ASE 365 - Lecture 12 - Review for test 1 Chapter 1:...

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Unformatted text preview: Review for test 1 Chapter 1: Concepts from dynamics Newtons laws (translation & rotation) Work and energy Systems of particles, rigid bodies Masses, dampers, springs Equivalent springs Equations of motion Review for test 1 (contd) Chapter 2: SDOF free response Undamped Damped (viscous) Underdamped Critically damped Overdamped Measurement of damping (logarithmic decrement, half-amplitude methods) Coulomb damping Review for test 1 (contd) Chapter 3: SDOF harmonic & periodic response Undamped (including resonance) Damped: complex frequency response approach to find amplitude and phase Systems excited by rotating unbalance Base motion excitation Vibration isolation: force transmissibility Review for test 1 (contd) Chapter 3: SDOF harmonic & periodic response (contd) Response to periodic excitation using Fourier series Complex Fourier series You can bring one handwritten 8 x 11 sheet of equations, notes, etc., to use in Test 1. Response to arbitrary inputs Response to unit impulse: Syste m: m,c,k ) ( sin 1 ) ( t u t e m t g d t d n - = ) ( t Response to time-shifted, non-unit impulse: t g(t ) ) ( ) ( - t g d F Syste m: m,c,k ) ( ) ( - t d F t S d S F( ) t S amplified by F(& )d& , time-shifted by e . e (t ) t d t g F t x t ) ( ) ( ) (- = s. ' of ion superposit a as expresses This : property sampling Recall d t F t F d t F t F ) ( ) ( ) ( ) ( ) ( ) (-- = - -- =-- d t g F t x t F d t g F d t F ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( : is to response , is to response Since ) (causality is this for Since -- = =- t d t g F t x t t g ) ( ) ( ) ( , ) ( + + +- =- +- = =- - t x x t x e d t g F d t g F d t g F t x t d d n d t t t n sin cos ) ( ) ( ) ( ) ( ) ( ) ( ) ( : at clock the Starting . in variable of change a Consider - 2 1 ) ( ) ( t t d t g F . ) ( sin cos ) ( ) ( ) ( < + + +- =- t t F t x x t x e d t g F t x x x d d n d t t n for of effect the account into take in ) and (with terms condition" initial " The : when and that so Define - = =- = =- =- =- 2 2 1 1 , t t s t t t s t ds d s t t s...
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This note was uploaded on 09/18/2011 for the course ASE 365 taught by Professor Staff during the Spring '10 term at University of Texas at Austin.

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ASE 365 - Lecture 12 - Review for test 1 Chapter 1:...

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