31.4 Calculate Rayleigh Damping Coefficients

With RAYLEI commands you may calculate the Rayleigh damping coefficients a and b from two frequencies to set up the damping matrices C according to

C = a M + b K (31.3)

The frequencies are specified explicitly or as eigenfrequencies either by their mode numbers or by the cumulative effective mass contribution in global directions.

    (syntax)

OFF

suppresses the calculation of Rayleigh damping coefficients.

FREQUE EXPLIC

(f2 > f1 > 0 )specifies the explicit frequencies f1 and f2 used for calculating the Rayleigh damping coefficients.

MODES NUMBER

(m2 > m1 > 0 )specifies that the frequecies used for calculating the Rayleigh damping coefficients are the eigenfrequencies of modes m1 and m2.

EFFMAS PERCEN

(effx $\ge$ 0 ) (effy $\ge$ 0 ) (effz $\ge$ 0 ) [EFFMAS PERCEN 90. 90. 90.] specifies that the eigenfrequencies used for calculating the Rayleigh damping coefficients, are specified by the cumulative effective mass contribution in the global XYZ directions as displayed for a free vibration eigenvalue analsysis [§31.5.5]. effx, effy, effz are the cumulative effective mass percentages in global X , Y , and Z direction respectively. In case the requested cumulative effective mass percentages cannot be reached for the calculated number of eigenfrequencies, the second frequency is the highest calculeted eigenfrequency. The first frequency is always the calculated first non-zero eigenfrequency.

DAMPIN

(c1 $\ge$ 0 ) (c2 $\ge$ 0 ) [c1=0.05] [c2=0.05] specifies the damping coefficients for the two frequencies indicated by either the FREQUE, MODES, or EFFMAS command. Values c1 and c2 are the damping coefficients in parts of the critical damping factor c_crit [Eq.(48.5)]; a value of 0.05 indicates 5%. If only one factor c1 is specified, then the damping is the same for both frequencies of the system.

Note, that if one of the damping ratios is zero, negative damping occurs for specific frequency ranges, which implies that energy is added to the system.