Hyperbolic and pseudo-hyperbolic equations in the theory of vibration

DOI10.1007/s00707-015-1537-6zbMath1388.74061OpenAlexW2279947089MaRDI QIDQ683565

Igor Fedotov, Julian Marais, Michael Y. Shatalov

Publication date: 8 February 2018

Published in: Acta Mechanica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00707-015-1537-6

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Vibrations in dynamical problems in solid mechanics (74H45) Pseudohyperbolic equations (35L82) PDEs in connection with mechanics of deformable solids (35Q74)

Related Items (12)

Determination of a time-dependent potential in a Rayleigh-Love equation with non-classical boundary condition ⋮ Existence of second spectrums of Timoshenko beam and Mindlin-Herrmann rod theories on the basis of atomistic studies ⋮ A residual power series method for solving pseudo hyperbolic partial differential equations with nonlocal conditions ⋮ Boundary value problems for the Rayleigh-Bishop equation in a quarter plane ⋮ Simultaneous determination of the time‐dependent potential and force terms in a fourth‐order Rayleigh–Love equation ⋮ Cauchy problem for one pseudohyperbolic system ⋮ Solutions to Rayleigh-Love equation with constant coefficients and delay forcing term ⋮ Boundary value problem for system of pseudo-hyperbolic equations of the fourth order with nonlocal condition ⋮ On solvability of the boundary value problem for one pseudohyperbolic equation ⋮ Solvability of the Cauchy problem for a pseudohyperbolic system ⋮ Dynamic stiffness method for exact longitudinal free vibration of rods and trusses using simple and advanced theories ⋮ Boundary value problems for one pseudohyperbolic equation in a quarter plane

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Longitudinal vibrations of a Rayleigh-Bishop rod
• Theory of free and forced vibrations of a rigid rod based on the Rayleigh model
• The Cauchy problem for hyperbolic equations not resolved with respect to the highest time derivative
• Pseudo-differential operators and Cauchy problem for differential equations with variable coefficients
• Mixed problems for hyperbolic equations. I: Energy inequalities
• Mixed problems for hyperbolic equations. II: Existence theorems with zero initial datas and energy inequalities with initial datas
• Axially Symmetric Waves in Elastic Rods

This page was built for publication: Hyperbolic and pseudo-hyperbolic equations in the theory of vibration