Numerical determination of minimum mass structures with specified natural frequencies

✍ Scribed by A. Miele; A. Mangiavacchi; B. P. Mohanty; A. K. Wu

• Publisher: John Wiley and Sons
• Year: 1978
• Tongue: English
• Weight: 898 KB
• Volume: 13
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620130205

✦ Synopsis

The problem qf the axial vibration of a cantilever beam is investigated both analytically and numerically.

The mass distribution that minimizes the total mass for a given value of the frequency parameter p is determined using both the sequential ordinary gradient-restoration algorithm (SOGRA) and the modified quasilinearization algorithm (MQA). Concerning the minimum value of the mass, SOGRA leads to a solution precise to at least 4 significant digits and MQA leads to a solution precise to at least 6 significant digits.

Comparison of the optimal beam (a variable-section beam) with a reference beam (a constant-section beam) shows that the weight reduction depends strongly on the frequency parameter p. This weight reduction is negligible for p +O, is 11.3 per cent for p = 1, is 55.3 per cent for p = 1.4, and approaches 100 per cent for p +n/2.