51 lines
1.9 KiB
Markdown
51 lines
1.9 KiB
Markdown
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#SMMS
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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.
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## Instability VS Resonance :
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Instability is when the response diverges (often leading to failure).
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Whereas Resonance is when the response is amplified (but stays bounded). Resonance rarely cause failure, but it has a significant impact on fatigue.
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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.
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## Vibration
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The vibration of a system is the transfer of kinetic energy (from the mass) to potential energy (from the stiffness), back and forth.
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## The m-c-k system
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(detailed in [[Accelerance]])
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![[m-c-k system]]
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The force in a dynamic system depends on time, and in the studies is modeled with a periodic sine wave :
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$$F(t) = F_0sin(\Omega t)$$
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With $\Omega (rad.s^{-1})$.
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$$m\ddot{x}+c\dot{x}+kx=F_0sin(\Omega t)$$
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with $x$ depending on time
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Frequency Response Function (FRF) (with $\omega_0 = \sqrt{\frac{k}{m}}$ )
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![[FRF (linear)]]
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# Non-linear dynamics
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(see [[Structural dynamics (non-linear)]])
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# Damping
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There are 4 ways to damp a structures :
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### Stiffening
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$k$ increases so $\omega_0$ increases as well, so the system does not resonate at the same $\omega_0$ anymore.
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### Filter
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![[dynamic filter]]
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Used to decrease $\omega_0$ and isolate further the system and its environment (both ways).
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### Sub-System
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![[dynamic subsystem]]
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### Damping
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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).
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It directly affect the amplitude of the curve (and can decrease a bit $\omega_0$)
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![[damping]]
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# Exams
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- bring paper sheets
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- documents authorized
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- evaluates thinking, not calculus
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