In this paper the non-stationary response of single-degree-of-freedom structural systems with fractional damping is addressed. By considering a proper variable transformation, the equation of motion is reverted to a set of equivalent coupled linear equations, the number of which depends on an appropriate discretization of the fractional derivative operator. It is shown that the additional equations correspond to a set of half oscillators with a fractal representation, whose Mandelbrot dimension is equal to the order α of the fractional derivative. Then, based on a preliminary eigenvector expansion, the response statistics are built in a closed form for stochastic inputs of relevant interest

Non-stationary response of fractionally-damped viscoelastic systems

FAILLA, Giuseppe;
2011-01-01

Abstract

In this paper the non-stationary response of single-degree-of-freedom structural systems with fractional damping is addressed. By considering a proper variable transformation, the equation of motion is reverted to a set of equivalent coupled linear equations, the number of which depends on an appropriate discretization of the fractional derivative operator. It is shown that the additional equations correspond to a set of half oscillators with a fractal representation, whose Mandelbrot dimension is equal to the order α of the fractional derivative. Then, based on a preliminary eigenvector expansion, the response statistics are built in a closed form for stochastic inputs of relevant interest
2011
978-88-906340-1-7
Fractional calculus; Viscoelasticity; Fractal theory
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12318/18595
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