1 Lateral Vibration Attenuation of a Beam with Piezo-Elastic Supports Subject to Varying Axial Tensile and Compressive Loads 5 The structural impedance of the first mode iny-direction Z1.!/ DY2 1 Zm.!/ C 1 Zk0 .!/ D Y2 i !m C k .1Ci / i ! (1.4) seen from the terminals 3 and 4 of the gyrator is the result of the parallel impedance of the modal mass Zm.!/ D 1 i !m and the complex stiffness Zk0 .!/ D i ! k0 . From (1.1) and (1.2), the receptance becomes ˛.!/ D Cp 1C!Cp Rp i C 1 Y2 m !2 sc !2 Ci !2 sc (1.5) with the angular eigenfrequency !sc Dr k m . Furthermore, the term 1 Y2 m in (1.5) is replaced by K33 Cp !sc, as suggested in [10], leading to the final expression of the transducer receptance ˛.!/ D Cp 1C!Cp Rp i CK33 Cp !sc !2 sc !2 Ci !2 sc : (1.6) 1.3.2 Transducer Receptance Model Fit In the model fit process, the parameters Cp; Rp; K33; !sc and in (1.6) are varied to solve the least squares curve fitting problem min Cp; Rp; K33;!sc; jj ˛.Cp; Rp; K33; !sc; ; !/ ˛exp.!/jj 2 2 (1.7) where ˛exp.!/ is the experimental data of the transducer receptance. Therefore, the lsqnonlin algorithm in MATLAB is used. Figure 1.4 shows the amplitude and phase response j˛.!/j and arg˛.!/ of the experimental data and the calculated receptance after the curve fitting for the axial load Fx D0N. Both, the model and the experimental data show a very good agreement. Fig. 1.4 Calculated transducer receptance (red solid line)with fitted parameters and experimental data (black solid line) for Fx D0N 150 200 250 0 −30 ω/2π in Hz argα in ◦ 150 200 250 1.2 1.6 2.1 |α| in F
RkJQdWJsaXNoZXIy MTMzNzEzMQ==