46 3. SYSTEMATIC MODAL TEST PLANNING
Table 3.2: Selected modes of the example shell structure
Mode Body X-Bending Y-Bending Z-Axial n=0 BulgeBreathing Torsion Skirt Dome 1 Dome 2Shell 1 Shell 2 Skirt Dome 1 Dome 2Shell 1 Shell 2Freq (Hz)
Body & Breathing
Kinetic Energies (%)
Body Mode Kinetic Energy Types (%) Component Kinetic Energies (%) Component Strain Energies (%)
6. Contrasting kinetic and strain energy distributions in fundamental bending, axial, torsion
modes.
Regarding the sixth observation, the contrasting kinetic and strain energy distributions
(i.e., dominant kinetic energy toward the top, dominant strain energy toward the foundation)
conform to fundamental mechanical expectations.
Graphical illustrations indicating the character of the fundamental (Y ) bending mode and
the lowest frequency shell breathing mode are provided in Figure 3.8. Kinetic (KE) and strain
or potential energy (PE) distributions are indicated in “pie” format.
3.1.4 CLOSURE
Comprehensive understanding of a structure’s modal characteristics employing modal kinetic
and strain energy metrics has been demonstrated with two key illustrative examples, namely:
(a) the International Space Station P5 test article, which has benefitted from an end-to-end
integrated test-analysis project and (b) the axisymmetric shell finite element model, which ad-
dresses aspects of the “many modes” problem.
Unpacking of fundamental orthogonality relationships mathematically yields modal ki-
netic and strain energy distributions. Physically meaningful distributions of modal kinetic and
strain energy distributions occur only if component mass and stiffness matrices are subdivided
into constituent, decoupled partitions; otherwise the assembled system kinetic and strain energy
distributions must be identical (a mathematical consequence of the algebraic eigenvalue prob-
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