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# Vibration ME 6442

GPA 3.62

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This 0 page Class Notes was uploaded by Chloe Reilly on Monday November 2, 2015. The Class Notes belongs to ME 6442 at Georgia Institute of Technology - Main Campus taught by Jerry Ginsberg in Fall. Since its upload, it has received 23 views. For similar materials see /class/234241/me-6442-georgia-institute-of-technology-main-campus in Mechanical Engineering at Georgia Institute of Technology - Main Campus.

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Date Created: 11/02/15

P P P 0Q P P P P P P P P OQOQ 0Q OQOQ Pg P P P P P P ID Iqu 0F 45 3 lines from bottom 0qu 0qu UFOqu Mechanical and Structural Vibration Theory and Applications Jerry H Ginsberg Errata to the First Printing 11 February 2004 15 second line and L2 x2 7 x1 respectively 15 2nd eq and eq 146 darken overdots above A for damping terms 16 eq 148 insert overdots in damping term 01W 02 1 1 02 C2 062 41 6th line following gure A3 y 41 2nd equation Vs kg y2 41 3rd equation from bottom V K11x2 express Pdis in terms 51 2nd and 3rd equations delete all overdots in expressions for A733 and A751 51 3rd equation from bottom Result should be 73in 0866LF10 52 2nd gure the downward force on the small gear is kAg MAZ 54 equation at top of page insert overdots in damping term 4mm 61 Exercise 147 third line spring stiffness k1and 61 Figure for Exercise 147 distance from pivot to force point is 2L3 67 eq 2145 2nd equation change to 7 ie sin wt exp iwt 7 exp 7 11 67 eq 216 2nd equation insert parentheses around iwt in both exponentials 69 3rd equation A 4605 1947i 69 11 lines from bottom we write abs while 70 eq 213 Change sign preceding Z52 to a plus A2 cos wt Z52 A Pg 70 eq 214 1nsert a minus sign before 17151 in both lines ie exp 717151 7 4905 10 5 Pg 98 3rd equation n gt Pg 109 eq 2320 9 t 7 T Pg 110 4th line from bottom the force k E Pg 111 Figure 219 the heading for the left graph should be C 005 Pg 112 Exercise 25 Part b 2nd line from bottom Write the complex amplitude in Pg 113 2nd and 3rd lines of Exercise 214 Delete dots above A Pg 116 Exercise 231 2nd line following 1tem 3 frequency wnat the ratio Pg 117 gure for Exercise 235 delete subscript 1 from label for displacement arrow Pg 119 5th line in Exercise 263 time wnatt over Pg 123 Figure 32 lower 0 label for vertical axis to the bottom left corner Pg 126 5th line in Example 32 insert L 2 m 1t may be assumed that the wheel remains in contact with the ground See Exercise 336 Pg 129 last equation F exp 7 f exp 7iQt Pg 134 2nd line following gure The two curves intersect the Pg 143 rst graph right label should be 200 Pg 144 Figure 311 labels for spring and dashpot should be capitalized Pg 144 eq 341 7mw2fgO Pg 145 eq 342 41537 Kg i 04 Mq39 Pg 149 5th equation y Helm 1 Pg 151 7th equation V 5662 gt Pg 151 2nd line after equation for V 2M9 which ie insert overdot Pg 156 2nd equation exp 7inw1t Pg 160 4th line from bottom of page and GN21 to GNg are N N N Pg 161 eq 3725 1st line 73 1 73 2 3 Pg 178 3rd paragraph 2nd line is well below the accelerometer s natural Pg 178 eq 3757 2nd line i K 71714110 Z 7 1 Qinrlg i K 71714110 7 712wa n 7 1 Qinrlg 7 7127 U71 Z71 Pg 180 2nd set of gures heading for the left graph should be wnatT 407T 2 P P Pg P P P OQOQ P P P P P P P OQOQOQOQOQ Pg Pg Pg Pg Pg Pg 1qu 0F Iqu 240 1st line j 