An Optimal Design Problem in Wave Propagation

J. C. Bellido () and A. Donoso
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J. C. Bellido: Universidad de Castilla-La Mancha
A. Donoso: Technical University of Denmark

Journal of Optimization Theory and Applications, 2007, vol. 134, issue 2, No 11, 339-352

Abstract: Abstract We consider an optimal design problem in wave propagation proposed in Sigmund and Jensen (Roy. Soc. Lond. Philos. Trans. Ser. A 361:1001–1019, 2003) in the one-dimensional situation: Given two materials at our disposal with different elastic Young modulus and different density, the problem consists of finding the best distributions of the two initial materials in a rod in order to minimize the vibration energy in the structure under periodic loading of driving frequency Ω. We comment on relaxation and optimality conditions, and perform numerical simulations of the optimal configurations. We prove also the existence of classical solutions in certain cases.

Keywords: Optimal design; Wave propagation; Classical solutions (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10957-007-9260-7

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