Mechanics 2: Laboratories
Lab Code
Lab Title
AM2.1a
and
AM2.1b
Free and Forced Vibrations CTL
Engineering
Free and Forced
Vibration
(Undamped and
Damped)
AM2.2
Unsymmetrical Beam
CTL Eng
Bending
Static and Dynamic Balance CTL
Engineering
Mohr’s Circle,
Moment of inertia
AM2.3
Lab Location
Topics
Static and Dynamic
Balancing (For
example in vehicles)
CTL Safety Video

It is CTL policy that before students begin
work in the facility they are required to watch
the CTL Safety Induction video and complete
a short quiz
 Direct link to the course:
https://canvas.bham.ac.uk/courses/70971
 Self-enrolment link (for student use only):
https://canvas.bham.ac.uk/enroll/7WTN4K
 Dress code requirements for CTL
CTL Dress Code
CTL Dress Code
Labs
Requirements
Phase I –Engineering
Lab coats, safety glasses, closed shoes and
covered legs
Wet Lab
Bio lab
Lab coats, covered legs, , closed shoes and
safety glasses (where appropriate)
Dry Lab
Lab coats and closed shoes
Mechanics 2: Laboratories
Equipment: AM2.1: Free and Forced Vibrations
Mechanics 2: Laboratories
Background: AM2.1: Free and Forced Vibrations
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Definition: Vibration is the oscillating motion of a body or system of
connected bodies displaced from a position of equilibrium.
Two types of vibration: Free and forced
Free: occurs when the motion is maintained by gravitational or elastic
resorting forces (e.g. vibration on an elastic rod). Initial disturbance,
system left to vibrate without influence of external forces
Forced: Caused by an external periodic or intermittent force applied to
the system
Both these types of vibration can either be damped or undamped
Undamped: excludes frictional effects (does not occur in reality), no
energy dissipation
Damped: accounts for internal and external frictional forces. Dissipation
of energy occurs- vibration amplitude decays.
References: Hibbeler- Chapter 22 (13th or 14th Edition)
RUSSELL C. HIBBELER, (2017); Engineers Mechanics: Dynamics, Global Edition, 14th Edition
Mechanics 2: Laboratories
Why study vibrations?: AM2.1: Free and Forced Vibrations
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Vibrations definition: oscillating motion of bodies in response to a
disturbance
Oscillations occur due to the presence of a restoring force
Vibrations occur everywhere:
– Human body: Eardrums, walking, running, vocal cords
– Vehicles: residual imbalance of engines, wheels
– Rotating machinery: Turbines, pumps, fans, reciprocating
machines
– Musical instruments
Excessive vibrations can have detrimental effects: fatigue, failure,
noise, loosening etc.
When vibration frequency coincides with the natural frequency,
resonance occurs
𝝎𝒏 =
𝒌
𝒎
Mechanics 2: Laboratories
Fundamentals AM2.1: Free and Forced Vibrations
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A vibratory system involves the transfer of potential
to kinetic energy and vice versa
Where there is a mechanism for dissipating energy
(damping) the oscillation gradually diminishes
A vibratory system consists of three basic
components:
– A means for storing potential energy (spring,
gravity)
– A means for storing kinetic energy (mass,
inertial component)
– A means to dissipate vibrational energy
(damper)
Mechanics 2: Laboratories
Why study vibrations?: AM2.1: Free and Forced Vibrations
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Free vibrations happen in many structures, where the structure vibrates
at its natural frequency. Forced vibrations may occur where an external
force causes the structure to vibrate at any frequency including the
natural frequency of the structure. Where the forced vibration frequency
equals the natural frequency, the structure will resonate at a potentially
dangerous amplitude, damaging the structure. History has several
examples of this problem. These include the collapse of the Tacoma
Narrows Bridge in the US in 1940, and the temporary closure of the
Millennium Bridge in London 2000-2002.
 Designers need to understand how free and forced vibrations affect
structures, the magnitude of the oscillations they can cause and how to
reduce (damp) them. TecQuipment’s Free and Forced Vibrations
(TM1016) uses a metal beam, held as a simply supported beam or
supported by a spring. It shows the magnitudes of oscillations due to
free and forced vibrations in simple structures and how damping affects
their vibrations.
References: TecQuipment User Guide
Mechanics 2: Laboratories
Equipment: AM2.2: Unsymmetrical Beam Bending
References: TecQuipment
User Guide
Mechanics 2: Laboratories
Equipment: AM2.2: Unsymmetrical Beam Bending
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The Unsymmetrical Bending experiment gives
students a visualisation and proof of basic
concepts such as principal second moments of
area and the construction of a Mohr’s Circle.
References: TecQuipment User Guide
Mechanics 2: Laboratories
Equipment: AM2.3: Static and Dynamic Balancing
References: TecQuipment
User Guide
Mechanics 2: Laboratories
Fundamentals AM2.3: Static and Dynamic Balancing
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Many machines use large rotating parts - particularly vehicles. These rotating
parts can create a problem. If they are not well balanced, the imbalanced
centrifugal forces will create vibrations as the part rotates. This may be
acceptable at low rotational velocities but can be harmful or even destructive at
high velocities. Even relatively slow-moving vehicle tyres need careful balancing
or they will cause dangerous vibrations throughout the vehicle suspension and
uneven tyre wear. High speed rotating parts in jet engines must have perfectly
balanced centrifugal forces, or the engine can literally shake itself to pieces
resulting in an immediate and catastrophic engine explosion.
 Simple static balancing may allow engineers to balance the moving part for low
speed operation, but only dynamic balancing will show the more precise
adjustments needed to correct for higher speed operation where centrifugal
forces become important. Therefore, engineers need to know the difference
between static and dynamic balancing, the advantages of each and how to
calculate angles and positions for balance.
 TecQuipment’s Static and Dynamic Balancing (TM1002) uses a motor to turn a
horizontal shaft with adjustable balance blocks. Students use it to learn how to
statically and dynamically balance a shaft with different combinations of rotating
masses.
References: TecQuipment
User Guide