7_Modal analysis

 

Modal analysis is a method for analyzing the vibration characteristics of a system.

Modal analysis can reveal important characteristics of a system, such as natural frequencies and mode shapes.

With this information, it is important to predict whether the structure is resonant and how it will deform under vibration.

 

simple mass spring damper model

where $m$ is mass, $c$ is damping coefficient, $k$ is spring constant, $x(t)$ is external force, and $f(t)$ is displacement.

motion equation

Motion equation for a single degree of freedom system with no damping and no external loads are as follows

Single degree of freedom system means that a single object moves in only one direction.

 

Also, motion equation for a multi degree of freedom system with no damping and no external loads are as follows.

 

To use Hypermesh to solve a simple natural frequency problem.

 

Geometric information

L : 4550mm

I : 2700mm

material : alloy steel

E : 210 GPa

v : 0.28

density : 1.519e-5 kg/mm^3

cross section : 80mm*130mm (rectangle)

where $I$ is moment of inertia, $K$ is stiffness

 

Hmm.... I don't think I understand mechanical vibration well enough, so I'll have to study the rest of this in a future post.