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L05 - Basic Elements - Mass and Damping.pdf

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McMaster University
Mechanical Engineering

Lecture 5 - Mass and Damping Mass or Inertia Elements – Assumed to be a rigid body that can undergo changes in kinetic energy – Depending on the model chosen, different parts factor into the mass – Masses often appear in combination - consolidate into a single mass – Mass can have energy •Potential energy when held in gravity •Kinetic energy when moving Inertia Properties of a Mass Damping Elements – In real systems, the vibrating energy dissipates into heat and sound – This reduction in system energy reduces the amplitude of response of a system – The mechanism by which this occurs is known as damping (coefficient is ‘c’) • Three types of damping – Viscous Damping (Primary focus in this course) F  CX  – Damping due to the resistance offered by the fluid in which the system operates – Example: fluid flow through an orifice (shock absorber) – Magnitude of damping force in a real system depends on many different factors - Therefore hard to estimate damping over time F  N – Coulomb/Dry Friction Damping – Damping due to friction between rubbing surfaces that are dry – Highly nonlinear (consider stiction) – Could consider constant in magnitude but changes with direction F  k X – Material/Solid/Hysteretic Damping  – Damping due to friction between internal planes in a deformed material – Could be a function of the driving frequency W  4  X Modeling of damping •One approach is
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