Identification of the dynamic characteristics of nonlinear structures

[AK] 
 ( 
based on 
(5-26). 
Due
to the specific modeshape of the first mode, the stiffness error introduced between
coordinates 
has been totally missed out as shown in 
while it is
located as shown in 
when FRF data are used.
exact stiffness errors (a)
location using mode (modal data) 
location using FRF data round mode 1 (c)
Fig.5.27 Comparison of Modelling Error Location Using Modal and FRF Data
5.7 
CONCLUSIONS
Most mechanical structures are nonlinear to some extent and the nonlinearites are usually
localised. The ability to locate a structure’s localised nonlinearity has some important
engineering applications. In this chapter, a nonlinearity location technique has been
developed based on the correlation between an analytical model of the structure (which
contains modelling errors) and modal test data which are measured at different response
levels. In the practical case where the measured coordinates are incomplete, an
interpolation technique to estimate the unmeasured coordinates based on the analytical
model has been discussed. The sensitivity of certain modes to localised structural
nonlinearity has been established. It is recommended that a sensitive mode should always
be used in the location process so that reliable location can be obtained. Numerical case
studies have been undertaken to verify the technique developed.
To assess the practical feasibility of the location technique, an experiment was carried out.
A localised stiffness nonlinearity was simulated using a electro-dynamic shaker and

---

5
Location of Structural Nonlinearity
169
analogue computer circuit based on feed-back system control theory. The experimental
results demonstrate the practical applicability of the proposed method.
It has been shown that the location technique can be generalised when measured FRF data
are employed. Also, the relationship between nonlinearity location and modelling error
location in analytical model improvement has been examined and it can be shown that the
modelling error location method given in 
can be generalised when FRF data are
used.
The information concerning the location of structural nonlinearities on practical structures
can be used subsequently in nonlinear substructuring analysis, system failure and
malfunctioning detection and mathematical modelling of nonlinear structures.

---

5
Location of Structural Nonlinearity
170
Mode No.
1
2
3
4
5
Nat. Freq. (Hz.)
52.80
97.10
156.59
228.58
258.55
mode
shapes
0.657
0.674
0.345
0.408
0.415
0.490
0.291
0.692
0.682
-0.162
0.152
-0.274
0.547
0.150
-0.605
-0.336
-0.703
-0.134
-0.386
-0.312
-0.502
-0.245
-0.467
-0.229
0.650
-0.667
0.241
-0.579
0.232
0.569
-0.776
0.760
-0.277
0.553
-0.500
-0.172
0.274
0.448
-0.190
-0.595
0.280
-0.303
0.679
-0.779
-0.134
0.604
-0.693
0.398
-0.345
0.465
0.703
-0.7 12
-0.303
0.436
0.408
0.543
-0.303
-0.570
0.829
-0.127
0.150
0.279
-0.426
0.196
-0.513
-0.329
0.708
0.27 1
-0.700
-0.385
-0.5 12
0.264
0.523
-0.276
0.696
-0.69 1
-0.238
0.474
0.235
0.586
-0.763
-0.742
0.278
0.490
-0.565
-0.190
-0.291
-0.436
-0.141
-0.479
0.249
0.277
-0.796
-0.882
-0.199
0.606
0.682
-0.340
-0.476
0.357
Table 5.1 Measured Modal Parameters of the Frame

---