Vibration for 1 degree of freedom systems Flashcards
What is the equation for elastic force and from a mass, and elastic potnential and kinetic energy? What are assumptions we often make in spring systems?
What objects can represent a spring?
Note:
* Mass (inertia) and springs (elasticity) is what often cause vibrations.
* Damping is also involved. However it will be mentioned on its own here as only mass and springs are required for vibrations, really. Damping effect vibrations.
What happens when a Mass-spring system undergoes Simple harmonic motion (SHM)?
What is the equation for damping force and what are its assumptions?
What are ‘lumped parameter’ models of mass-spring systems?
- Complex models can be simpliefed as such below using these assumptions
For a spring and damper in paralell, what is the displacement and force relationship like?
Try name as many equivalent springs as possible!
What is a single degree of freedome system, SDFS?
where there is only one direction of motion. i.e., up and down, side to side.
What is the equation for displacement for an undamped free vibration?
Try deriving it! What does each bit mean?
What is the equation for natural frequency and time period of an undamped free vibration?
How is energy conserved in an undamped free vibration?
What is the equation for displacement for an damped free vibration?
Try deriving it! What does each bit mean?
Note:
* damped frequency is often less than natural frequency.
* The final equation uses natural frequency and damped frequency. (natural frequency is to the power of e.
For an initial displacement, with no velocity for a free vibrating damped system, what is the equation?
What does it mean.
It describes the envelope that shows the dampening effect. See how it should in theory never reach zero. However, this is a limitation of modelling reality.
What does the graph for a critically damped response for free vibrations look like for initial displacement and velocity?
What is the logarithmic decrement equation?
state it and how it works
What is the response to a force on a SDOF system (or forced vibrating)?
What is the frequency response function, FRF, equation?
Try deriving it! To do with SDOF systems
What are the three categories, which note the dominant effect on a forced vibration system? What condition is required for them to be in that category?
What are the effects of damping on rensonance?
What is the equation that describes the force on an unbalanced rotating system?
Note: this force can cause SHM motion, which then can mean we can determine its displacement as a result, using Frequency Response Function, X/F.
