Numerical Determination of Minimum Mass Structures with Specified Natural Frequencies.
RICE UNIV HOUSTON TEX AERO-ASTRONAUTICS GROUP
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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 beta 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 beta. This weight reduction is negligible for beta approaches 0, is 11.3 for beta 1, is 55.3 for beta 1.4, and approaches 100 for beta approaches pi2. Author
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