The Art of Practical and Precise Strain Based ... - Webprofile.info

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