Giuseppe Failla

Wavelets : Theoretical concepts and vibrations related applications

In this paper we provide a review of wavelet analysis in the context of applications to vibrations problems. First, we give an introduction to the important concepts and mathematical properties of wavelets within the framework of time-frequency analysis of signals. Next, wavelet analysis is discussed as applied to relevant themes in vibrations, such as time-varying spectra estimation, random field synthesis, system identification, damage detection, and material characterization. In view of the large number of related books and journal articles published in recent decades, the list of selected references in the paper is not meant to be exhaustive. Nevertheless, the cited references aim to point out the salient features of wavelet analysis, and to identify significant contributions in each theme, with the goal of expediting additional research and development efforts.

The mechanically based non-local elasticity: an overview of main results and future challenges

The mechanically based non-local elasticity has been used, recently, in wider and wider engineering applications involving small-size devices and/or materials with marked microstructures. The key feature of the model involves the presence of non-local effects as additional body forces acting on material masses and depending on their relative displacements. An overview of the main results of the theory is reported in this paper.

A Galerkin Approach for Power Spectrum Determination of Nonlinear Oscillators

A numerical method to estimate spectral properties of nonlinear oscillators with random input is presented. The stationary system response is expanded into a trigonometric Fourier series. A set of nonlinear algebraic equations, solved by Newton’s method, leads to the determination of the unknown Fourier series coefficients of single samples of the response process. For cubic polynomial nonlinearities, closed-form expressions are used to find the nonlinear terms at each step of the solution scheme. Further, a simple procedure yields an approximation of an arbitrary nonlinearity by a cubic polynomial. Power spectral density estimates for the response process are constructed by averaging the square modulus of the computed Fourier coefficients over various samples or by means of well-established smoothing techniques of spectral analysis. Two applications are presented illustrating the effectiveness of the method as compared to statistical linearization and digital Monte-Carlo simulation.

New perspectives in offshore wind energy

The design of offshore wind turbines is one of the most fascinating challenges in renewable energy. Meeting the objective of increasing power production with reduced installation and maintenance costs requires a multi-disciplinary approach, bringing together expertise in different fields of engineering. The purpose of this theme issue is to offer a broad perspective on some crucial aspects of offshore wind turbines design, discussing the state of the art and presenting recent theoretical and experimental studies.

Seismic analysis of offshore wind turbines on bottom-fixed support structures

This study investigates the seismic response of a horizontal axis wind turbine on two bottom-fixed support structures for transitional water depths (30–60 m), a tripod and a jacket, both resting on pile foundations. Fully coupled, nonlinear time-domain simulations on full system models are carried out under combined wind–wave–earthquake loadings, for different load cases, considering fixed and flexible foundation models. It is shown that earthquake loading may cause a significant increase of stress resultant demands, even for moderate peak ground accelerations, and that fully coupled nonlinear time-domain simulations on full system models are essential to capture relevant information on the moment demand in the rotor blades, which cannot be predicted by analyses on simplified models allowed by existing standards. A comparison with some typical design load cases substantiates the need for an accurate seismic assessment in sites at risk from earthquakes.

Some properties of multi-degree-of-freedom potential systems and application to statistical equivalent non-linearization

This paper presents some properties of two restricted classes of multi-degree-of-freedom potential systems subjected to Gaussian white-noise excitations. Specifically, potential systems which exhibit damping terms with energy-dependent polynomial form are referred to. In this context, first systems with coupled stiffness terms and damping terms depending on the total energy are investigated. Then, systems with uncoupled stiffness terms and damping terms depending on the total energy in each degree-of-freedom are considered. For these two classes, it is found that algebraic relations among the stationary statistical moments of the energy functions can be derived by applying standard tools of Ito calculus. Further, it is noted that these relations are very useful within the framework of an equivalent statistical non-linearization technique to build approximate solutions for arbitrary non-linear systems.

Response Power Spectrum of Multi-Degree-of-Freedom Nonlinear Systems by a Galerkin Technique

This paper deals with the estimation of spectral properties of randomly excited multi-degree-of-freedom (MDOF) nonlinear vibrating systems. Each component of the vector of the stationary system response is expanded into a trigonometric Fourier series over an adequately long interval T The unknown Fourier coefficients of individual samples of the response process are treated by harmonic balance, which leads to a set of nonlinear equations that are solved by Newtons method. For polynomial nonlinearities of cubic order exact solutions are developed to compute the Fourier coefficients of the nonlinear terms, including those involved in the Jacobian matrix associated with the implementation of Newtons method. The proposed technique is also applicable for arbitrary nonlinearities via a cubicization procedure over the interval T Upon determining the Fourier coefficients, estimates of the response power spectral density matrix are constructed by averaging their squared moduli over the samples ensemble. Examples of application prove the reliability of the technique by comparison with digital simulation data.

Finite-Element Formulation of a Nonlocal Hereditary Fractional-Order Timoshenko Beam

AbstractA mechanically-based nonlocal Timoshenko beam model, recently proposed by the authors, hinges on the assumption that nonlocal effects can be modeled as elastic long-range volume forces and moments mutually exerted by nonadjacent beam segments, which contribute to the equilibrium of any beam segment along with the classical local stress resultants. Long-range volume forces/moments linearly depend on the product of the volumes of the interacting beam segments, and on pure deformation modes of the beam, through attenuation functions governing the space decay of nonlocal effects. This paper investigates the response of this nonlocal beam model when viscoelastic long-range interactions are included, modeled by Caputo’s fractional derivatives. The finite-element method is used to discretize the pertinent fractional-order equations of motion. Closed-form solutions are obtained for creep tests by typical tools of fractional calculus. Numerical results are presented for various nonlocal parameters.

Stationary Response of Beams and Frames with Fractional Dampers through Exact Frequency Response Functions

AbstractThis paper proposes an original approach to the stochastic analysis of beams and plane frames with arbitrary number of fractional dampers, subjected to stationary excitations. External and internal, translational and rotational dampers are considered, with constitutive behavior modeled by the Riemann-Liouville fractional derivative. Starting from the Euler-Bernoulli formulation for bending vibration of a beam, and treating discontinuous response variables at the application points of dampers by the theory of generalized functions, it is shown that an appropriate use of dynamic Green’s functions of the bare beam provides the exact frequency response to point or distributed polynomial load, in terms of four integration constants only, regardless of the number of dampers. Based on this result, exact closed-form expressions are built for the stationary response of a single beam and a plane frame, under stationary point/polynomial loads, for any number of dampers. The stationary response in every frame...

Progress on the experimental set-up for the testing of a floating offshore wind turbine scaled model in a field site:

This document describes design and realization of a small-scale field experiment on a 1:30 model of spar floating support structure for offshore wind turbines. The aim of the experiment is to investigate the dynamic behaviour of the floating wind turbine under extreme wave and parked rotor conditions. The experiment has been going on in the Natural Ocean Engineering Laboratory of Reggio Calabria (Italy). In this article, all the stages of the experimental activity are presented, and some results are shown in terms of motions and response amplitude operators. Finally, a comparison with corresponding results obtained using ANSYS AQWA software package is shown, and conclusions are drawn. The presented experimental set-up seems promising to test offshore floating structures for marine renewable energy at a relatively large scale in the Natural Ocean Engineering Laboratory field site.