29.1 VIBRATION MODELLING
· The most significant vibration in engineered systems is periodic. In these systems there is often an approximate spring-mass-damper system that gives us a second order response to disturbances.
· In vibration modeling we typically assume that all components are linear. In a linear system the forcing (input) frequencies are directly related to response (output) frequencies.
· In non-linear vibration systems we end up with the frequency of the forcing function being transformed to other frequencies. This tends to make the vibrations seem less clear, and appear more chaotic.
· There are a few types of descriptive terms for these systems,
-
Damping Factor - The damping factor will indicate if vibrations will tend to die off. If the damping factor is too low the vibrations may build continually until failure.
-
Forced Vibration - When a periodic excitation is applied to these systems they will tend to show a steady state response
-
Free Vibration - When displaced/disturbed and released there is an oscillation at a natural frequency for any system. This is one measure of a system, and is typically induced by displacing a system and letting it go.
-
Natural Frequency - Each system will have one or more frequencies that it will prefer to vibrate at. When we excite a system at a natural frequency the system will resonate, and the response will become the greatest.
-
Response - This is a measure of how a system behaves when it is disturbed. For example, this could be measured by looking at the position of a point on a mechanism.
-
Steady State Response - After a system settles down it will assume a regular periodic response, this is steady state. The steady state excludes the transient.
-
Transient Response - When a forcing function on a system changes, there will be a short lived response that tends to be somewhat irregular. The transient will eventually die off, and the system will settle out to a steady state.
· These systems can be modeled a number of ways, but we typically start with a differential equation.
