Mechanical Vibration week 2 and 3 notes
Mechanical Vibration week 2 and 3 notes MCHE 485
University of Louisiana at Lafayette
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This 10 page Class Notes was uploaded by Nick C on Sunday February 7, 2016. The Class Notes belongs to MCHE 485 at University of Louisiana at Lafayette taught by Sally Mcinery in Spring 2016. Since its upload, it has received 16 views. For similar materials see Mechanical Vibrations in Mechanical Engineering at University of Louisiana at Lafayette.
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Date Created: 02/07/16
Energy Kinetic Energy - energy of motion Potential Energy - stored energy Linear Kinetic Gravitational Potential Q: What about the spring potential? Spring Potential Lagrange's Equations/Method (Sec. 1.5) * Energy-based method * Allows us to ignore internal/interaction forces (if we want to) * Usually based around: - generalized coordinates - virtual displacements Generalized Coordinates Lagrange's Equation (with no external forces or damping) Simple Linear Example of Lagrange's Method Simple Rotational Example of Lagrange's Method A Less-Simple Example (Newton/Euler) A Less-Simple Example (Lagrange) Lagrange's Method with Viscous Damping Lagrange's Method with External Forces To understand external forces, we need to introduce... Virtual Displacements * Infinitesimally small changes in generalized coordinates * Occur in zero time (no time elapses during the move) * Do not violate system constraints An Even-Less-Simple Example (Ex. 1.14-1.15) An Even-Less-Simple Example (cont.) Chapter 2 – Single DOF Forced Vibration Step Inputs (Sec. 2.2) Instantaneous change between 2 (desired) states/setpoints Can be a change in position, velocity, accel., force, etc. ex) Move from point A to point B right now Change velocity from 0 to 60 mph (right now) Note: The book calls "position-based" inputs seismic inputs. Intuitively, we know that the solution is oscillation about the steady-state offset, so let's assume a solution of the form:
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