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Strain-Based Measurement Introduction:H( w)=1--------------------------------------------------------------æ w1 -----èÐ èæ w 0øö2 ö 2 2z w ø+ -----èæ w 0øö2(EQ 1-28)andjw ( )=2zatan------------------------æ w w----- Ð ----- 0 öè w øw 0(EQ 1-29)Where:j(w) = The phase relationship between the output and the input forcingfunction.w 0=K----MRadians/SecondWhere: w 0 = 2p f 0(EQ 1-30)RMz = ----------------2 MK(EQ 1-31)The implications of equations (1-28) and (1-29) are shown graphicallyin Figure 1-28 and are stated as follows:1. As w approaches zero radians/second: The second-order system is stiffness-dominated orÒspring-controlledÓ where the transfer function H(w) approaches unity in value.2. As w approaches infinity radians/second: The second-order system is mass-dominatedwhere the reaction of the mass to the input approaches zero, or the value of the transferfunction value itself approaches zero.3. As w approaches infinity: The phase angle between the input and the output approaches180 degrees.4. When the phase angle between the input and the output equals 90 degrees, w = w 0 which istermed the natural frequency of the system.5. If this system possessed zero damping (an impossibility), the value of the transfer functionwill approach infinity at the natural frequency of the system.CHAPTER 1-54 The Art of Practical and Precise Strain Based Measurement 2nd Edition © 1999
Applications Note 1-9:6. When the phase angle between the input and the output equals 90 degrees, the natural frequencyof the system may be determined and from this quantity, the stiffness and mass-ratio of the systemcan be directly determined by means of equation (1-30)FIGURE 1-28. The Second-Order System Magnitude and Phase Response:4z = .1Magnitude ofResponse32z = .31z = .5z = 5z = 2z = 1z = .7.5.125.2.5 1 2 3w/w 0logThe Second-Order Magnitude ResponsePhaseAngle0-30-60-90-120z = 5-150z = .1z = .7z = 2-180If the second-order system possessed a damping factor that approacheszero in value, the flat frequency response range of the second-order sensorThe Art of Practical and Precise Strain Based Measurement 2nd Edition © 1999 CHAPTER 1-55
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The Art of Practical andPrecise Str
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Special Credits:Mrs. Helen Pierson,
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Table of ContentsBy James G. Pierso
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ContentsApplications Note 4-10:Lead
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ContentsCHAPTER 8Electrical Conside
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CHAPTER 1Strain-BasedMeasurementInt
Page 15 and 16: Applications Note 1-1: Introduction
Page 17 and 18: Applications Note 1-1: Introduction
Page 19 and 20: Applications Note 1-2:The Art of Ap
Page 21 and 22: Applications Note 1-31. The presenc
Page 23 and 24: Applications Note 1-3result in a pe
Page 25 and 26: Applications Note 1-4:The measureme
Page 27 and 28: Applications Note 1-4:uncertainty i
Page 29 and 30: Applications Note 1-5:All strain-ba
Page 31 and 32: Applications Note 1-6:Applications
Page 33 and 34: Applications Note 1-6:ical size of
Page 35 and 36: Applications Note 1-6:and where:j i
Page 37 and 38: Applications Note 1-6:5. millivolts
Page 39: Applications Note 1-6:.Electrodynam
Page 44 and 45: Strain-Based Measurement Introducti
Page 104: Strain-Based Measurement Introducti
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