Chladni Figures and the Tacoma Bridge: Motivating PDE Eigenvalue Problems via Vibrating Plates

DOI10.1137/10081931XzbMath1251.65155MaRDI QIDQ2913271

Felix Kwok, Martin J. Gander

Publication date: 26 September 2012

Published in: SIAM Review (Search for Journal in Brave)

zbMATH Keywords

vibrating platesnumerical exampleseigenvaluesRitz methodfinite difference discretizationbiharmonic operatorQR-algorithmChladni figureslarge scale sparse matrixspectral discretizationsTacoma Bridge

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Boundary value problems for higher-order elliptic equations (35J40) Estimates of eigenvalues in context of PDEs (35P15) Finite difference methods for boundary value problems involving PDEs (65N06) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items (10)

On the Definition of Dirichlet and Neumann Conditions for the Biharmonic Equation and Its Impact on Associated Schwarz Methods ⋮ Random nodal lengths and Wiener chaos ⋮ Direct optimization of BPX preconditioners ⋮ Computation and Applications of Mathieu Functions: A Historical Perspective ⋮ Semiclassical bounds for spectra of biharmonic operators ⋮ A review and study on Ritz method admissible functions with emphasis on buckling and free vibration of isotropic and anisotropic beams and plates ⋮ Stochastic Models for Chladni Figures ⋮ Minimization of inhomogeneous biharmonic eigenvalue problems ⋮ Numerical methods for spectral theory ⋮ Is There More Than One Dirichlet--Neumann Algorithm for the Biharmonic Problem?

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