4.2 KINETIC ENERGY AND STRAIN ENERGY The distributions of kinetic and strain energies in one particular mode are the following respective term-by term products: ^ ` > @ ^ ^ ` ` ^ `n n n KE M ) ) , ¦ DOF i in TOT n KE KE 1 , 1 (10) ^ ` > @ ^ ^ ` ` ^ `n n n SE K ) ) , n DOF i in TOT n SE SE O ¦ 1 , (11) The individual terms in each of these “energy” vectors are directly associated with the dynamic system degrees of freedom. As such, they provide appropriately weighted metrics for kinetic and strain energy distributions that are not indicated by the geometric modes shape (e.g., “heavier” degrees of freedom have greater kinetic energy than “lighter” degrees of freedom with equivalent modal displacements). Further insight into the character of individual modes is gained by summations of subgroups. 4.3 CLASSIFICATION BY ENERGY ACTIVITY DIRECTION Modal kinetic and strain energy grouped sums, partitioned by global direction yield the direction of overall modal activity for a particular mode. These metrics are not weighted by level of boundary reaction (as is the case for modal effective mass). ^ ` ^`^`^`^ `^`^` ¦ ¦ ¦ ¦ ¦ ¦ RZ n RY n RX n TZ n TY n TX n n KE KE KE KE KE KE KE , , , , , (12) ^ ` ^`^`^`^`^`^` ¦ ¦ ¦ ¦ ¦ ¦ RZ n RY n RX n TZ n TY n TX n n SE SE SE SE SE SE SE , , , , , 4.4 CLASSIFICATION BY COMPONENT ENERGY DISTRIBUTION Modal kinetic and strain energy grouped sums, partitioned by subsystem component yield the distribution of component activity for a particular mode. It should be noted that the component kinetic and strain energies are not necessarily distributed in the same manner as one another. ^ ` ^ ` ^ ` ^ ` ,....... , , 3 2 1 ¦ ¦ ¦ n n n n KE KE KE KE (13) ^ ` ^ ` ^ ` ^ ` ,........ , , 3 2 1 ¦ ¦ ¦ n n n n SE SE SE SE 4.5 ILLUSTRATIVE EXAMPLE MODAL METRICS Classification of system modes for the illustrative example shell structure in accordance with energy distributions and modal effective mass is provided for a selected subset of modes in Table 2 Table 2: Selected Modes of the Example Shell Structure (Metrics>1% shown) The general characteristics of the first two overall “Y” and “X” bending modes are indicated by directional kinetic energies and modal effective masses. Moreover, the general increase in component kinetic energies for these modes with height above the base indicates overall activity distribution. Distribution of interior structural loading for the first two bending modes correctly indicates highest loads occurring in the skirt. Characteristics of the other overall body modes (11, 14, 15 24) are also clearly revealed by kinetic energy, strain energy and modal effective mass distributions. 371
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