Existence and location of eigenvalues for fluid-solid structures

DOI10.1016/0045-7825(89)90078-9zbMath0734.73063OpenAlexW2058308883MaRDI QIDQ811207

J. Planchard, Muthusamy Vanninathan, Carlos Conca

Publication date: 1989

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0045-7825(89)90078-9

zbMATH Keywords

homotopytube bundlebounded, multiply connected regionbounds for the eigenvaluescharacteristic values of a linear, compact, selfadjoint operatorcontinuity argumentsgeneral theorems for compact operatorsinviscid compressible fluidlinear non-standard eigenvalue problem for the Laplacian

Mathematics Subject Classification ID

Spectral theory and eigenvalue problems for partial differential equations (35P99) Vibrations in dynamical problems in solid mechanics (74H45) Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) (74F10)

Related Items (12)

A maxmin principle for nonlinear eigenvalue problems with application to a rational spectral problem in fluid-solid vibration. ⋮ Rational Krylov for nonlinear eigenproblems, an iterative projection method. ⋮ Solving large-scale finite element nonlinear eigenvalue problems by resolvent sampling based Rayleigh-Ritz method ⋮ Added mass and damping in fluid-structure interaction ⋮ Generalized Fiedler Pencils for Rational Matrix Functions ⋮ Homogenization and Bloch wave method for fluid tube bundle interaction ⋮ A successive quadratic approximations method for nonlinear eigenvalue problems ⋮ A quadratic eigenvalue problem involving Stokes equations ⋮ Nonlinear eigenvalue problems: a challenge for modern eigenvalue methods ⋮ Linearizations for Rational Matrix Functions and Rosenbrock System Polynomials ⋮ Resolvent sampling based Rayleigh-Ritz method for large-scale nonlinear eigenvalue problems ⋮ Sensitivity Analysis of Nonlinear Eigenproblems

Cites Work

• Global behaviour of large elastic tube bundles immersed in a fluid
• Eigenfrequencies of a tube bundle immersed in a fluid
• A spectral problem arising in fluid-solid structures
• Eigenfrequencies of a tube bundle placed in a confined fluid
• The behavior of eigenvalues and singular values under perturbations of restricted rank
• Natural frequencies of tube bundle in an incompressible fluid
• Free vibration of clusters of cylinders in liquid-filled channels
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