(c) Euler-Bernoulli beam theory can also be used to determine the theoretical mode shapesassociated with these natural frequencies. As a self-directed study, you should investigate therelevant equations to describe the mode shapes associated with these natural frequenciesand 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 frequenciesand their associated transverse mode shapes for the cantilever beam.Assume the beam is in a fixed-free constrained condition. You should also utilise thefollowing information:E-Young's modulus for mild steel = 210GPap - the density for the beam, for mild steel = 7850Kgm-³(f) Compare the experimental, Theoretical and FE results showing the relationship between eachset 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 anyrecommendation on how to improve the results.(h) Draw together the most important results and their significances 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 frequency011@d2@d3wn = azExperimentally measuredvalue (Hz)12.0290.84214.7Deliverable(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.EIPALA(b) Research Euler-Bernoulli beam theory and utilising the physical measurements of thecantilever beam. Calculate the first three natural frequencies of your experimental systemusing Euler Bernoulli beam theory.Theoretical details:The fixed-free cantilever beam system is an example of a continuous distribution of mass systemand can have many natural frequencies. Euler Bernoulli beam theory yields a formula tocalculate the natural frequencies of your experimental system.Node, distance from fixed endof the beam (m)E-Young's modulus for mild steel = 210GPaL-Length of the beamA- the cross-sectional area of the beamp - the density for the beam, for mild steel = 7850Kgm-³an - is a constant, for a fixed-free beamWhere I is the second moment of area [2]1=bd²b-breadth of the beamd-depth of the beam0.3350.187, 0.350a₁ = 1.875 a₂ = 4.694 a3 = 7.855

Euler-Bernoulli beam theory can also be used to determine the theoretical mode shapes associated…

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 edo chaper for the cantilever heam

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 edo chaper for the cantilever heam

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

(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

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

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