Mechanical Vibrations - MECH 315. In this project, a structural I-Beam was analyzed in order to find it's natural frequencies and modes. The analysis was performed using the the FEA software ABAQUS.

1. 1
Finite Element Analysis and Natural Modes Investigation
MECH 315: Mechanics 3
McGill University
Monday, April 16th,
2018
Gregory Labelle ─ 260684471
Stasik Nemirovsky ─ 260660024
Laurence Sirard ─ 260640295
Submitted to:
Christopher Agellon

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Table of Contents
Introduction........................................................................................................................................... 3
Section 1................................................................................................................................................ 3
Section 2................................................................................................................................................ 3
Section 3................................................................................................................................................ 4
Conclusion .......................................................................................................................................... 13

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Introduction
Mechanical vibrations are present everywhere around us; in the houses we live in, the vehicles we
drive and in most if not all objects we use on a daily basis. Therefore, it is essential for one to
understand the effects and challenges associated with these vibrations, as well as how to mitigate the
risks that may lead to failure. This is especially important for mechanical engineers when designing
machinery, structural components or any other products. The objective of this project was to analyze
the natural modes of a meaningful object or system from our daily life. In this report, the chosen
object is a steel “I” beam. An “I” beam is a structural beam that is very commonly used in
construction of large buildings and industrial plants, which makes it an object of high interest to
mechanical and civil engineers.

4. 4
Section 1
As can be seen in Figure 1, the structure under consideration
is an I beam of 0.2m width, 0.02m web thickness, 0.6m depth
and 0.1m flange thickness. There is no fillet, so all angles are
90°. The length of the whole I-beam is 20m and its boundary
conditions are identical at both ends by being fixed to a wall.
The chosen material is steel with a uniform density of 7850
kg/m2
along the beam. The material used is isotropic which mean the material properties are the same
in all directions. The beam can be deformed both elastically or plastically. Young’s Modulus is 190
GPa with a Poisson Ratio of 0.3 and the yield stress is 210 MPa with zero plastic strain. A permanent
load of 1000Pa is applied to the beam to simulate the weight of a floor.
Figure 1: Geometric model

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Section 2
As described above, the structure that was tested is an I-beam. The first step was to create the 1D
structure of the I-beam in a sketch an extrude it. Then the material had to be set. It was assumed that
the beam was made of steel. Elastic and plastic properties of steel were included so that we would get
frequencies as close to reality as possible. The load was then applied to the beam by specifying a
pressure load. Usually, in class, the load is given as a point force but in this case, the force has
already been transformed into a stress. A frequency is added to the load so that we can find the
modes of vibration and not just the static displacement of the beam under the applied pressure. The
boundary conditions are then specified so that the structure can be modeled as a beam encased
between two walls. In terms of the software input, this means that the linear and angular
displacement of the surface of the extremities of the beam (where the beam touched the walls) are
zero. There will be reaction forces and moments to make sure the boundary conditions are respected;
setting the boundary conditions or making the displacement zero is equivalent to adding reaction
moments and forces. The mesh for the beam is then created. On ABAQUS, only 1000 elements can
be modeled on the student version, so the shape functions were chosen to be linear to maximize the
amount of elements relative to the nodes. The increase in precision of the quadratic shape functions
does not outweigh the decrease in amounts of nodes that this operation would cause. Finally, the file
was submitted to ABAQUS’ job analysis and the results were obtained from it.

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Section 3
Figure 2: Material Density

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Figure 3: Elastic Properties

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Figure 4: Plastic Properties

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Figure 5: Natural Modes and Frequencies

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Figure 6: 1st Natural Mode

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Figure 7: 2nd Natural Mode

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Figure 8: 3rd Natural Mode

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Figure 9: 4th Natural Mode

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Figure 10: 5th Natural Mode
Conclusion
As stated in the project’s objective, the natural modes of a structural I-Beam were successfully found,
using the software ABAQUS. By inputting a geometric model, relevant material properties and
optimizing the constructed mesh, the first 10 natural modes of a 20ft steel I-Beam were discovered
and 5 of them were graphically displayed. These results are highly valuable to anyone designing
structural supports using I-Beams, as it provides clear guidelines of frequencies to avoid. It is within
the documented history that large bridges collapsed due to faulty designs. Taking into account
vibration analysis considerations is not only a privilege we have as engineers in the 21st
century, it is
our responsibility.