(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) ModelthecantileverbeamusingSolidWorksandextractthefirstthreenaturalfrequenciesand 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?? - the density for the beam, for mild steel = 7850Kgm(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 significancesOnly Do F 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 frequencyU11@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 [1] 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, 0.350[1]a₁ = 1.875 a₂ = 4.694 a3 = 7.855[2] Task DescriptionUse the lab details below and the table of results to complete the assignment. You are provided withthe pre-measured experimental data.Background:Systems that oscillate continuously tend to be problematic for engineers. These vibrations can lead toloss of function in electronic components, failure due to fatigue, discomfort and long-term healthproblems such as vibration white finger. It is important to factor a vibration analysis into the designprocess, particularly when designing components that mount near or on vibrating parts such asmotors or engines.Relevant Theory:This theory requires the beam to be represented as a lumped mass with equivalents stiffness/dampingmodel as shown below.OscilloscopeBeamShakerChargeAmplifierAccelerometerThe shaker transmits a constant sinusoidaly varying force into the beam. The amplitude of this forceis set by the signal generator and should remain fixed at all times. The frequency of the force is alsoset by the signal generator and can be varied during the experiment. The vibrations are measured bythe accelerometer. This reading can be integrated electronically by the charge amplifier to givevelocity or position measurements.Experimental Methods - identifying natural Frequencies and mode shapes:Frequency sweep can be performed using the signal generator to identify the first three "modal"frequencies where the amplitudes of vibration increased significantly. The shape of the beam at eachfrequency can be defined by plotting a sinusoid curve through the "nodes" (where there is nomovement) and the "peaks".

Experimental Results : Experimental results of natural frequencies are given in pre-measured dats of…

Answered: (d) Describe the methodology of finite…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

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(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) ModelthecantileverbeamusingSolidWorksandextractthefirstthreenaturalfrequencies
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
?? - the density for the beam, for mild steel = 7850Kgm
(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

Only Do F

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
U11
@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 [1] 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
[1]
a₁ = 1.875 a₂ = 4.694 a3 = 7.855
[2]

Task Description
Use the lab details below and the table of results to complete the assignment. You are provided with
the pre-measured experimental data.
Background:
Systems that oscillate continuously tend to be problematic for engineers. These vibrations can lead to
loss of function in electronic components, failure due to fatigue, discomfort and long-term health
problems such as vibration white finger. It is important to factor a vibration analysis into the design
process, particularly when designing components that mount near or on vibrating parts such as
motors or engines.
Relevant Theory:
This theory requires the beam to be represented as a lumped mass with equivalents stiffness/damping
model as shown below.
Oscilloscope
Beam
Shaker
Charge
Amplifier
Accelerometer
The shaker transmits a constant sinusoidaly varying force into the beam. The amplitude of this force
is set by the signal generator and should remain fixed at all times. The frequency of the force is also
set by the signal generator and can be varied during the experiment. The vibrations are measured by
the accelerometer. This reading can be integrated electronically by the charge amplifier to give
velocity or position measurements.
Experimental Methods - identifying natural Frequencies and mode shapes:
Frequency sweep can be performed using the signal generator to identify the first three "modal"
frequencies where the amplitudes of vibration increased significantly. The shape of the beam at each
frequency can be defined by plotting a sinusoid curve through the "nodes" (where there is no
movement) and the "peaks".

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