Exact solution of the Mindlin-Herrmann model for longitudinal vibration of an isotropic rod

DOI10.1007/s10665-015-9827-5zbMath1360.35275OpenAlexW1919963362MaRDI QIDQ525485

H. M. Tenkam, Roumen Anguelov, I. A. Fedotov, M. Yu. Shatalov

Publication date: 4 May 2017

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

Full work available at URL: https://doi.org/10.1007/s10665-015-9827-5

zbMATH Keywords

Green's functionself-adjoint operatoreigenfunction orthogonalitieslongitudinal-transversal vibrationMindlin-Herrmann model

Mathematics Subject Classification ID

Vibrations in dynamical problems in solid mechanics (74H45) Fundamental solutions to PDEs (35A08) PDEs in connection with mechanics of deformable solids (35Q74) PDEs in connection with mechanics of particles and systems of particles (35Q70) Initial-boundary value problems for second-order hyperbolic systems (35L53)

Related Items (2)

Internal inertia gradient effect on two mode magneto‐elastic wave propagation ⋮ Dynamic stiffness method for exact longitudinal free vibration of rods and trusses using simple and advanced theories

Cites Work

• Theory of free and forced vibrations of a rigid rod based on the Rayleigh model
• Another approach to vibration analysis of stepped structures
• Higher-order rod approximations for the propagation of longitudinal stress waves in elastic bars
• On Extensional Oscillations and Waves in Elastic Rods
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