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

Strain-Based Measurement Introduction:k 0k 2---- and z=k 1-----------------2 k 0 k 2(EQ 1-16)where: w 0 is the natural frequency and z is the damping factor.Equation 1-15 becomes:1 dk----- 0 2z+ -------------- + k2 20 = KF inw 0 d t dk 0w 0dt(EQ 1-17)Where: K = The static sensitivity of the sensor.The second order transfer function in the frequency domain can be shown toequal:H( w)=K--------------------------------------------------------æ w1 Ð æ-----ö 2 + 2 jzæ-----w ööè èw 0ø èw 0øø(EQ 1-18)Where the magnitude of this function will equal:H( w)=K-----------------------------------------------------------w1 -----èæ Ð èæ øö2øö 2 + 2zw ----------èæ øö2w 0w 0(EQ 1-19)and where the phase response is given by:zjw ( ) = atan2------------------------æ w w----- Ð ----- 0 öè w øw 0(EQ 1-20)Examples of the second-order response, Figure 1-26, are abundant. Allspring-member-based sensors will show a second-order response, up tothe first resonance frequency, with varying degrees of damping. NoteCHAPTER 1-48 The Art of Practical and Precise Strain Based Measurement 2nd Edition © 1999