8_Modal analysis(2)

I didn't finish the previous post because I felt like needed to study more about mechanical vibration.

 

In fact, it's still obviously not perfect, but I'm going to use what I've learned, so there will be some errors.

 

In the previous post, I mistakenly wrote the formula for the first natural frequency as a circle.

 

First natural frequency formula for beam is

 

where $L$ is length, $E$ is young's modulus, $I$ is moment of inertia and $m$ is mass

analytic solution is 24.05Hz

 

FEA Calculations with COMSOL Multiphysics

 

Run - COMSOL - 2D - Beam - Add - Study

Preset Studies for Selected Physics Interfaces - Eigenfrequency - Done

 

Right-click the Geometry - More Premitives - Polygon

Create four points : (0, 0), (0.925, 0), (3.625, 0), (4.55, 0)

 

Beam - Linear Elastic Material

Young's modulus : 210e9

Poisson's ratio : 0.28

Density : 1.519e4

 

Beam - Cross Section Data

Section type : Rectangle

y : 0.13

z : 0.08

 

in problem, we have two constraint that pin and roller 

Right-click the Beam - More Constraints - Pinned

select the left node(0.925, 0)

 

Right-click the Beam - Prescribed Displacement/Rotation

Displacement in y direction : Prescribed : 0

 

Mesh

Elemment size : Fine

 

Study - Compute

the Eigenfrequency in the Mode shape in Results.

Eigenfrequency

shape

 

Analycis solution : 24.05

COMSOL : 23.64

error : 1.7%

 

And, do the same process using HyperMesh.

Explain the important part.

 

Beam section

Section Type : BAR

 

When setting constraints, the entire node is constrained to have only planar motion by constraining dofs 3, 4, and 5, and then additional pin and roller constraints are set.

 

Create - Load Collector

name : EIGRL

Card Image : EIGRL

ND : 1

 

Create - Load Step

Analysis type : Normal Modes

SPC : spc

METHOD(STRUCT) : EIGRL

 

shape

Analycis solution : 24.05

HyperMesh : 23.59

error : 1.9%