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Principles of Structural Vibration

by: Rowan Spinka DVM

Principles of Structural Vibration MAE 513

Rowan Spinka DVM
GPA 3.62


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Class Notes
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This 30 page Class Notes was uploaded by Rowan Spinka DVM on Thursday October 15, 2015. The Class Notes belongs to MAE 513 at North Carolina State University taught by Staff in Fall. Since its upload, it has received 30 views. For similar materials see /class/224031/mae-513-north-carolina-state-university in Aerospace Engineering (AE) at North Carolina State University.

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Popular in Aerospace Engineering (AE)


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Date Created: 10/15/15
Chapter 4 Transient Vibration Equation of Motion m3amp m or Ft 5c 24a 3c mix Ftm Where Ft is an impluse function What is an Impulse Function A pulse function Energy of a pulse function Impulse Function A direct view of Impulse response Free Response vs Impusle response Transfer Function vs Impulse Response Impact test for system identification Matlab Simulation Approximated impulse response systemlm function fftx fzeros2l hlOO if tgt000l hO end f l 2 2 f2 45xl 2x2 h Matlab Simulation Step response systemlm function fftx fzeros2l hlOO flX2 f2 45xl 2x2 h Extension to arbitrary excitation response Convolution integral xf If fMU dcf 0 Homework 4 1 Produce the impulse response for an overdamped and an underdamped system using Matlab 2 As problem 1 but produce step responses Verify settling time and damped frequency on the chart Initial condition is zero Chapter 3 Harmonically Excited Vibration Equation of Motion mxcxkx Fosinwt at AMMM I H F x 2a x wjx 2 05m wt m 3 Complete Solution of F gm of an under damped system IQ 3111 wt 95 k xil 72 aw if Jae Mammal 1 Forced Harmonic Vibration General Form of the Particular Solution x 2a x mix 2 05m wt m xXSinat Output Amplitude and Phase Fa X Vk mw22 0m2 Dimensionless Expression Aamp L 39317 ii 2 i2 iz i Graphical Representation Resonance Resonance Frequency Sharpness of g 0 Resonance Q n 2 w u 02 39 CU1 f2 f1 2 1 2 FIGURE 3101 Application of Frequency Response Chart Determine the output amplitudes Determine the output phase angles Example A Stereo System Other Methods Complex Variable Method Fourier Transform Method Vector Method Xk 1 7 317 F vth Zrtdt 313 0 2 1 t r Ik r quot77 77 Wk Complex Variable Method mxcx kx FO Sincot x 2a x mix Osm at m Complex Force F Foe w Complex Output x eimt W Xewe w Complex Displacement f Xe w Complex Frequency Re Sponse X Ik H60 2 FO I cocon 12Cwa Fourier Transform Method x 2gb x mix 2 05m wt m S2 2gwnsiwgizi m 52m Complex Frequency Re Sponse X Ik F0 1 wwn z2 wwn Vector Method Applications Rotating Unbalance Rotor Unbalance Whirling of Rotating Shafts Vibration Isolation Rotating Unbalance EO M mjc391 2 F1 2 m39c39 wze sin wt M m39c39 F1 CJ39c kx Finally Wcjckx memzsinat 39 F0 s1n a FIGURE 321 Harmonic disturbing force resulting from rotating unbalance Frequency Response 180 Phase angle 0 30 40 50 Frequency rmio a M me O 0 20 30 40 50 a Frequency r0110 an FIGURE 322 Plot of Eqs 324 and 325 for forced Vibration with rotating unbalance Rotor Unbalance Static Unbalance Dynamic Unbalance FIGURE 331 System with static unbalance FIGURE 332 System FIGURE 333 Arotor with dynamic unbalance balancing machine Whirling of Rotating Shafts 17 39 92rea2cosat 6 m m r r2f9ew2sinwt 6 m Synchronous whirl 17 39 92rew2 005wt 9 m m r r2f9ea25inat 6 m 9w ff0 G S O O h wltltwn wwn wgtgtwn FIGURE 343 Phase of different rotation speeds Example 341 k r a2rea2cas m 2M 2 602 Sin Vibration Isolation lax y Aka tan w m3 39 Ck 39 mwz mg2 00 OJO 05 717 cu 22w2cw2 20 30 E aquot FIGURE 352 Plot of Eqs 358 and 359 Homework 3 Chapter 3 Text Problems 37 39 318 320 329 355


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