Harris'''''''' Shock and Vibration Handbook Part 2 doc

... M 2 N 3 − M 3 N 2 = (11.7) (25 .1) − (−15.3)(7.1) = 4 02 4(1,000)(68 − 26 ) ᎏᎏ 4(500)(−10.5) 3.58 ᎏ 7 .22 4(500) ᎏ 8(1,000) 1 ᎏᎏ 1 − (3.58/7 .22 ) 2 h ᎏ l h ᎏ l 2g ᎏ ρ A 2 VIBRATION OF A RESILIENTLY ... amplitudes: x c0 = ΂΃ 2 − ΂ cos 2 φ+sin 2 φ ΃΂ ΃ 2 u 0 ΂΃ 4 − A ΂΃ 2 + ΂΃ 2 (3.58) β 0 = − ΄΂ cos 2 φ+sin 2 φ ΃΂ ΃ + ΂ 1 − ΃Έ Έ sin φ cos φ ΅΂ ΃ 2 u 0 /ρ y ΂΃ 4...

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... −µ 2 12M 1x ᎏ h 3 ∂ 2 w ᎏ ∂y 2 ∂ 2 w ᎏ ∂x 2 Ez ᎏ 1 −µ 2 τ xy ᎏ G E ᎏ 1 −µ 2 1 ᎏ E E ᎏ 1 −µ 2 1 ᎏ E ∂ 2 w ᎏ ∂x ∂y ∂ 2 w ᎏ ∂y 2 ∂ 2 w ᎏ ∂x 2 ∂ 2 w ᎏ ∂x 2 ∂ 2 w ᎏ ∂y 2 ∂ ᎏ ∂y ∂ 2 w ᎏ ∂x 2 ∂ 2 w ᎏ ∂y 2 VIBRATION ... =ρ 2 = h 2 / 12, For n = 1: ω 0 = Ί ๶ = Ί ๶ = 21 70 rad/sec = 345 Hz (30 × 10 6 )(36)386 ᎏᎏ ( 12) (0 .28 ) π 2 ᎏ (40) 2 EI g ᎏ Sγ...

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... Z 11 Z 22 −Z 11 Z 22 1 1 ᎏ Z 12 Z 12 Z 21 − Z 11 Z 22 −Z 22 Z 11 1 1 ᎏ Z 21 E I R 12 R 22 R 11 R 21 A F A F T 12 T 22 T 11 T 21 E I E A Y 12 Y 22 Y 11 Y 21 I F VIBRATION TESTING MACHINES 25 .11 8434_Harris _25 _b.qxd ... 09 /20 /20 01 12: 02 PM Page 23 .24 23 .17 FIGURE 23 .7 Time-histories of response to shock motions defined in Fig. 23 .2 and c...

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... (30.33) M 0 ᎏᎏᎏ 4(a x 2 k y + a y 2 k x ) − I z ω 2 12 ᎏ λ 2 + 1 4ηλ 2 +η+3 ᎏᎏ λ 2 + 1 4ηλ 2 +η+3 ᎏᎏ λ 2 + 1 1 ᎏ ͙ 2 ෆ ω xβ ᎏ ω z THEORY OF VIBRATION ISOLATION 30 .23 FIGURE 30 .20 Plan view of the ... decoupled ρ y ᎏ a x a z 2 ᎏ ρ y 2 ρ y ᎏ a x a z 2 ᎏ ρ y 2 ρ y ᎏ a x 1 ᎏ 2 ෆ ρ y ᎏ a x ω xβ ᎏ ω z ω ᎏ ω z ηa z ᎏ ρ y ω 2 ᎏ ω z 2 a x 2 ᎏ ρ y 2 u 0 B 2 ᎏ...

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... ( 32. 24) F 0 ᎏ mω n 2 1 ᎏᎏᎏ s 2 + 2( c/c c )ω n s +ω n 2 F 0 ᎏ ms 1 ᎏᎏ s 2 + (c/m)s + k/m F 0 ᎏ ms SHOCK AND VIBRATION ISOLATORS AND ISOLATION SYSTEMS 32. 35 8434_Harris_ 32_ b.qxd 09 /20 /20 01 12: 32 ... allowable SHOCK AND VIBRATION ISOLATORS AND ISOLATION SYSTEMS 32. 17 8434_Harris_ 32_ b.qxd 09 /20 /20 01 12: 32 PM Page 32. 17 32. 40 FIGURE 32. 23 Steady-stat...

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... −ω 2 /ωn 2 ) sin ωt − 2 (ω/ω n ) cos ωt ᎏᎏᎏᎏ (1 −ω 2 /ω n 2 ) 2 + (2 ω/ω n ) 2 x ᎏ F 0 /k F 0 ᎏ mω 2 ω n 2 F 0 ᎏ ω 2 k F 0 cos ω n t ᎏᎏ cω n π ᎏ 2 F 0 ᎏ 2kζ F 0 ᎏ k 2 ω/ω n ᎏᎏ 1 −ω 2 /ω n 2 sin ... THE HANDBOOK 1 .21 8434_Harris_01_b.qxd 09 /20 /20 01 11:39 AM Page 1 .21 INTRODUCTION TO THE HANDBOOK 1.11 8434_Harris_01_b.qxd 09 /20 /20 01 11:39 AM Page 1.11 1.1...

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... −ω 2 /ω a 2 ᎏᎏᎏᎏ (1 −ω 2 /ω a 2 )(1 −ω 2 /ω 0 2 ) − (ω 2 /ω 0 2 )µ x 0 ᎏ δ st 1 −β a 2 ᎏᎏᎏ (1 −β a 2 )(1 −β 2 ) −β 2 µ x 0 ᎏ δ st (1 −β a 2 ) 2 + (2 β a ) 2 ᎏᎏᎏᎏᎏᎏ [(1 −β a 2 )(1 −β 2 ) −β 2 µ] 2 + ... −β a 2 2ζβ a 3 ᎏᎏ (1 −β a 2 ) 2 + (2 β a ) 2 (1 −β a 2 ) + (2 β a ) 2 ᎏᎏ (1 −β a 2 ) 2 + (2 β a ) 2 c a ᎏ c ca k a ᎏ m a ω ᎏ ω a 1 + 2 β...

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... range 12. 32 CHAPTER TWELVE 8434_Harris_ 12_ b.qxd 09 /20 /20 01 11:15 AM Page 12. 32 REFERENCES 1. Levy, S., and W. D. Kroll: Research Paper 21 38, J. Research Natl. Bur. Standards, 45:4 (1950). 2. Ref. ... piezoelectric materials vary with temperature. VIBRATION TRANSDUCERS 12. 23 8434_Harris_ 12_ b.qxd 09 /20 /20 01 11:15 AM Page 12. 23 CHAPTER 13 VIBRATION MEASUREMENT INSTRUMEN...

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... criteria, specifications, and the accuracy required.These factors are discussed in Chaps. 14, 20 , 22 , 23 , 27 , and 28 . MEASUREMENT PLANNING Careful pretest planning (and, in the case of a complex ... turbulence and harmonics and axial Electrically induced 1 × rpm or 2 times line Radial Should disappear when power turned off vibrations frequency and axial 8434_Harris_16_b....

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... 8 and 23 ) Vibration Deterministic Line spectrum (see Chap. 22 ) Random Power spectral density (see Chaps. 11 and 22 ) TEST CRITERIA AND SPECIFICATIONS 20 .3 8434_Harris _20 _b.qxd 09 /20 /20 01 12: 12 ... constitute the shock or vibration. The most common spectral descriptions of both deterministic and random shock and vibration envi- ronments are summarized in Table...

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