MME3360b
Assignment 03
10% of final mark
Due date:
March 19, 2012
Five problems each worth 20% of assignment mark
1
PROBLEM 1
For the assembly of 1D springs shown below determine eigenvalues, eigenvectors, natural frequencies
and vibration periods for all mode present in the model. Use direct stiffness method.
Node 1
Node 2
k1
Node 3
k2
Node 4
k3
x
k4
Horizontal lines denote 1D springs
Nodes 1 and 4 are fixed
Nodes 2 and 3 can move only in x direction
All nodes have mass 1kg
Spring stiffness k1 = k2 = k3 = k4 = 1000N/mm
Make your own 1kg mass and build an assembly; confirm results with SolidWorks Simulation
Save model as problem 01.SLDASM
2
PROBLEM 1
Paper part
Solution with Direct Stiffness Method:
Calculate f1 and corresponding d2/d3
Calculate f2 and corresponding d2/d3
Screen shots of results showing probed displacements d2 and d3 for frequencies f1 and f2
This will be a confirmation of hand calculations
Electronic part
Assembly problem 01.SLDASM complete with frequency study ready to run.
Make sure you have included all parts.
3
PROBLEM 2
Download 2DOF torsion.sldasm from course web site and save as problem02.sldpasm.
Treat the system as 2DOF torsional vibration system by applying proper restraints. Find natural frequencies
and modes of vibration. Assume that the two large cylinders do not contribute to torsional stiffness.
Confirm results with SW solution as in problem 1. Find all input data from the SW assembly.
1
2
3
Fixed restraint
2DOFtorsional.sldasm
4
PROBLEM 2
Paper part
Solution with Direct Stiffness Method:
Calculate f1 and corresponding φ2/φ 3
Calculate f2 and corresponding φ2/φ3
Electronic part
Assembly problem 02.SLDPRT complete with frequency study ready to run.
Screen shots of results showing probed displacements φ2 and φ3 for frequencies f1 and f2
Probe here
Probe here
5
PROBLEM 2
mr
I
2
2
Mass moment of inertia of a
cylinder about its axis
J
d
4
32
Polar moment of inertia
of a circular cross section
T
GJ


l
Torsional stiffness
E
G
2(1   )
Shear modulus
6
PROBLEM 3
Fixed
restraint
1000N
load normal
to end face
I BEAM.SLDPRT- chapter 12
7
PROBLEM 3
Complete the following studies in SW Simulation
Study 01 – original configuration
Find FOS
yield
Study 02 – original configuration
Find FOS
buckling
Based on the results of Study 01 and Study 02 propose a field repair to make sure that FOS
buckling
> FOS yield
Create the field repair in a new configuration and run two more studies:
Study 03 – field repair configuration
Find FOS
yield
Study 04 – field repair configuration
Find FOS
buckling
Save it as problem03.SLDPRT
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PROBLEM 3
Paper part
Summary of all results, explanation of field repair design.
Electronic part
Part problem03.SLDPRT with two configurations and four studies ready to run.
Include von MIses stress plots, FOS plots and deformed buckling shape plots (not displacements plots) where
applicable.
.
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PROBLEM 4
y
1
600mm
Element 1
2
F= 1000N
x
k
Element 2
3
4
200mm
E
AISI 1020
Spring stiffness
k = 150000N/m
Beam cross section (both beams)
50mm x 20mm
Paper part
Using direct stiffness method calculate nodal displacements and reactions.
Construct graph showing transverse displacements of element 1 in the coordinate system shown above
Screen print of SW displacement results.
Electronic part:
Make your own SW model to confirm result, make comparison for node 2 only. For SW model use
Save model “ready to run” as problem04.SLDASM
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PROBLEM 5
y
1
2
Moment
50Nm
Fixed
support
Hinge
support
E
ABS
Geometry
link02.sldprt (chapter 15) – delete split line from SW model
Paper part
Using direct stiffness method to calculate nodal displacements and reactions.
Find transverse displacement along the element length (see the next slide).
SW plot of DY displacements
Electronic part:
Confirm result with equivalent SW model (make make a plot of DY displacements).
Save model “ready to run” as problem05.SLDPRT
11
PROBLEM 5
The relation between nodal forces and nodal displacements:
x
=
Shape function is defined on nodal displacements so once we know nodal displacements we
can calculate displacement anywhere along the element
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Summary of deliverables
You will have created the following models:
Problem 1
problem 01.SLDASM
Problem 2:
problem 02.SLDPRT
Problem 3:
problem 03.SLDPRT
Problem 4:
problem 04.SLDASM
Problem 5:
problem 05.SLDPRT
All problems have paper parts.
Remember to include all part files necessary for assemblies.
Upload everything to the assignment drop-off box.
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