Wuhan University of Technology13.2 Fundamental mode analysis(1)Vref(v()(1)= w v(1) = v(0),(0)Ukwi-.(0)(0)UklUkiuminmaxmv(owimv(1)13-6
13-6 Wuhan University of Technology 13.2 Fundamental mode analysis
Wuhan University of Technology13.2 Fundamental mode analysis11SDmax(v(s-1)1max(v(s))max(v(s))13-7
13-7 Wuhan University of Technology 13.2 Fundamental mode analysis
Wuhan University of Technology13.3 Proof of convergenceThattheStodolaiterationprocessmustconvergetothefirstmodeshape,ingeneral, canbedemonstrated byrecognizingthat itessentially involvescomputing the inertial forces corresponding to any assumed shape, thencomputingthedeflectionsresultingfromthoseforces,thencomputingtheinertialforcesduetothecomputeddeflections,etc.Theconceptisillustrated in Fig. 131 and explained mathematically in the followingparagraph.13-8
13-8 Wuhan University of Technology 13.3 Proof of convergence That the Stodola iteration process must converge to the firstmode shape, in general, can be demonstrated by recognizing that it essentially involves computing the inertial forces corresponding to any assumed shape, then computing the deflections resulting from those forces, then computing the inertial forces due to the computed deflections, etc. The concept is illustrated in Fig. 131 and explained mathematically in the following paragraph