overview
P. 30
Analysis Overview
resources out there that can provide more information on free vibration of single
degree of freedom systems.
Table 1: Equations for a Single Degree of Freedom System
Equation Description
̈ + ̇ + = () Differential equation of motion
= √ Natural frequency as radians per second
1
= = √ Natural frequency as hertz
2 2
= Damping ratio
2√
1
= Quality factor
2
To understand why a vibration test engineer cares about these parameters, let’s take a
look at a transmissibility plot shown in Figure 15. Transmissibility looks at how a SDOF
system responds to a base excitation with a given damping and natural frequency.
When the excitation frequency is much larger than the system’s natural frequency, the
system isolates that base vibration. When the system’s natural frequency is much larger
than the base excitation frequency the system will neither amplify nor dampen an input
vibration. The worst case scenario is when the input frequency is equal to the system’s
natural frequency which will amplify that input by a factor approximately equal to Q.
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