Structural Synthesis for Prescribed Target Natural Frequencies and Mode Shapes

Table 6

Sequential optimization iteration history (Case  1).

(a)

Iter.	𝑝	𝑞	𝑀 (kg)	Max 𝑔𝜆	Max 𝑔𝜇
0	0.5	2	1125.	5.4𝐸−01	4.3𝐸−01
1	0.5	2	23.59	−3.9𝐸−01	1.3𝐸−06
2	0.95	1.1	77.70	5.9𝐸−08	2.3𝐸−08
3	0.99	1.01	130.31	4.2𝐸−08	5.4𝐸−10
4	0.999	1.001	167.60	2.5𝐸−09	4.9𝐸−09
5	0.9999	1.0001	188.46	8.7𝐸−10	9.0𝐸−10

(b)

Iter.	ℎ; (m)	𝑚1; (kg)	𝑚2; (kg)	𝑚3; (kg)	𝑚4; (kg)	𝑚5; (kg)	∑𝑚𝑗; (kg)
0	0.2000	200	200	200	200	200	1000
1	0.038	0.00	0.00	0.00	0.00	0.00	0.00
2	0.058	18.31	1.01	17.78	4.49	0.00	41.59
3	0.067	46.32	14.34	24.54	3.46	0.00	88.67
4	0.072	66.70	27.11	21.76	7.01	0.00	122.58
5	0.075	77.61	34.07	20.11	9.89	0.00	141.68