Mixed problems for the equation of longitudinal vibrations of a heterogeneous rod and for the equation of transverse vibrations of a heterogeneous string consisting of two segments with different densities and elasticities
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Publication:416947
DOI10.1134/S1064562412010334zbMath1238.35155MaRDI QIDQ416947
Publication date: 10 May 2012
Published in: Doklady Mathematics (Search for Journal in Brave)
Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Vibrations in dynamical problems in solid mechanics (74H45) Weak solutions to PDEs (35D30) PDEs in connection with mechanics of deformable solids (35Q74)
Related Items (3)
Boundary control of some distributed heterogeneous vibrating system with given states at intermediate time instants ⋮ The Dirichlet problem for the higher order composite type equations with discontinuous coefficients ⋮ The problem of boundary control of displacement at two ends by the process of oscillation of a rod consisting of two sections of different density and elasticity
Cites Work
- Reduction of the vibrations of an initially stationary rod consisting of two different segments to an arbitrary state
- Optimization of the boundary displacement control of vibrations of a rod consisting of two dissimilar parts
- Optimization of elasticity-induced boundary control for the vibrations of a rod consisting of two different segments
- An analytic form of optimal boundary controls of longitudinal oscillations of a rod consisting of two fragments with different densities and elasticities but equal impedances
- Longitudinal vibrations of a rod consisting of two segments with different densities and elasticity coefficients but with identical travel times on each segment
- Mixed problems describing longitudinal oscillations of a rod consisting of two segments with different densities and different elasticities but equal impedances
- Two-endpoint boundary control of vibrations described by a finite-energy generalized solution of the wave equation
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