(d) Describe the methodology of finite element model of the cantilever beam using SolidWorks.
(d) Describe the methodology of finite element model of the cantilever beam using SolidWorks.
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Only do D
the natural frequencies are w1 = 0.493Hz, w2 = 3.08Hz, w 3 = 8.63Hz the question is C
![Pre-measured experimental data:
Using the experimental data given below, complete the lab report as detailed in the deliverable.
Beam dimensions - breadth=0.0254m, depth=0.0032m, length=0.410m.
Damped natural frequency
011
@d2
@d3
wn = az
Experimentally measured
value (Hz)
12.02
90.84
214.7
Deliverable
(a) Mathematical modelling of the cantilever beam: Theoretically model the cantilever beam,
using the physical measurements of the cantilever beam, as one degree of freedom system.
Calculate the first natural frequency of the beam.
EI
PALA
(b) Research Euler-Bernoulli beam theory and utilising the physical measurements of the
cantilever beam. Calculate the first three natural frequencies of your experimental system
using Euler Bernoulli beam theory.
Theoretical details:
The fixed-free cantilever beam system is an example of a continuous distribution of mass system
and can have many natural frequencies. Euler Bernoulli beam theory yields a formula to
calculate the natural frequencies of your experimental system.
Node, distance from fixed end
of the beam (m)
E-Young's modulus for mild steel = 210GPa
L-Length of the beam
A- the cross-sectional area of the beam
p - the density for the beam, for mild steel = 7850Kgm-³
an - is a constant, for a fixed-free beam
Where I is the second moment of area [2]
1=bd²
b-breadth of the beam
d-depth of the beam
0.335
0.187, 0.350
a₁ = 1.875 a₂ = 4.694 a3 = 7.855](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3439725b-3e6e-42dc-b1ea-4b06aba6a92e%2Fa57cf66d-0308-48a2-8fda-6c8bfc0ac925%2F1mml3f_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Pre-measured experimental data:
Using the experimental data given below, complete the lab report as detailed in the deliverable.
Beam dimensions - breadth=0.0254m, depth=0.0032m, length=0.410m.
Damped natural frequency
011
@d2
@d3
wn = az
Experimentally measured
value (Hz)
12.02
90.84
214.7
Deliverable
(a) Mathematical modelling of the cantilever beam: Theoretically model the cantilever beam,
using the physical measurements of the cantilever beam, as one degree of freedom system.
Calculate the first natural frequency of the beam.
EI
PALA
(b) Research Euler-Bernoulli beam theory and utilising the physical measurements of the
cantilever beam. Calculate the first three natural frequencies of your experimental system
using Euler Bernoulli beam theory.
Theoretical details:
The fixed-free cantilever beam system is an example of a continuous distribution of mass system
and can have many natural frequencies. Euler Bernoulli beam theory yields a formula to
calculate the natural frequencies of your experimental system.
Node, distance from fixed end
of the beam (m)
E-Young's modulus for mild steel = 210GPa
L-Length of the beam
A- the cross-sectional area of the beam
p - the density for the beam, for mild steel = 7850Kgm-³
an - is a constant, for a fixed-free beam
Where I is the second moment of area [2]
1=bd²
b-breadth of the beam
d-depth of the beam
0.335
0.187, 0.350
a₁ = 1.875 a₂ = 4.694 a3 = 7.855
Transcribed Image Text:(c) Euler-Bernoulli beam theory can also be used to determine the theoretical mode shapes
associated with these natural frequencies. As a self-directed study, you should investigate the
relevant equations to describe the mode shapes associated with these natural frequencies
and calculate the first three mode shapes (shape of the cantilever beam as it vibrates)
associated with each of these natural frequencies.
(d) Describe the methodology of finite element model of the cantilever beam using SolidWorks.
(e) Model the cantilever beam using SolidWorks and extract the first three natural frequencies
and their associated transverse mode shapes for the cantilever beam.
Assume the beam is in a fixed-free constrained condition. You should also utilise the
following information:
E-Young's modulus for mild steel = 210GPa
p - the density for the beam, for mild steel = 7850Kgm-³
(f) Compare the experimental, Theoretical and FE results showing the relationship between each
set of results - experimental, theoretical and FE method. (Be clear and concise).
(g) Discuss the accuracy and precision of your results. Discuss any errors, limitation and any
recommendation on how to improve the results.
(h) Draw together the most important results and their significances
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