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
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Publication:845521
DOI10.1134/S1064562409060301zbMath1423.74486MaRDI QIDQ845521
P. V. Luferenko, Vladimir Il'in
Publication date: 29 January 2010
Published in: Doklady Mathematics (Search for Journal in Brave)
Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Control, switches and devices (``smart materials) in solid mechanics (74M05) Vibrations in dynamical problems in solid mechanics (74H45)
Related Items (3)
Boundary control of a hyperbolic system with one space variable ⋮ Mixed problems for the equation of longitudinal vibrations of a heterogeneous rod with a free or fixed right end consisting of two segments with different densities and elasticities ⋮ 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
Cites Work
- Optimization of boundary controls by displacements at two ends of a string for an arbitrary sufficiently large time interval
- Optimal boundary control by an elastic force at one end of a string with the other end being free for an arbitrary sufficiently large time interval
- Optimal boundary control by the displacement of one endpoint of the string with the other endpoint being free in an arbitrarily large time interval
- On the independence of optimal boundary controls of string vibrations on the choice of the coordination point of initial and terminal conditions
- Minimization of the \(L_{p}\)-norm with arbitrary \(p \geq 1\) of the derivative of a boundary displacement control on an arbitrary sufficiently large time interval t
- Optimization of the boundary control of string vibrations by an elastic force on an arbitrary sufficiently large time interval
- Boundary control of oscillations at one endpoint with the other endpoint fixed in terms of a finite-energy generalized solution of the wave equation
- Two-endpoint boundary control of vibrations described by a finite-energy generalized solution of the wave equation
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