Natural frequencies of structures with uncertain but nonrandom parameters

DOI10.1007/BF02192164zbMath0836.65061MaRDI QIDQ1905941

Yanyan Li

Publication date: 23 January 1996

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

zbMATH Keywords

numerical resultsupper and lower boundsinterval matricesinterval mathematicsuncertainty modelingelastic structuregeneralized interval eigenvalue problemnatural frequencies of a structure

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Vibrations in dynamical problems in solid mechanics (74H45) Interval and finite arithmetic (65G30)

Related Items (12)

Two non-probabilistic set-theoretical models to predict the transient vibrations of cross-ply plates with uncertainty ⋮ Interval static displacement analysis for structures with interval parameters ⋮ An approximate method for the standard interval eigenvalue problem of real non-symmetric interval matrices ⋮ Semidefinite programming for dynamic steady-state analysis of structures under uncertain harmonic loads ⋮ Exact bounds for the sensitivity analysis of structures with uncertain-but-bounded parameters ⋮ The new nonprobabilistic criterion of failure for dynamical systems based on convex models ⋮ Computing eigenvalue bounds of structures with uncertain‐but‐non‐random parameters by a method based on perturbation theory ⋮ Convex model and interval analysis method to predict the effect of uncertain-but-bounded parameters on the buckling of composite structures ⋮ Computation of bounds for eigenvalues of structures with interval parameters ⋮ Determining the range of real eigenvalues for the interval generalized eigenvalue problem ⋮ Comparison between non-probabilistic interval analysis method and probabilistic approach in static response problem of structures with uncertain-but-bounded parameters ⋮ Anti-optimization technique -- a generalization of interval analysis for nonprobabilistic treatment of uncertainty

Cites Work

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• A Galerkin finite element technique for stochastic field problems
• A deterministic method to predict the effect of unknown-but-bounded elastic moduli on the buckling of composite structures
• Parametric instability of stochastic columns
• On the Probability Densities of the Output of Some Random Systems
• A necessary and sufficient condition for the stability of interval matrices
• Bound invariant Lyapunov functions: a means for enlarging the class of stabilizable uncertain systems
• Nonprobabilistic, convex-theoretic modeling of scatter in material properties
• Essay on uncertainties in elastic and viscoelastic structures: From A. M. Freudenthal's criticisms to modern convex modeling
• A necessary and sufficient condition for the positive-definiteness of interval symmetric matrices

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