eigenvalue problem

Numerical methods and mathematical models of Elmer
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sage12
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Joined: 19 Sep 2018, 06:39
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eigenvalue problem

Post by sage12 » 19 Sep 2018, 06:40

Hi everyone,
i'm using the following unit system:

geometry: mm
material density: g/mm^3
young modulus: Pa


This is my sif file:

-----------------------------------------------------------------
Header
CHECK KEYWORDS Warn
Mesh DB "." "."
Include Path ""
Results Directory ""
End

Simulation
Max Output Level = 4
Coordinate System = Cartesian
Coordinate Mapping(3) = 1 2 3
Simulation Type = Steady state
Steady State Max Iterations = 1
Output Intervals = 1
Timestepping Method = BDF
BDF Order = 1
Solver Input File = case.sif
Post File = case.ep
End

Constants
Gravity(4) = 0 -1 0 9.82
Stefan Boltzmann = 5.67e-08
Permittivity of Vacuum = 8.8542e-12
Boltzmann Constant = 1.3807e-23
Unit Charge = 1.602e-19
End

Body 1
Target Bodies(1) = 1
Name = "Body 1"
Equation = 1
Material = 1
End

Solver 1
Equation = Linear elasticity
Eigen System Values = 10
Procedure = "StressSolve" "StressSolver"
Variable = -dofs 3 Displacement
Eigen System Select = Smallest magnitude
Eigen Analysis = True
Exec Solver = Always
Stabilize = True
Bubbles = False
Lumped Mass Matrix = False
Optimize Bandwidth = True
Steady State Convergence Tolerance = 1.0e-5
Nonlinear System Convergence Tolerance = 1.0e-7
Nonlinear System Max Iterations = 20
Nonlinear System Newton After Iterations = 3
Nonlinear System Newton After Tolerance = 1.0e-3
Nonlinear System Relaxation Factor = 1
Linear System Solver = Direct
Linear System Direct Method = Umfpack
End

Equation 1
Name = "Equation 1"
Active Solvers(1) = 1
End

Material 1
Name = "Material 1"
Density = 0.0028
Poisson ratio = 0.33
Youngs modulus = 73e9
End

Boundary Condition 1
Target Boundaries(1) = 10
Name = "vincoli"
Displacement 3 = 0
Displacement 2 = 0
Displacement 1 = 0
End

Boundary Condition 2
Target Boundaries(1) = 28
Name = "vincoli"
Displacement 3 = 0
Displacement 2 = 0
Displacement 1 = 0
End

---------------------------------------------------------------

Do the eigenvalues coming out from solver in Hz^2 unit?
so for the first frequency in hertz do i have to make the sqrt of the first eigenvalue?

because i found the first eigenvalue : 105500425.49 that correspond to 10271 Hertz. it is too high...where i'm wrong?

thank you

raback
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Re: eigenvalue problem

Post by raback » 24 Sep 2018, 13:23

Hi

The eigenvalue is c=w^2=(2pi*f)^2. Hence the frequency is sqrt(c)/(2*pi).

-Peter

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