The two phase drum with the deepest bass note

DOI10.1007/BF03167141zbMath0755.35029OpenAlexW2025817620MaRDI QIDQ1179779

Steven J. Cox

Publication date: 27 June 1992

Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf03167141

zbMATH Keywords

algorithmoptimal designgeometric conditionsSteiner symmetrizationvolume fractionsanalytic Jordan curvebound the length of this interfaceinterface separating the two materialsminimum least eigenvalueoptimal distribution of masstwo homogeneous materials of different density

Mathematics Subject Classification ID

Plates (74K20) Optimization of other properties in solid mechanics (74P10) Optimization problems in solid mechanics (74P99) Variational methods for second-order elliptic equations (35J20)

Related Items

Extremal eigenvalue problems for two-phase conductors, A way of updating the density function for the design of the drum, The rate at which energy decays in a damped String, Minimizing eigenvalues for inhomogeneous rods and plates, A two-grid binary level set method for eigenvalue optimization, Quantitative Stability for Eigenvalues of Schrödinger Operator, Quantitative Bathtub Principle, and Application to the Turnpike Property for a Bilinear Optimal Control Problem, Extremal spectral gaps for periodic Schrödinger operators, Efficient rearrangement algorithms for shape optimization on elliptic eigenvalue problems, Principal eigenvalue minimization for an elliptic problem with indefinite weight and Robin boundary conditions, Laplace eigenvalues on regular polygons: a series in \(1/N\), Linear convergence of a rearrangement method for the one-dimensional Poisson equation, The optimal design of tubular structures, Minimization of the First Nonzero Eigenvalue Problem for Two-Phase Conductors with Neumann Boundary Conditions, Extremal rearrangement problems involving Poisson's equation with Robin boundary conditions, Level set methods for optimization problems involving geometry and constraints. I: Frequencies of a two-density inhomogeneous drum, Optimal design of turbines with an attached mass, Minimization of the Principal Eigenvalue Under Neumann Boundary Conditions, Singular limits of sign-changing weighted eigenproblems, Finite element approximation to the extremal eigenvalue problem for inhomogenous materials

Uses Software

• eigs
• IRAM

Cites Work

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• On certain problems on the maximum and minimum of characteristic values and on the Lyapunov zones of stability