51 lines
1.9 KiB
Markdown
51 lines
1.9 KiB
Markdown
#SMMS
|
|
|
|
The study of how things behave when under a **dynamic load**. A dynamic load is one which changes with time fairly quickly in comparison to the structure's natural frequency.
|
|
|
|
## Instability VS Resonance :
|
|
|
|
Instability is when the response diverges (often leading to failure).
|
|
|
|
Whereas Resonance is when the response is amplified (but stays bounded). Resonance rarely cause failure, but it has a significant impact on fatigue.
|
|
|
|
As a rule of thumb, vibrations half the lifetime of structures, and it means inconfort for the payload. The payload being another contraption or a human, which leads to physical issues.
|
|
|
|
## Vibration
|
|
The vibration of a system is the transfer of kinetic energy (from the mass) to potential energy (from the stiffness), back and forth.
|
|
|
|
|
|
## The m-c-k system
|
|
(detailed in [[Accelerance]])
|
|
![[m-c-k system]]
|
|
|
|
The force in a dynamic system depends on time, and in the studies is modeled with a periodic sine wave :
|
|
$$F(t) = F_0sin(\Omega t)$$
|
|
With $\Omega (rad.s^{-1})$.
|
|
$$m\ddot{x}+c\dot{x}+kx=F_0sin(\Omega t)$$
|
|
with $x$ depending on time
|
|
|
|
Frequency Response Function (FRF) (with $\omega_0 = \sqrt{\frac{k}{m}}$ )
|
|
![[FRF (linear)]]
|
|
|
|
# Non-linear dynamics
|
|
(see [[Structural dynamics (non-linear)]])
|
|
|
|
# Damping
|
|
|
|
There are 4 ways to damp a structures :
|
|
### Stiffening
|
|
$k$ increases so $\omega_0$ increases as well, so the system does not resonate at the same $\omega_0$ anymore.
|
|
### Filter
|
|
![[dynamic filter]]
|
|
Used to decrease $\omega_0$ and isolate further the system and its environment (both ways).
|
|
### Sub-System
|
|
![[dynamic subsystem]]
|
|
### Damping
|
|
Changing $c$ is very difficult and not much is understood. The most difficult and the most effective way of damping. (example : see [[Viscoelasticity|viscoelastic]] materials).
|
|
It directly affect the amplitude of the curve (and can decrease a bit $\omega_0$)
|
|
![[damping]]
|
|
|
|
# Exams
|
|
- bring paper sheets
|
|
- documents authorized
|
|
- evaluates thinking, not calculus |