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Characteristics and Presentation of MDOF FRF Data Modal Analysis and Modal Testing S. Ziaei Rad 1 Receptance and Impedance FRF Parameters The Relation between different form of FRF can be stated as before: [Y ( )] i[ H ( )] [ A( )] i[Y ( )] [ A( )] [ H ( )] 2 A general element of the receptance is given by: H jk ( ) 2 Xj Fk , Fl 0 l 1,, N (l k ) Receptance and Impedance FRF Parameters Now, let’s look at the Impedance matrix [Z]: {X } [ H ]{F} 1 {F} [Z ]{F} [ H ] {F} Therefore, we can not simply write: 1 H jk ( ) Z jk Looking at the definition of a typical element of [Z]: Z jk ( ) 3 Fj Xk , Xl 0 l 1,, N (l k ) Receptance and Impedance FRF Parameters 4 To measure the receptance, we should make sure that just a single excitation force is applying on the structure. To measure an impedance property all DOFs except one should be grounded. Such a condition is almost impossible to achieve in practical situation. Therefore, only types of FRF which can expect to measure directly are those of the mobility or receptance type. Some Definitions 5 A Point Mobility (or receptance) is one where the response DOF and the excitation coordinate are identical. A Transfer Mobility is one where the response and excitation DOFs are different. A Direct Mobility is one where types of DOFs for response and excitation are identical. (both in x) A Cross Mobility is one where types of DOFs for response and excitation are not identical. (one in x and other in y direction) FRF Plot in MDOF System Typical mobility FRF plot for MDOF system (individual modal contribution) 6 Point and Transfer FRFs Point FRF 7 Transfer FRF Point and Transfer FRFs 8 There is an anti-resonance after each resonance in point FRF. In point FRF the modal constant for every mode is positive, it being the square of a number. In transfer FRF, there is an anti-resonance or a minima after each resonance. We expect a transfer FRF between two positions widely separated on the structure to exhibit fewer antiresonances than one for two points relatively close together. (the further apart are the two points, the more likely are the two eigen vectors elements to alternate in sign as one progress through the modes. Ponit and transfer FRF for 6DOF system k1 m1 x1 k3 k2 m2 x2 m3 x3 k4 m4 x4 m5 x5 m1=m2=m3=m4=m5=m6=1 Kg k1=k2=k3=k4=k5=k6=100000 N/m 9 k6 k5 m6 x6 FRFs of 6DOF System 10 H11 H21 H31 H41 H51 H61 Display of FRF Data For Damped Systems 11 Bode Plots Nyquist diagrams Real and Imaginary plots Three-dimensional plots 2DOF System k2 k1 m1 x1 m2 x2 1 0.02 m1=m2=1 Kg Hysteretic damping k1=k2=360 kN/M 2 0.04 jrkr H jk ( ) 2 r 2 ir2 12 Bode Plot H11 13 H12 Nyquist Plot H11 14 H12 Real and Imaginary H11 15 H12 3D Plot 16 Cr exp j r 1 2 1 jr r Cr exp j r 2 1 j r r 17 Dr 2 1 j r r r Cr exp j r 2 1 j r r 18 Conclusions 19 The purpose of this session has been to predict the form which will be taken by plots of FRF data using the different display format. Although the graphs were taken from some theoretical models, they can help to understand and interpret actual measured data.