Numerical Determination of Minimum Mass Structures with Specified Natural Frequencies

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...

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Bibliographic Details
Main Authors: Miele,A, Mangiavacchi,A, Mohanty,B P, Wu,A K
Format: Report
Language:English
Subjects:
ALGORITHMS
AXES
CANTILEVER BEAMS
COMPUTATIONS
Constraints
CONVERGENCE
DYNAMIC RESPONSE
FREQUENCY RESPONSE
Mechanics
NUMERICAL ANALYSIS
OPTIMIZATION
PE61102F
RESONANT FREQUENCY
Structural Engineering and Building Technology
VIBRATION
WEIGHT REDUCTION
WUAFOSR2304A3
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Summary: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 pi/2. (Author)