Random Vibrations of Elastic Systems

Geometric phase and topology of elastic oscillations and vibrations in model systems: Harmonic oscillator and superlattice

The Random Vibrations of a String*

where the qk represent charges, Lik inductances, Rik resistances, Gik reciprocals of capacitance, the Ejk are random e.m.f's**, and primes denote differentiations with respect to time. The theory of such systems of equations, quite carefully examined during the war years in applications to noise in electrical networks, turns out also to be applicable to the various mechanical systems—in particu...

Uniform stability of damped nonlinear vibrations of an elastic string

Abstract. Here we are concerned about uniform stability of damped nonlinear transverse vibrations of an elastic string fixed at its two ends. The vibrations governed by nonlinear integro-differential equation of Kirchoff type, is shown to possess energy uniformly bounded by exponentially decaying function of time. The result is achieved by considering an energy-like Lyapunov functional for the ...

Disordered Systems and Optimization : Elastic Lines and Random Magnets

The behavior of many physical systems, especially at low temperatures, is governed by the properties of their ground states. Usually it is not a trivial task to find the ground state configuration, especially in the case of disordered, complex systems. However, with quenched disorder this can be often done efficiently with the means of combinatorial optimization. In this thesis we study two suc...

Vibrations of thin elastic structures and exact controllability

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