Analytic Solution for Nonlinear Multimode Beam Vibration Using a Modified Harmonic Balance Approach and Vieta’s Substitution

Table 2

(a) Modal contributions for various excitation frequencies, . (b) Modal contributions for various excitation frequencies, .

(a)

Normalized modal contribution	= 1	7.5	15	25
1st mode	99.94	99.88	99.67	99.54
2nd mode	0.05	0.10	0.29	0.40
3rd mode	0.01	0.01	0.04	0.06

(b)

Normalized modal contribution
1st mode	99.59	99.78	96.03	78.20
2nd mode	0.36	0.19	3.56	20.25
3rd mode	0.05	0.03	0.42	1.55