Explicit solution for a vibrating bar with viscous boundaries and internal damper

DOI10.1007/s10665-011-9513-1zbMath1276.74022arXiv1110.5674OpenAlexW2047927092MaRDI QIDQ383406

Vojin Jovanovic, Sergiy Koshkin

Publication date: 4 December 2013

Published in: Journal of Engineering Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1110.5674

zbMATH Keywords

longitudinal vibrationsmodal decompositionvibratory responseviscous boundary conditions

Mathematics Subject Classification ID

Vibrations in dynamical problems in solid mechanics (74H45) Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Fundamental solutions, Green's function methods, etc. for initial value and initial-boundary value problems involving PDEs (65M80)

Related Items (2)

A Fourier series solution for the longitudinal vibrations of a bar with viscous boundary conditions at each end ⋮ D'Alembert sums for a vibrating bar with viscous ends

Cites Work

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• Boundary control, quiet boundaries, super-stability and super-instability
• The \(n\)-fold basis property of the characteristic functions of certain regular boundary-value problems
• Complex eigensolution for longitudinally vibrating bars with a viscously damped boundary
• A Closed Form Solution of a Longitudinal Bar With a Viscous Boundary Condition
• Vibrations of a shallow cable with a viscous damper

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