Stability and dispersion analysis of improved time discretization for simply supported prestressed Timoshenko systems. Application to the stiff piano string

DOI10.1016/j.wavemoti.2012.11.002zbMath1454.74103OpenAlexW2023681921MaRDI QIDQ1756366

Juliette Chabassier, Sebastien Imperiale

Publication date: 14 January 2019

Published in: Wave Motion (Search for Journal in Brave)

Full work available at URL: https://hal.inria.fr/hal-00757096/file/TimoshenkoTheta_SUBMITTED_2.pdf

zbMATH Keywords

stability analysisimplicit time discretizationdispersion analysisenergy techniquesprestressed Timoshenko systemtheta schemes

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Systems arising from the discretization of structural vibration problems (70J50)

Related Items (6)

An energy preserving time scheme based on the mortar element method for effective transmission conditions between fluid and solid domains in transient wave propagation problems ⋮ Construction and analysis of fourth order, energy consistent, family of explicit time discretizations for dissipative linear wave equations ⋮ Vibration of a Timoshenko beam supporting arbitrary large pre-deformation ⋮ Space/time convergence analysis of a class of conservative schemes for linear wave equations ⋮ Mathematical and Numerical Study of Transient Wave Scattering by Obstacles with a New Class of Arlequin Coupling ⋮ Conservative finite difference time domain schemes for the prestressed Timoshenko, shear and Euler-Bernoulli beam equations

Cites Work

• Energy preserving schemes for nonlinear Hamiltonian systems of wave equations: application to the vibrating piano string
• Natural frequencies and modes of a Timoshenko beam
• A conservative space-time mesh refinement method for the 1-D wave equation. I: Construction
• Elastic waves in Timoshenko beams: the ‘lost and found’ of an eigenmode
• The Shear Coefficient in Timoshenko’s Beam Theory
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