The following quantities are presented in a table of dynamic analysis results.
- Eigenvalue
- Eigenvectors
- Frequency
- Pulsation
- Period
- Precision. Calculation accuracy determined for individual methods used in the program in the final stage of calculations according to the following formulas.
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PCG, PCG deflection |
Equation of eigenproblem: K Vi - λ B Vi = 0 residual vector: : ri = K Vi - λi B Vi  |
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Iterative solver, Lanczos method |
Equation of eigenproblem: K Vi - λ B Vi = 0 residual vector: ri = K Vi - λi B Vi  |
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Direct solver |
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Precision should not be confused with tolerance determined in the Modal Analysis Parameters dialog. Tolerance is defined according to 
and is calculated for each iteration. The final accuracy of calculations is determined in the final stage of structure calculations. An increase of calculation accuracy can be obtained through decreasing the tolerance or increasing an iteration number.
- Damping - Damping for a considered mode.
- Energy - Structure potential energy relating to a deformed structure for a considered structure.
- Average participation coefficient - An average coefficient of the values of spectral participation coefficients for individual directions. It is defined according to one of the following formulas (selected in the Job Preferences dialog).
Sum of absolute values -
Square root of the sum of squares -
Sums of Masses
- Current . Participation masses expressed in percentages for a current vibration mode.
- Relative. Sums of participation masses expressed in percentages for the first to the current vibration mode.
- Total. Total sums of participation masses.
- Participation coefficients. Modal participation coefficients for each degree of freedom. The participation coefficients are defined as follows.
for a given mode, i=1, 2, …, ndir (number of directions).
where
D - Unit vector defined as follows.
D(j) = 1.0 if "j" corresponds to i-th degree of freedom
D(j) = 0.0 if j ≠ i,
V Eigenform vector "i" normalized in the way so that VT M V = 1.0
Spectral Coefficients
- Spectral coefficient. Spectral excitation multiplier (the value of the accelerating excitation spectrum).
- Spectral participation coefficient. Coefficient obtained by multiplying the appropriate components of participation coefficients' vector and a direction vector.
If: the participation coefficients (γx, γy, γz) and the direction vector (x, y, z), then spectral participation coefficients are defined according to the following formula.
- Spectral mode coefficient. Spectral mode coefficients are the product of a spectral coefficient and appropriate spectral participation coefficient.
For Eurocode 8 and French seismic code PS92 you can display results of seismic calculations by selecting the T j /T i period ratios and the T j /T i limit.
These results are helpful when choosing a quadratic combination of the eigenvibration mode. Depending on the T j /T i ratio, the line with the last eigenvibration mode for a given case, in the columns 'T j /T i ' and 'T j /T i limit', shows the suggested quadratic combination of the eigenvibration mode. If the ratio value for at least one mode of a given case exceeds the value determined by the limit, then CQC combination should be used, if all values of the T j /T i ratio are less than the T j /T i limit - the SRSS combination.
The table with dynamic analysis results may present as follows.
Tj/Ti period ratios (Ti - period of the analyzed eigenvibration mode, Tj period of the j-th eigenvibration mode where j = i + 1).
T j /T i limit according to the following.
Point 6.6.2.3 of the PS92 code from the formula
100*ζi - Absolute damping value for the analyzed eigenvibration mode.
100*ζj - Absolute, maximum damping value for the analyzed case.
Point 3.3.3.2 of the EC8 code (a constant value for all eigenvibration modes that equals 0.9).