1 N phinormj phisortjsqrtmujj 248 eq 4249 2nd 1111444 1T M 4591 0 248 eq 4250 second line 183 eq 389 and 4 lines before 202 last line Figure 326 as 214 Exercise 342 subscript in Td should be roman type h1iac2w2 if 3w OifwglxlltL2 2aciL if gt L2 215 2 lines before Exercise 345 90 of the highest critical 224 eq 424 iwg 0 225 eq 427 lower left element of rectangular matrix should be KltN71gt1 W3MltN71gt0 226 eq 428 1st line last element of column matrix is Nj 230 5th line after gure Because 9 is the pitch 235 2nd equation lower left element of matrix should be 718 1075 239 2nd equation 3NxN 0 end 1TMi 442 4524 M 441 Q22 250 last equation 0719 A43k ltkgtgt 11 11 ltkgt ltkgt 7 ltk71gt 255 rst equation 172m hi 256 5th line of equations 7m cos 9 a k 7 mwi Z527 267 2nd text line M is no L Mg 272 6th line of Exercise 410 i2 0 at t 0 284 Exercise 45 7th line and b m1 5 kg m2 Then delete the following sentence Pg Pg 286 Exercise 412 part 1 Nm L412 286 Exercise 412 part 1 list line Determine the normal mode 2 3 Pg 286 Exercise 413 2nd line of 4th item described above is Pg 287 Exercise 420 equation w Pg 287 Exercise 421 last line and normal modes of this system Pg 291 Exercise 447 one line before end qn Re Yn exp i20t and P 298 eq 522 Gm K 1 17 7 w my1 ID Pg 309 equation V koyg Pg 314 7 lines before eq 549 1nsert Q kA ICA k 01K 7 1 Simultaneously P 314 eq 549 2nd line m 01 K2 Pg 319 Exercise 512 9th line cases W 0001 and W 001 0Q Pg 322 Exercise 523 partb last line platform at a designated Pg 322 Exercise 523 part c7th line 1nsert partb corresponding to 20 HZ Use Pg 325 2nd paragraph 3rd line work of the Swiss mathematician Pg 328 eq 617 change superscript L 2 73115 A AyEA dac Zcuxct2 Pg 339 eq 6127 9 Pg 340 2nd line q ie delete repeated terms Pg 344 eq 6137 L dziJn KZJ 21316 W dcc d 7139 d21Jn On A 7E dag dx2 0 qu dac Pg 349 4 th line of Matlab commands psin H y 0 1 Pg 409 Exercise 617 7th 8th and 9th lines Where a is 95 and 105 of the fundamental and second natural frequencies plot the Pg 409 Exercise 619 insert at end of last sentence at midspan as a function of w Pg 410 Exercise 627 last line C 2000EIL3 Pg 413 Exercise 656 reword 1st sentence When a cantilerbeam is modeled by a certain Ritz series the inertia Pg 440 rst gure change to 4 in vertical axis Pg 444 2nd equation xaSyIrlptOtiC Pg 445 2nd line of text by letting 1c0shcy 0 This Also insert close brace at end of equation 4 P 445 4th line of equation for B4 0Q C1 lim 2sin cyj 7 P Pg 453 Figure 712 Spring force on the right mass should be k wlmL P P P P 449 line following equation for 12 where a4 pAL4w2EI OD 455 2 lines before eq 7626 are not inertially coupled Interestingly 0 464 4th equation 2nd line insert close brace at end of equation 481 4th line of equations expikL 181 exp708kL 182 494 eq 7940 2nd line 0320 1 L 22 pAqquxwpIqlezmdx 7777 339 n P 495 10 lines before end of Example 714 function of a Ld and 039 0 Pg 496 1st line cross section rotation X at this frequency Pg 501 Exercises 725 and 726 insert at beginning of second sentence Use Appendix C to decompose Pg 501 Exercise 729 2nd line Example 75 and Exercise 712 What Pg 501 Exercise 733 change second sentence to A torque Ph t is applied at the midpoint Pg 503 Exercise 752 last line range 0 lt u lt 2000 rads Pg 513 equation for K5 The denominators for K516 K535 K553 and K5 should be L Pg 520 1st line Once we have formed and we Pg 529 Exercise 86 7th