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Numerical determination of minimum mass structures with specified natural frequencies
Author(s) -
Miele A.,
Mangiavacchi A.,
Mohanty B. P.,
Wu A. K.
Publication year - 1978
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620130205
Subject(s) - beam (structure) , reduction (mathematics) , mathematics , vibration , constant (computer programming) , natural frequency , cantilever , mathematical analysis , value (mathematics) , minimum weight , physics , geometry , optics , materials science , statistics , acoustics , computer science , composite material , programming language
The problem of 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 β 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 β. This weight reduction is negligible for β → 0, is 11.3 per cent for β = 1, is 55.3 per cent for β = 1.4, and approaches 100 per cent for β → π/2.