Dynamics and Nonlinear Control of Oscillations in a Complex Crystalline Lattice
| Authors: | Aero Eron, Institute for Problems of Mechanical Engineering RAS, Russian Federation
Andrievsky Boris, Institute for Problems of Mechanical Engineering RAS, Russian Federation
Fradkov Alexander, Institute for Problems of Mechanical Engineering RAS, Russian Federation
Vakulenko Sergey, Institute for Problems of Mechanical Engineering RAS, Russian Federation |
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| Topic: | 2.3 Non-Linear Control Systems |
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| Session: | Nonlinear Control in Physics and Mechanics |
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| Keywords: | Energy control, Speed gradient, Complex lattice, Nonlinear oscillations, Shock waves |
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Abstract
A highly nonlinear system of acoustic and optical oscillations in a complex crystalline lattice consisting of two sublattices is analyzed. The system is obtained as a generalization of the linear Carman–Born–Kun Huang theory. Large displacements of atoms up to structure stability loss and restructuring are admitted. It is shown that the system has nontrivial solutions describing structures and defects. Strong interaction of for media without center of symmetry, energy of the optical mode by means of torque applied examined. Control algorithm based on speed-gradient method is proposed. Simulation demonstrate that application of control may allow to eliminate or reduce influence of initial conditions.
