Homogenization and Control of Lattice Structures

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  • Homogenization and Control of Lattice Structures Book Detail

  • Author :
  • Release Date : 1985
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  • Pages : 40
  • ISBN 13 :
  • File Size : 86,86 MB
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Homogenization and Control of Lattice Structures by PDF Summary

Book Description: Under certain natural conditions the dynamics of large, low-mass lattice structures with a regular infrastructure are well approximated by the dynamics of continua (e.g., trusses may be modeled by beam equations). Using a technique from the mathematics of asymptotic analysis called "homogenization," the author shows how such approximations may be derived in a systematic way that avoids errors made using "direct" averaging methods. He also develops a model for the combined problem of homogenization and control of vibrations in lattice structures, and presents some preliminary analyses of this problem. In section 2 he gives an example derived from Bensoussan, Lions, and Papanicolaou (1978) illustrating some of the subtleties of homogenization, particularly in the context of control problems. In section 3 he derives a homogenized representation for the dynamics of a lattice structure undergoing transverse deflections. He shows that the behavior of the lattice is well approximated by the Timenshenko beam equation, and that this equation arises naturally as the limit of the lattice dynamics when the density of the lattice structure goes to infinity in a well-defined way. The problem of vibration control of a lattice is posed and discussed in section 4. In section 5, he derives a diffusion approximation for the thermal conductivity of a one-dimensional lattice structure. This property is useful in analyzing new materials for large space structures. An operational calculus for homogenization is sketched in the Appendix.

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Dynamics of Lattice Materials

Dynamics of Lattice Materials

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Provides a comprehensive introduction to the dynamic response of lattice materials, covering the fundamental theory and applications in engineering practice Off