Vibs1_review_notes - Mechanical Vibrations I Mechanical...

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Mechanical Vibrations I Lecture Notes -1- 06/16/06 12:25 PM Mechanical Vibrations I m k c x(t) f(t) Author: Allyn W. Phillips, PhD University of Cincinnati UC Course Nr.: 20-MECH-480 Revision: 16-Jun-2006 Copyright 2001-2006
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Mechanical Vibrations I Lecture Notes -2- 06/16/06 12:25 PM Course Outline Topics Review Dynamics o Units o Complex Numbers o Free Body Diagrams o Absolute vs. Relative Motion o Differential Equations o Matrices & Linear Algebra o Kinematics Rolling Contact Coordinate Systems SDOF / MDOF Concepts o Newton’s Method Frequency, Damping, Mode Shape & Scaling o Lagrange’s Method Energy Method (SDOF only) o Eigenvalue / Eigenvector Solutions Superposition o Free Vibrations o Forced Vibrations Steady-State Transient SDOF / MDOF Applications o SDOF Estimating Frequency & Damping Half Power Log Decrement Transmissibility Isolation o MDOF Frequency Response Function Concepts Stiffness / Compliance Impedance / Mobility Modal Parameter Estimation Impedance / FRF Methods
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Mechanical Vibrations I Lecture Notes -3- 06/16/06 12:25 PM Course Material Sequence Introduction to Mechanical Vibrations [AWP #1] Newton’s Method [AWP #2] o Units [TD 0] o Matrices & Linear Algebra [TMH A] o Free Body Diagrams [TD 2.2, 5.1] Single and Multiple Body o Absolute vs. Relative Motion Force Balance Mass – absolute acceleration Damping – relative velocity Stiffness – relative displacement o Linear & Torsional Rolling Contact o Equation of Motion [TD 5.1-3] Single DOF MCK v. RLC – Equivalence [TMH 2.6] Homogeneous Solution of Equation of Motion [AWP #4] o Differential Equations [TMH D] Linear, Constant Coefficient Harmonic Functions (sin, cos) [TD 1] Complex Exponentials o Free Vibrations [TD 2.1, 2.6] Oscillatory Motion [TD 1] Harmonic Motion Periodic Motion o Vibration Terminology [TD 1] Frequency Damping [TD 2.6, 2.8, 2.9] Viscous Coulomb Structural Mode Shape [TD 5.1] Modal Scaling o Eigenvalue / Eigenvector Solutions [TD C] Superposition o Effects of Changing Mass, Stiffness, Damping o Modal Parameter Estimation Damping Log Decrement [TD 2.7, AWP #5] Lagrange’s Method [TD 7.23, TMH B, AWP #6] o Energy Terms Kinetic
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Mechanical Vibrations I Lecture Notes -4- 06/16/06 12:25 PM Potential Dissipative o Contrast with Newton’s Method Global vs. Local Control Volume o Equation of Motion Show Equivalence to Newton’s Method o Single DOF reduces Energy Method [TD 2.3] Conservative System - only Steady-State Solution of Equation of Motion [AWP #7] o Forced Vibrations [TD 3.1] Harmonic Excitation o Laplace Transform [TD B] Converts Differential Equations to Algebraic Equations Transfer Function o Fourier Transform [TD 1.2, 13.7, DLB] Frequency Response Function [AWP #8] MCK Variations SDOF Concept Applications [ TD 3 ] o Harmonic Unbalance Force [TD 3.2, AWP #9] o Transmissibility [TD 3.5, AWP #10] o Isolation [TD 3.6, AWP #10] o Dampers Mass Tuned Absorber o Modal Parameter Estimation [AWP #12] Frequency Damping Half Power [TD 3.10, AWP #8] Mode Shape Quadrature MDOF Systems [AWP #11] o Equations of Motion Matrix Solution o Natural Frequencies o
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