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The resulting mode shapes are defined as continuous functions; this is advantageous as they can be directly used in the second approach, i.e., the classic modal-interaction approach in order to obtain the coupled equations of the system.
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The resulting modes shapes were very similar.
This is because the draft pads housed in the draft gear have their own individual behaviour which cumulatively results in different mode shapes of the draft gear.
At first, the initial shape imperfections are modeled using the buckling mode shapes resulting from an eigenvalue buckling analysis.
On the other hand, incomplete instrumentation of the monitored system results in measured mode shapes which are incomplete and may lead to non-unique identification results.
Table 9 Results of mode shape angle in China Southern Power Grid Location Mode Frequency (Hz) Angle (rad) Anshun Mode I 0.677 3.621 Mode II 0.484 0.122 Gaopo Mode I 0.685 3.370 Mode II 0.479 −0.310 Xingren Mode I 0.693 3.102 Mode II 0.478 −0.176 Luodong Mode I Mode II 0.490 3.555 Luoiping Mode I 0.659 0.000 Mode II 0.471 0.000 Figure 9 Results of mode shape angle in China Southern Power Grid.
Exact natural frequencies and Jacobi polynomials as exact mode shapes, which result directly from eigenvalues and eigenfunctions of eigenvalue singular problems of classical orthogonal polynomials, are reported for these classes.
In both cases, the results (natural frequencies and mode shapes) are also found using a finite element (FE) solution approach.
Results for natural frequencies, mode shapes and critical buckling loads for intact and damaged plates are compared.
The obtained nonlocal nonlinear frequencies of the nanobeam are first validated based on published analytical results that use linear mode shapes.
Numerical results for frequencies and mode shapes are presented for various boundary conditions and mode numbers for a wide range of values of the size, thicknesswise and spanwise location of the delamination.
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