Related papers: Theory of vibrators with variable-order fractional…
Semi-active vibration reduction techniques are defined as techniques in which controlled actions do not operate directly on the system's degrees of freedom (as in the case of active vibration control) but on the system's parameters, i.e.,…
The focus of this work is to dissect the physical mechanisms that drive and sustain flow-induced, transverse vibrations of cylinders. The influence of different mechanisms is quantified by using a method to partition the fluid dynamic force…
This article analysis differential equations which represents damped and fractional oscillators. First, it is shown that prior to using physical quantities in fractional calculus, it is imperative that they are turned dimensionless.…
In this manuscript the development of a reduced order model for the analysis of long flexible cylinders in an offshore environment is proposed. In particular the focus is on the modelling of the vortex induced vibrations (VIV) and the aim…
Several approaches to the formulation of a fractional theory of calculus of "variable order" have appeared in the literature over the years. Unfortunately, most of these proposals lack a rigorous mathematical framework. We consider an…
This study presents the analytical formulation and the finite element solution of fractional order nonlocal plates under both Mindlin and Kirchoff formulations. By employing consistent definitions for fractional-order kinematic relations,…
A detailed analysis of three pendular motion models is presented. Inertial effects, self-oscillation, and memory, together with non-constant moment of inertia, hysteresis and negative damping are shown to be required for the comprehensive…
This paper examines the oscillatory behaviour of complex viscoelastic systems with power law-like relaxation behaviour. Specifically, we use the fractional Maxwell model, consisting of a spring and fractional dashpot in series, which…
This paper deals with the inverse problem of recovering an arbitrary number of fractional damping terms in a wave equation. We develop several approaches on uniqueness and reconstruction, some of them relying on Tauberian theorems on the…
Nonlocal and fractional-order models capture effects that classical partial differential equations cannot describe; for this reason, they are suitable for a broad class of engineering and scientific applications that feature multiscale or…
Relativity, time reversal invariance in mechanics and principle of causality can be in the bases of a type of vibration of the extensive objects. It is because, the detailed analysis of the relativistic movement of an extensive body entail…
We give an informal summary of ongoing work which uses tools distilled from the theory of fibre bundles to classify and connect invariant fields associated with spin motion in storage rings. We mention four major theorems. One ties…
In the present paper, we address a class of the fractional derivatives of constant and variable orders for the first time. Fractional-order relaxation equations of constants and variable orders in the sense of Caputo type are modeled from…
We introduce a fractional theory of the calculus of variations for multiple integrals. Our approach uses the recent notions of Riemann-Liouville fractional derivatives and integrals in the sense of Jumarie. Main results provide fractional…
The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and…
This Ph.D. thesis provides a comprehensive review of the state-of-the-art in the field of Variational Quantum Algorithms and Quantum Machine Learning, including numerous original contributions. The first chapters are devoted to a brief…
The parametrisation method for invariant manifolds is a powerful technique for deriving reduced-order models in the context of nonlinear vibrating systems, allowing accurate computations of nonlinear normal modes. Thanks to arbitrary order…
The new perturbation theory for the problem of nonstationary anharmonic oscillator with polynomial nonstationary perturbation is proposed. As a zero order approximation the exact wave function of harmonic oscillator with variable frequency…
The effect of damping in the wave turbulence regime for thin vibrating plates is studied. An experimental method, allowing measurements of dissipation in the system at all scales, is first introduced. Practical experimental devices for…
The use of fractional momentum operators and fractionary kinetic energy used to model linear damping in dissipative systems such as resistive circuits and a spring-mass ensambles was extended to a quantum mechanical formalism. Three…