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Lecture

# L06 - Lumped mass and Harmonic Motion.pdf

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McMaster University

Mechanical Engineering

MECHENG 4Q03

veldhu

Fall

Description

Lecture 6 - Lumped Mass Assumptions
• Lumped Analysis - Inertia Effect of Stiffness Elements
– Generally ignore mass in stiffness elements
• This assumption can lead to significant error, especially if the mass of the
stiffness element is not negligible compared to system mass
– Concept of a lumped mass
• Determine the inertia effects of the stiffness elements referred to a point on a
lumped mass
• Equivalent kinetic energy that can be referred to the same lumped mass point
• Example: 1 DOF spring-mass systems
• Consider the distribution of mass in the spring
– Calculate an equivalent mass value located at the end
Harmonic Motion
• Periodic Motion
– Motion that is repeated after equal intervals of time
– Motion can be very complicated but it must repeat
• Cycle
– Movement of a vibrating object from equilibrium, to one extreme position, back
through equilibrium, to the other extreme position, and back to equilibrium
Descriptors
• Amplitude A
– Maximum displacement of the vibrating body from equilibrium
• Phase angle ()
– Shift in corresponding points of wave shape
• Period τ (s)
– Time taken to complete one cycle
• Frequency f (Hz) = 1 / period
– Number of cycles per unit time (cycles/sec)
– For a rotational system relates to RPM * Be careful with the units used:
• Circular frequency (rad/= 2 f (Hz) - Practical (RPM)
• Natural frequency

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