Computation of Rayleigh Damping Coefficients for the Seismic Analysis of a Hydro-Powerhouse

Table 1

Rayleigh damping coefficients obtained by different methods.

Methods		β	According to	Involved orders
Modal methods	∖	∖	Constant damping ratio: 0.07	1–80
Case	0.4053	0.0064	First and second orders	1, 2
Case	0.4709	0.0008	First and last orders	1, 80
Case	0.9553	0.0010	Optimization by least square method	1–80
Case	0.5286	0.0012	Weighted least squares, weight coefficients: 1/ωi	1–80
Case	0.4064	0.0063	Weighted least squares, weight coefficients: exp(−ωi)	1–80
Case	4.2364	0.0011	Two orders have largest mode participation masses	13, 25
Case	0.7878	0.0015	Weighted least squares, weight coefficients: mi/M	1–80