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#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
Damping
Changing c
is very difficult and not much is understood. The most difficult and the most effective way of damping. (example : see Viscoelasticity 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