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Modal shapes for the TPM at cantilever position are shown in Figure 11.
Eigenvalues for a large number of plate aspect ratios are provided, as well as some modal shapes for both symmetric and antisymmetric vibration modes.
The stiffness and frequency dependent inertia properties of a square element, given in Appendices for both a non-conforming and a conforming element, are used to predict the vibration frequencies and modal shapes for a square plate subjected to four sets of boundary conditions.
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Summarizing, the procedure adopted was the following: Such that δ z,r is the vertical displacement measured by the geometric survey, and δ z,mode is the one extracted from modal shape for the corresponding nodes; we run the ratios δ z,r /δ z,mode.
The influence of the mass magnitude on the natural frequencies and modal shapes of vibration is studied for a boron-epoxy plate and also in the case of a generic anisotropic material.
Local models are only needed to be run under linear elastic conditions for the selected modal shapes of the structure, being the local time history of fatigue damage variable computed by modal superposition for each loading event.
Local models are only required to be run only for the selected modal shapes of the structure, the local time history of fatigue damage variable being reconstructed by modal superposition for each loading event.
Results are then extended to perform a detailed modal analysis, which suggests peculiar scaling laws for the natural frequencies and modal shapes of the structure.
c Third-order modal shapes of catenary.
d Forth-order modal shapes of catenary.
a First-order modal shapes of catenary.
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