COMMENTS ON “IDENTIFICATION OF MULTI-DEGREE-OF-FREEDOM NON-LINEAR SYSTEMS UNDER RANDOM EXCITATIONS BY THE ‘REVERSE PATH’ SPECTRAL METHOD”
✍ Scribed by J.A. FITZPATRICK; H.J. RICE
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 65 KB
- Volume
- 237
- Category
- Article
- ISSN
- 0022-460X
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✦ Synopsis
The authors of reference [1] are to be commended for implementing the &&reverse path'' non-linear spectral analysis method for identifying the constituents elements of simulated three-and "ve-degree-of-freedom (d.o.f.) non-linear systems. However, we feel that the paper requires some comment as to origins of the analysis methods used and the originality of their method. In the "rst instance, the attribution of the &&reverse path'' modelling technique to Bendat [2] is misleading. The actual technique for remodelling single-d.o.f. systems in this way was "rst proposed by Rice and Fitzpatrick [3] and has since been applied to a number of systems using both simulated data [4,5] and actual experimental data from a system with a linear element and four non-linear elements [5,6]. This work was, in fact, referred to by Bendat in his book on non-linear system identi"cation [2].
The second issue is that the authors refer incorrectly to a paper by Rice and Fitzpatrick [7] which extended the original non-linear spectral analysis (or &&reverse path'') method to multi-d.o.f. systems. The authors state: &&A similar approach has been used for the identi"cation of two-d.o.f. non-linear systems where each response location is considered as a single d.o.f. mechanical oscillator''. This is incorrect as the complete coupled system was considered and the identi"cation was for this. The approach of Richards and Singh is identical to our method using essentially, a force balance and the various block diagrams in their paper are similar to those already published. In addition, the equations given by us as (1), ( 2) and (3) are identical to those used by Richards and Singh. Our equations are completely general and make no assumption about the actual location of the non-linearities. The only requirement is that the analysis is for discrete multi-d.o.f. con"gurations. Indeed, whereas the method proposed by Rice and Fitzpatrick does not make any a priori assumptions about the locations of the non-linearities, that of Richards and Singh requires that the locations of the non-linearities are known in order to accommodate local linear sub-models. Identi"cation of the location of non-linearities in real structures is, of course, a further issue which has been addressed, for example, by Xu and Rice [8].