(Available for: Spectrum and Time History)
Specifies the inclusion of a correction representing the contribution of higher order modes not explicitly extracted for the modal/dynamic response, providing greater accuracy without additional calculation time. Select Y (for yes) or N (for no).
During spectrum (either seismic or force spectrum) or time history analyses, the response of a system under a dynamic load is determined by superposition of modal results. One of the advantages of this type of modal analysis is that only a limited number of modes are excited and need to be included in the analysis. The drawback to this method is that although displacements may be obtained with good accuracy using only a few of the lowest frequency modes, the force, reaction, and stress results may require extraction of far more modes (possibly far into the rigid range) before acceptable accuracy is attained.
This option automatically calculates the net (in-phase) contribution of all non-extracted modes and combines it with the modal contributions, avoiding the long calculation time and excessively conservative summation methods. For more information, see Inclusion of Missing Mass Correction.
Use Included Missing Mass Components on the Control Parameters tab as an alternative method of ensuring that sufficient modes are considered in the dynamic model. This report is compiled for all spectrum and time history shock cases, whether missing mass is to be included or not. It displays the percentage of system mass along each of the three global axes and the percentage of total force which has been captured by the extracted modes. For more information, see Include Missing Mass Components.
The percentage of system mass active along each of the three global axes (X-, Y-, and Z-) is calculated by summing the modal mass (corresponding to the appropriate directional degree-of-freedom) attributed to the extracted modes and dividing that sum by the sum of the system mass acting in the same direction:
Summed over i = 1 to n, by 6 (X-direction degrees of freedom):
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% Active Massx |
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Summed over 1 = 2 to n, by 6 (Y-direction degrees of freedom):
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% Active MassY |
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Summed over 1 = 3 to n, by 6(Z-direction degrees of freedom):
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% Active Massz |
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Where:
Me = vector (by degree-of-freedom) of sum (over all extracted modes) of effective modal masses
M = vector corresponding to main diagonal of system mass matrix
The maximum possible percentage of active mass that is theoretically possible is 100%, with 90-95% usually indicating that enough modes have been extracted to provide a good dynamic model.
The percentage of active force is calculated by the following factors:
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Separately summing the components of the effective force acting along each of the three directional degrees-of-freedom
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Combining them algebraically
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Doing the same for the applied load
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Taking the ratio of the effective load divided by the applied load
Examples
Summed over i = 1 to n, by 6 (X - Direction degrees of freedom):
Fex = SFe[i]
Fx = SF[i]
Summed over i = 2 to n, by 6 (Y - Direction degrees of freedom):
Fey = SFe[i]
Fy = SF[i]
Summed over i = 3 to n, by 6 (Z - Direction degrees of freedom):
Fez = SFe[i]
Fz = SF[i]
Where:
FeX, FeY, FeZ = effective force (allocated to extracted modes) acting along the global X-, Y-, and Z-axes, respectively
Fr = vector of effective forces (allocated to extracted modes)
FX, FY, FZ = total system forces acting along the global X-, Y-, and Z-axes, respectively
F = vector of total system forces
The maximum possible percentage which is theoretically possible for this value is also 100%. In practice it may be higher, indicating an uneven distribution of the load and mass in the system model. There is nothing inherently wrong with an analysis where the included force exceeds 100%. If the missing mass correction is included, the modal loadings are adjusted to automatically conform to the applied loading. The percentage of included force can often be brought under 100% by extracting a few more modes. At other times, the situation can be remedied by improving the dynamic model through a finer element mesh, or, more importantly, equalizing the mass point spacing in the vicinity of the load.