line Derive linear interpolating functions Also delete parenthetical last sentence Pg 530 Exercise 516 3rd line Use a single nite element for bar BD Pg 539 2nd line of equations ago13 1 Pg 541 3rd line of equation for V1 index in rst summation sign should be Pg 544 eq 9131 2nd line BT Q BT MT A Pg 546 3rd line of equations Mjn pAL jn Pg 546 equation for V 2nd line delete exponent two for q term Pg 546 equation for V 3rd line delete exponent 2 and x from second factor 7T4EI 2L3 SJwt Pg 546 equation for V 4th line K1 3394 Pg 556 2nd equation quJ Limyj 17 Pg 558 eq 923 M 7 1 W1 W122 Pg 558 eq 924 insert K1100 KqFCT Pg 558 1st sentence after eq 924 should be 1n the special case where the xed interface modes are those of a bar that is immobilized at both ends the off diagonal partitions of Kl are identically zero Pg 558 last sentence of paragraph following eq 924 should be 1f 2 is de ned to have zero displacement and rotation at interfaces each work term will be zero Pg 559 4th line following eq 926 eqs 923 These matrices Pg 560 paragraph following equation for K620 insert after second sentence All Kl ff should evaluate to zero according to the note on page 558 Pg 564 Exercise 923 change second sentence Determine the constraint modes and Jacobian constraint matrix corresponding to using clamped clamped exural modes as the xed interface modes for bar AB Pg 564 Exercise 926 change 1st sentence Select clamped clamped exural and xed free torsional modes as the xed interface Pg 572 3rd line after 1st set of equations eigenvalues to those derived from undamped modal analysis Also compare Pg 572 3rd set of equations Mathcad zero identity 3 0 S stackaugment7Kzero augmentzero R 7 stackaugmentzero K augmentK 0 Pg 572 4th set of equations insert after MATLAB lambda diaglambda Pg 572 4th set of equations 2nd line 00001 imag lambda lt 0 Pg 592 Exercise 106 2nd line insert at end to 16 and let Afj be a set of random numbers in the range 7005 lt Afj lt 005 Pg 598 1st line after eq 11111 When the quadratic coef cients of T actually N Pg 598 eq 11112 insert term 7 ZEjnqn N 7 J 7L1 Pg 599 1st line after eq 11116 use eqs 11112 and 11115 to form Pg 599 eq 11117 insert term 7 J 7 F0 P P 0Q P P P 0Q P 0Q P 0Q P 0Q P P P P P P OQOQOQ Pg Pg Pg Pg Pg Pg 0 Iqu UFOqu 600 eq 11119 2nd line insert term 7 7 J 7 F0 600 eq 11121 d 0 lslaigcl lpblixl QNJFO 606 1st line after eq 1121 into eq 11121 and 607 1st line after eq 11211 leads to v Au Which 620 eq 11413 7 M MK n12N N T N T 621 eq 11417 Numerators should be and 622 3rd equation from bottom 7 wgyn 7 2wz39n 622 2nd equation from bottom 7 wgzn 7 2mg 623 3rd set of equations from the bottom 1st row of 0 should be 0 7 w 0 0 626 upper left graph Delete the small circle at the top of the larger ellipse 634 MATLAB program steps 2nd and 3rd lines eigval eig S sigj R sigj Relamj sortrealeigval Imlamj sortimageigval end 634 Mathcad program steps 1st line ltjgt genvals R 7 S 71 635 3rd paragraph lines 4 and 5 and following equation exp AnT 639 4th equation 81 fjn lt 8x L 642 Exercise 114 1 1 1 1 T EmL2 Egg 7 1 cos 9 7 g cos 02 wg 7 EITw2 645 Exercise 1123 1st line a height of 2E3 above 646 Exercise 1127 insert after 2nd sentence The rotation rate is w 06 km12 657 eq 1231 right sides are 3me cos wt and 3me sin wt 665 last set of equations M53 M414 Iii GQA 76213 2amp59 670 eq 1256 2nd line 3me cos wt 7

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