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3  Computation and estimation of transfers

The objective of this session is to illustrate equations given in the modal basis (??) and (3). For this, one first analyzes the frequency response then simulation the test process using time transients and some signal processing steps.

To help through various steps, one will use different MATLAB toolboxes

To get the data

3.1  Computation of transfer functions in the frequency domain

The objective of this part is to understand the influence of terms in equation (2) for the computation of transfers as a sum of modal contributions (see course notes section 2.2.4)

   H(ω) =  [c] [−Mω2+K]−1 [b] ≈ 
[c]{φj}{φj}T [b]
 −ω 2+iωζjωjj2

and thus to analyzed equations of motion in the modal basis

  [Is2+[\ 2ζjωj \ ]s+[\ ωj2 \ ]]{qr}=[φT b]{u}  et  {y} = [cφ] {qr}     (3)

A FEM mesh of the considered engine cover was done earlier and can be loaded using

 load cc_model
 cf=feplot; cf.model=model; cf.def=def;fecom('ColorDataEvalY');

The data contains two data structures

>> model % model contains the model
model = 
    Node: [2031x7 double]  % sdtweb('node') 
     Elt: [2021x18 double] % sdtweb('elt')
>> def  % contains the modes
def = 
      def: [10195x30 double]
      DOF: [10195x1 double]
     data: [30x1 double]
      fun: [1 2 0 8 0 0]
    label: 'Normal modes'
      lab: {30x1 cell}

model gives nodes, elements, properties ... def contains the first 30 modes.

The following commands allow the generation of transfer functions. Fill in the ??? to obtain an input at 426y (DOF 426.02) and an output at 1976y (DOF 1976.02) (one uses the low level calling format sys=nor2ss(def,damp,InDOF,OutDOF,'Hz acc')).

 load cc_model
 cf=feplot; cf.model=model; cf.def=def;fecom('ColorDataEvalY');
 f=linspace(0,5000,2048)'; % frequencies
 sys=nor2ss(def,damp, ??? , ??? ,'Hz acc');
 qbode(sys,f*2*pi,'iiplot "simul1" -po');
 ci=iiplot;iicom('sub1 1'); % pointer to responses
 ci.Stack{'simul1'} % Data structure containing response

3.2  Time simulation and FRF estimation

From the FEM model, one builds a state-space model using SDT commands, then generate the transient and draws the response using cc_simul

 load cc_model
 cf=feplot; cf.model=model; cf.def=def;
 uf.t=linspace(0,.5,2048)';  % time vector
 uf.u0=uf.t*0;uf.u0(find(uf.t<=1e-4))=1;  % ch1 (input =impact 0.1 ms);
 uf.window='None';  uf.noise=0; uf.filt=[];
 uf.sys=nor2ss(def,damp,426.02,1976.02,'Hz acc'); % State space model

Run the script above. Questions:

End of lab work 2

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