MSR/smms/Structural dynamics (linear).md
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2024-10-15 08:56:10 +02:00

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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

!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 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