Structural Synthesis for Prescribed Target Natural Frequencies and Mode Shapes

Table 16

Sequential optimization iteration history (Case  3).

(a)

Iter	𝑝	𝑞	𝑀 (kg)	Max 𝑔𝜆	Max 𝑔𝜇
0	0.9	1.1	108.75	2.08𝐸−01	2.08𝐸−01
1	0.9	1.1	23.03	4.95𝐸−08	−4.44𝐸−02
2	0.95	1.05	24.03	1.59𝐸−08	−2.70𝐸−12
3	0.97	1.03	186.09	1.94𝐸−08	−7.50𝐸−10

(b)

Iter	ℎ; (m)	𝑚1; (kg)	𝑚2; (kg)	𝑚3; (kg)	𝑚4; (kg)	𝑚5; (kg)	∑𝑚𝑗; (kg)
0	0.0500	30.0	30.0	10.0	10.0	10.0	90.0
1	0.0300	4.46	0.00	2.87	0.000	4.45	11.78
2	0.0300	5.58	0.00	3.12	0.000	4.08	12.78
3	0.0606	74.21	0.00	37.31	11.64	40.23	163.38